Practice final. 1D Kinematics

Transcription

1 Practice final 1D Kinematics 1) Which of the following quantities has units of a displacement? (There could be more than one correct choice.) A) 32 ft/s2 vertically downward B) 40 km southwest C) 9.8 m/s2 D) -120 m/s E) 186,000 mi 2) Which of the following quantities has units of a velocity? (There could be more than one correct choice.) A) 40 km southwest B) -120 m/s C) 9.8 m/s2 downward D) 186,000 mi E) 9.8 m/s downward 3) You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be A) greater than 70 km/h. B) equal to 70 km/h. C) less than 70 km/h. D) exactly 38 km/h. E) It cannot be determined from the information given because we must also know directions traveled. 4) Which of the following situations is impossible? A) An object has velocity directed east and acceleration directed west. B) An object has velocity directed east and acceleration directed east. C) An object has zero velocity but non-zero acceleration. D) An object has constant non-zero acceleration and changing velocity. E) An object has constant non-zero velocity and changing acceleration. 5) An auto manufacturer advertises that their car can go "from zero to sixty in eight seconds." This is a description of what characteristic of the car's motion? A) average speed B) instantaneous speed C) average acceleration D) instantaneous acceleration E) displacement

2 6) A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at half this speed, that is at 70 km/h? A) Before marker 1 B) At marker 1 C) Between marker 1 and marker 2 7) Suppose a ball is thrown straight up and experiences no appreciable air resistance. What is its acceleration just before it reaches its highest point? A) zero B) slightly less than g C) exactly g D) slightly greater than g 8) A ball is thrown downward in the absence of air resistance. After it has been released, which statement(s) concerning its acceleration is correct? (There could be more than one correct choice.) A) Its acceleration is constantly increasing. B) Its acceleration is constant. C) Its acceleration is constantly decreasing. D) Its acceleration is zero. E) Its acceleration is greater than g. 9) The figure shows a graph of the position x of two cars, C and D, as a function of time t. According to this graph, which statements about these cars must be true? (There could be more than one correct choice.) A) The magnitude of the acceleration of car C is greater than the magnitude of the acceleration of car D. B) The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D.

3 C) At time t = 10 s, both cars have the same velocity. D) Both cars have the same acceleration. E) The cars meet at time t = 10 s. 10) A child standing on a bridge throws a rock straight down. The rock leaves the child's hand at time t = 0 s. If we take upward as the positive direction, which of the graphs shown below best represents the velocity of the stone as a function of time? 11) What must be your average speed in order to travel 350 km in 5.15 h? A) 66.0 km/h B) 67.0 km/h C) 68.0 km/h D) 69.0 km/h 12) A motorist travels 160 km at 80 km/h and 160 km at 100 km/h. What is the average speed of

4 the motorist for this trip? A) 84 km/h B) 89 km/h C) 90 km/h D) 91 km/h 13) A car is traveling north at After 12 s its velocity is in the same direction. Find the magnitude and direction of the car's average acceleration. A) 0.30 m/s2, south B) 2.7 m/s2, south C) 0.30 m/s2, north D) 2.7 m/s2, north 14) A cart starts from rest and accelerates uniformly at 4.0 m/s2 for 5.0 s. It next maintains the velocity it has reached for 10 s. Then it slows down at a steady rate of 2.0 m/s2 for 4.0 s. What is the final speed of the car? A) 20 m/s B) 16 m/s C) 12 m/s D) 10 m/s 15) A jet plane is launched from a catapult on an aircraft carrier. In 2.0 s it reaches a speed of 42 m/s at the end of the catapult. Assuming the acceleration is constant, how far did it travel during those 2.0 s? A) 16 m B) 24 m C) 42 m D) 84 m 16) A car increases its forward velocity uniformly from 40 m/s to 80 m/s while traveling a distance of 200 m. What is its acceleration during this time? A) 8.0 m/s2 B) 9.6 m/s2 C) 12 m/s2 D) 24 m/s2 17) Acceleration is sometimes expressed in multiples of g, where is the acceleration of an object due to the earth's gravity. In a car crash, the car's forward velocity may go from to in How many g's are experienced, on average, by the driver? A) 20 g B) 14 g C) 24 g D) 26 g

5 18) A stone is thrown with an initial upward velocity of 7.0 m/s and experiences negligible air resistance. If we take upward as the positive direction, what is the velocity of the stone after 0.50 s? A) 2.1 m/s B) 4.9 m/s C) -2.1 m/s D) -4.9 m/s E) 0.00 m/s 19) A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. How long does it take for the laser to reach the maximum height? A) 8.0 s B) 11 s C) 14 s D) 16 s 20) A ball is thrown straight up with a speed of 36 m/s. How long does it take to return to its starting point, assuming negligible air resistance? A) 3.7 s B) 7.3 s C) 11 s D) 15 s 21) A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance? A) 20 m B) 30 m C) 50 m D) 70 m 22) An object is dropped from a bridge. A second object is thrown downwards 1.0 s later. They both reach the water 20 m below at the same instant. What was the initial speed of the second object? Neglect air resistance. A) 4.9 m/s B) 15 m/s C) 9.9 m/s D) 20 m/s E) 21 m/s

6 23) Which of the following numbers has 4 significant figures; which has 5 significant figures? (a) 3001 (b) (c) (d) ) Estimate the thickness, in meters, of an ordinary sheet of paper. A) 10-4 m B) 10-5 m C) 10-6 m D) 10-7 m E) 10-8 m 25) Express the number 13.5 gigameters in meters without using scientific notation. A) 135,000 m B) 135,000,000 m C) 135,000,000,000 m D) 13,500,000,000 m 26) Which of the following numbers is the smallest? A) B) C) D)

7 1) The graph in the figure shows the position of a particle as a function of time as it travels along the x-axis. (a) What is the average speed of the particle between t = 2.0 s and t = 4.0 s? (b) What is the average velocity of the particle between t = 2.0 s and t = 4.0 s? 2) The figure shows the velocity-versus-time graph for a basketball player traveling up and down the court in a straight-line path. Find the displacement of the player (a) during the first two seconds. (b) between t = 4 s and t = 8 s. 3) A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline. (a) What was the ball's acceleration? (b) How long was the incline? 4) If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery (a) what distance you have traveled? (b) what is your displacement? 5) A car with good tires on a dry road can decelerate (slow down) at a steady rate of about 5.0 m/s2 when braking. If a car is initially traveling at 55 mi/h (a) how much time does it take the car to stop? (b) what is its stopping distance?

8 1D Kinematics Answers 1. B,E 2. B,E 3. C 4. E 5. C 6. A 7. C 8. B 9. D,E 10. C 11. C 12. B 13. A 14. C 15. C 16. C 17. A 18. A 19. A 20. B 21. D 22. B 23. A,D 24. A 25. D

9 26. A 1. a=1m/s, b = 0m/s 2. a=4m, b = 8m 3. a=4.4m/s, b = 120m 4. a=5.25km/h, b = 1.25km/h south 5. a=4.9s, b = 60m 2D Kinematics 1) If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. A) True B) False 2) The magnitude of a vector can never be less than the magnitude of any of its components. A) True B) False 3) If a vector has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0 to 90 B) 90 to 180 C) 180 to 270 D) 270 to 360 E) It cannot be determined without additional information. 4) The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements must be correct for these two vectors? A) Vector is parallel to vector. B) Vector is antiparallel (in the opposite direction) to vector. C) Vector must be perpendicular to vector. D) The magnitude of vector must be equal to the magnitude of vector. E) The angle between vector and vector must be 90. 5) Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?

10 6) For general projectile motion with no air resistance, the horizontal component of a projectile's velocity A) remains zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases. 7) Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice.) A) The speed of the object is constant but its velocity is not constant. B) The acceleration of the object is +g when the object is rising and -g when it is falling. C) The acceleration of the object is zero at its highest point. D) The speed of the object is zero at its highest point. E) The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant downward. 8) In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. Compare the times of fall of the two pebbles. A) The thrown pebble hits first. B) The dropped pebble hits first. C) They hit at the same time. D) We cannot tell without knowing which pebble is heavier. 9) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same

11 initial speed, but in different directions. Mary throws her snowball downward, at 30 below the horizontal; Debra throws her snowball upward, at 30 above the horizontal. Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice.) A) Debra's snowball will have a higher speed than Mary's snowball. B) Mary's snowball will have a higher speed than Debra's snowball. C) Both snowballs will hit the ground with the same speed. D) Both snowballs hit the ground at the same time. E) Mary's snowball reaches the ground before Debra's snowball. 10) The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the +x-axis is closest to A) 340 B) 160 C) 250 D) 110 E) 23 11) A displacement vector is 34.0 m in length and is directed 60.0 east of north. Selecting from the choices in the table below, what are the components of this vector? Northward Eastward choice component component m 17.0 m m 28.1 m m 11.5 m m 29.4 m m 18.2 m A) choice 1 B) choice 2 C) choice 3 D) choice 4 E) choice 5 12) The magnitude of is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 with the +y-axis. The components of A) = -3.1 m, = 4.6 m. B) = 3.1 m, = -4.6 m. C) = 4.6 m, = -3.1 m. D) = -4.6 m, = 3.1 m. E) = -4.6 m, = -3.1 m. are closest to: 13) A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

12 A) 14 m B) 16 m C) 20 m D) 24 m 14) You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to A) 28 m/s B) 20 m/s C) 40 m/s D) 37 m/s 15) A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance. A) 21 m/s B) 22 m/s C) 24 m/s D) 25 m/s E) 6.3 m/s 16) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/s horizontally in a city where the acceleration due to gravity is 9.81 m/s2. The puck experiences no significant air resistance as it falls. The height of the platform above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground? A) 77.2 B) 72.6 C) 12.8 D) 12.6 E) ) A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground? A) 5.00 seconds B) 10.0 seconds C) 15.0 seconds D) 20.0 seconds 18) When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal? A) 75 B) 57 C) 33

13 D) 15 19) A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0 above the horizontal. What is the horizontal component of the boy's velocity? A) 18.1 m/s B) 15.6 m/s C) 8.45 m/s D) 12.6 m/s E) 9.33 m/s 20) A ball is thrown with an initial velocity of 20 m/s at an angle of 60 above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory? A) 10 m/s B) 17 m/s C) 20 m/s D) zero 21) As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of and The projectile rises and then falls into the sea at point P. The time of flight of the projectile is and air resistance is negligible. At this location, g = 9.80 m/s2. What is the horizontal distance D? A) 2250 m B) 2520 m C) 2790 m D) 3060 m E) 3330 m 1) A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector? 2) The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively.

14 (a) What is the magnitude of this vector? (b) What angle does this vector make with the positive +y-axis. 3) A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the acceleration due to gravity is 9.80 m/s2. (a) How far from the base of the table will it strike the floor? (b) How long will it be in the air? 4) A hunter points a rifle horizontally and holds it 3.30 m above the ground. The bullet leaves the barrel at 325 m/s and experiences no significant air resistance. The acceleration due to gravity at this location is 9.80 m/s2. (a) How long does it take for the bullet to strike the ground? (b) How far horizontally does it travel? 5) A projectile is shot horizontally at 23.4 m/s from the roof of a building 55 m tall and experiences negligible air resistance. (a) Determine the time necessary for the projectile to reach the ground below. (b) Determine the distance from the base of the building that the projectile lands. (c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground. 6) As shown in the figure, a heavy rock is shot upward from the edge of a vertical cliff. It leaves the edge of the cliff with an initial velocity of 15 m/s directed at 25 from the vertical and experiences no appreciable air resistance as it travels. How high is the cliff? 7) At target practice, a rifle bullet is fired at an angle of 30 below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below if air resistance is negligible? Forces 1) When an object hangs at static equilibrium from two ropes, which of the following is true in every possible case? a. Each rope supports the objects weight. b. The tension in the two ropes adds to the objects total weight. c. The vertical components of each ropes tension support half the objects weight. d. The vertical components of tension add together to equal the objects weight.

15 2) A 70 kg person stands on a scale in an elevator that is moving at constant downward velocity of 2 m/s. What does the scale report? a. 560 N. b. 700 N. c. 840 N. d. 960 N. 3) Which of these is true about mass? I. It is the amount of matter an object consists of. II. It is an objects weight. III. Inertia is a consequence of having mass. IV. It changes with the strength of gravity g. a. I only. b. II only. c. I and II. d. I and III. e. All of these are true for mass. 4) An object initially at rest moves a distance x when a force F is applied for a time t. How far will the object move if a force of 2F is applied for the same time t? a. ( 2/2)x b. 2x c. 2x d. 2 2x 5) The free-body diagram shows all forces acting on a box supported by a horizontal surface. The length of the arrow shows magnitude. Which statement below is correct? a. The box is accelerating downwards because the force of gravity is greater than the normal force. b. The box is accelerating to the right, but not upwards. c. The box is accelerating upwards, but not to the right. d. The box is accelerating upwards and to the right. 6) A 10 kg mass is accelerated upward by a rope at 2 m/s 2. The tension in the rope is: a. 50 N. b. 80 N. c. 100 N. d. 120 N. 7) A 1.5-kg mass has an acceleration of (4.0i 3.0j) m/s 2. Only two forces act on the mass. If one of the forces is (2.0i 1.4j) N, what is the magnitude of the other force? a. 4.1 N. b. 6.1 N. c. 5.1 N. d. 7.1 N.

16 8) To determine the coefficient of friction between a block of mass 1.0kg and a 100cm long surface, an experimenter places the block on the surface and begins lifting one end. The block just begins to slip when the end of the surface has been lifted 60cm above the horizontal. The static coefficient of friction between the block and the surface is most nearly: a b c d ) You push downward on a trunk at an angle 25 below the horizontal with a force of If the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move? A) 81 kg B) 93 kg C) 73 kg D) 112 kg 10) If you pound a feather with a hammer, which one feels a greater force? A) always the feather B) always the hammer C) The size of the force is always exactly the same on both of them. D) If the feather moves, then it felt the greater force. Otherwise the force was the same on both. 11) You pull on a crate with a rope. If the crate moves, the rope's pull on the crate must have been larger than the crate's pull on the rope, but if the crate does not move, both of these pulls must have been equal. A) True B) False 12) A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40.0 on either side of the vertical direction. What is the tension in each cable? A) 231 N B) 400 N C) 800 N D) 2560 N

17 E) 3920 N 13) A crate is sliding down an inclined ramp at a constant speed of 0.55 m/s. The vector sum of all the forces acting on this crate must point A) down the ramp. B) up the ramp. C) perpendicular to the ramp. D) vertically downward. E) None of the above choices is correct. 14) You push on box G that is next to box H, causing both boxes to slide along the floor, as shown in the figure. The reaction force to your push is A) the push of box G on box H. B) the push of box H on box G. C) the push of box G against you. D) the upward force of the floor n box G. E) the acceleration of box G. 15) An object is moving with constant non-zero velocity. Which of the following statements about it must be true? A) A constant force is being applied to it in the direction of motion. B) A constant force is being applied to it in the direction opposite of motion. C) A constant force is being applied to it perpendicular to the direction of motion. D) The net force on the object is zero. E) Its acceleration is in the same direction as it velocity. 16) The figure shows two boxes, with m1 > m2, that are on a level frictionless surface. We can apply a horizontal force either toward the right on m1 or toward the left on m2. The magnitude of the force that the boxes exert on each other is A) zero newtons in either case. B) larger if is applied toward the right.

18 C) larger if is applied toward the left. D) the same in either case. 17) A person is using a rope to lower a 5.0-N bucket into a well with a constant speed of 2.0 m/s. What is the magnitude of the force exerted by the rope on the bucket? A) 0.00 N B) 2.0 N C) 5.0 N D) 10 N E) 49 N 18) A person who normally weighs 700 N is riding in an elevator that is moving upward but slowing down at a steady rate. If this person is standing on a bathroom scale inside the elevator, what would the scale read? A) more than 700 N B) less than 700 N C) 700 N D) It could be more or less than 700 N, depending on whether the magnitude of the acceleration is greater than or less than 9.8 m/s2. 19) When a 45-kg person steps on a scale in an elevator, the scale reads a steady 480 N. Which of the following statements must be true? (There could be more than one correct choice.) A) The elevator is accelerating upward at a constant rate. B) The elevator is accelerating downward at a constant rate. C) The elevator is moving upward at a constant rate. D) The elevator is moving downward at a constant rate. E) From the given information, we cannot tell if the elevator is moving up or down. 20) ) A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the road under the prevailing conditions was How fast was the car going when the driver applied the brakes? A) 10.7 m/s B) 12.8 m/s C) 21.4 m/s D) 32.9 m/s E) 45.7 m/s 21) What is the mass of an object that experiences a gravitational force of 685 N near Earth's surface where g = 9.80 m/s2? A) 69.9 kg B) 68.5 kg

19 C) 71.3 kg D) 72.7 kg 22) A net force of 125 N is applied to a certain object. As a result, the object accelerates with an acceleration of 24.0 m/s2. The mass of the object is A) 3000 kg. B) 2880 kg. C) 144 kg. D) kg. E) 5.21 kg. 23) A block is on a frictionless table, on earth. The block accelerates at 3.0 m/ when a horizontal force is applied to it. The block and table are set up on the Moon where the acceleration due to gravity is 1.62 m/. The weight of the block on the Moon is closest to A) 11 N. B) 9.5 N. C) 8.1 N. D) 6.8 N. E) 5.5 N. 24) Two boxes P and Q on a perfectly smooth horizontal surface are connected by a light horizontal cord. The mass of P is greater than that of Q. A horizontal force is applied to box Q as shown in the figure, accelerating the bodies to the right. The magnitude of the force exerted by the connecting cord on body P is A) zero. B) less than F but not zero. C) equal to F. D) greater than F. 35) Two objects of unequal masses, M and m (M > m), are connected by a very light cord passing over an ideal pulley of negligible mass. When released, the system accelerates, and friction is negligible. 25) A 45.0-kg person steps on a scale in an elevator. The scale reads 460 N. What is the magnitude of the acceleration of the elevator? A) 4.91 m/s2 B) 9.81 m/s2 C) 46.9 m/s2 D) m/s2 E) m/s2

20 26) In the figure, what does the spring scale read? The pulleys are ideal and the strings and scale are also massless. A) exactly 2.0 N. B) exactly 1.0 N C) 0.50 N D) 0.00 N E) more than 19.6 N 27) A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle θ below the horizontal, and the box remains a rest. The box rests on a horizontal surface that has some friction with the box. The normal force on the box due to the floor is equal to A) W. B) W + P. C) W + P cos θ. D) W + P sin θ. E) W - P sin θ. Choose 2 of the 3 problems to complete. Only the first 2 will be graded if you complete all 3, unless you mark which 2 to be graded. 1) A 6.00 kg block is placed on a 30 degree incline and connected to another block on a degree incline. Although the surfaces are frictionless the blocks do not move. What is the mass in kilograms of the block on the degree incline? 2) In the figure, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is If F = 10 N and M = 1.0 kg, what is the tension in the connecting string?

21 3) The three blocks shown are released from rest and are observed to move with accelerations that have a magnitude of 1.5 m/s 2. What is the magnitude of the friction force on the block that slides horizontally? Disregard any pulley mass or friction in the pulley and let M = 2.0 kg. 4) A 10-kg object is hanging by a very light wire in an elevator that is traveling upward. The tension in the rope is measured to be 75 N. What are the magnitude and direction of the acceleration of the elevator? 5) A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is What horizontal force must be applied to the box to cause it to start sliding along the surface? 6) Three objects are connected by weightless flexible strings as shown in the figure. The pulley has no appreciable mass or friction, and the string connected to the block on the horizontal bench pulls on it parallel to the bench surface. The coefficients of friction between the bench and the block on it are µs = 0.66 and µk = You observe that this system remains at rest. (a) Find the mass of the hanging object A. (b) What is the magnitude of the friction force on the block on the bench?

22 1. D 2. C 3. D 4. C 5. B 6. D 7. C 8. B 9. A 10. C 11. B 12. D 13. E 14. C 15. D 16. C 17. C 18. B 19. A,E 20. B 21. A 22. E 23. A 24. B 25. E 26. B 27. A Short free response kg N N 4. a)22kg b)270 N N m/s2,downward Forces Answers

23 Circular motion and gravitation 1) An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors. A) Both vectors point in the same direction. B) The vectors point in opposite directions. C) The vectors are perpendicular to each other. D) The acceleration is zero but the velocity is constant. 2) The Moon is accelerated toward the earth, so it is gradually getting closer to the earth. A) True B) False C) The moon is not accelerated toward the earth. Answer: B 3) When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path? A) the normal force from the road B) the friction force from the road C) gravity D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration. Answer: B 4) A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road? A) tangent to the curve in the forward direction B) tangent to the curve opposite to the direction of the car's motion C) perpendicular to the curve outward D) perpendicular to the curve inward E) There is no friction on the car because its speed is constant. Answer: D 5) If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water. A) True B) False Answer: B 6) Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve? A) the car with the new tires B) the car with the bald tires

24 C) Neither car will slide. D) It depends on if the pavement is wet or dry. 7) Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one? A) 16F B) 8F C) 4F D) F E) F/4 Answer: D 8) A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity? A) when it gets above the atmosphere B) when it is half-way there C) when it is closer to the Moon than it is to Earth D) It is never beyond the pull of Earth's gravity. Answer: D 9) An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is A) zero. B) the same as on the surface of the earth. C) one-half of its weight on the surface of the earth. D) one-third of its weight on the surface of the earth. E) one-quarter of its weight on the surface of the earth. Answer: E 10) A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth? A) g B) g/2 C) g/4 D) g/8 E) g/16 Answer: D 11) Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B? A) The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B.

25 B) The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B. C) The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B. D) The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater. E) We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets. Answer: E 12) If Earth had twice its present mass but it orbited at the same distance from the sun as it does now, its orbital period would be A) 4 years. B) 3 years. C) 2 years. D) 1 year. E) 6 months. Answer: D 13) Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits? A) T/R B) T/R2 C) T2/R3 D) T3/R2 E) T2/R 14) An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object? A) 0 m/s2 B) 0.17 m/s2 C) 5.0 m/s2 D) 6.0 m/s2 Answer: D 15) You are driving at on a freeway curve of radius What is the magnitude of your acceleration? A) 36.0 m/s2 B) 1.20 m/s2 C) 20.8 m/s2 D) m/s2 16) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive?

26 A) 1.2 km B) 5.8 km C) 0.64 km D) 9.2 km E) 7.0 km Answer: D 17) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding? A) 9000 N B) 9800 N C) 300 N D) 900 N E) 3000 N 18) A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string? A) 700 m/s B) 26 m/s C) 19 m/s D) 13 m/s Answer: B 19) One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts walk on the inside surface of the space station. How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts? A) 28 s B) 39 s C) 6.2 s D) 4.4 s 20) A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is At what speed will the car begin to skid sideways? A) 9.3 m/s B) 24 m/s C) 34 m/s D) 35 m/s E) 19 m/s

27 Answer: E 21) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70-kg pilot at that point? A) 3300 N B) 690 N C) 2600 N D) 490 N E) 1400 N 22) In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km? A) 79 m/s B) 310 m/s C) 260 m/s D) 160 m/s E) 510 m/s Answer: D 23) In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25? A) 8.9 m/s B) 2.3 m/s C) 3.0 m/s D) 4.9 m/s E) It depends on the mass of the passengers. 24) A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18, what is the speed of the mass? A) 0.55 m/s B) 2.0 m/s C) 3.8 m/s D) 1.3 m/s E) 1.1 m/s Answer: E 25) A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction

28 between the car's tires and the road surface is the same in both cases? A) 160 m/s B) 80 m/s C) 70 m/s D) 40 m/s E) 30 m/s Answer: D 26) A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth? A) 91 min B) 8.7 min C) 4.6 min D) 1.5 min E) min Answer: D 27) A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction? A) 29.1 B) 13.5 C) 33.8 D) 56.2 E) ) A highway curve of radius 100 m, banked at an angle of 45, may be negotiated without friction at a speed of A) 22 m/s. B) 31 m/s. C) 44 m/s. D) 67 m/s. Answer: B 29) What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere. (G = N m2/kg2) A) N B) N C) N D) N E) N

29 30) Mass Radius Orbital radius Orbital period Moon A kg unknown m s Moon B kg m m unknown Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = N m2/kg2) A) N B) N C) N D) N E) N Answer: E 31) The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit? A) 61 N B) 110 N C) 9000 N D) 16,000 N 32) The captain of a spaceship orbiting planet X discovers that to remain in orbit at from the planet's center, she needs to maintain a speed of What is the mass of planet X? (G = N m2/kg2) A) kg B) kg C) kg D) kg 33) You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be m. You have previously determined that the planet orbits m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 19.5 m/s2. What are the masses of (a) the planet and (b) the star? (G = N m2/kg2) A) (a) 2.4 kg kg, (b) 1.2 kg kg B) (a) 4.3 kg kg, (b) 1.2 kg kg C) (a) 2.4 kg kg, (b) 7.1 kg kg D) (a) 4.3 kg kg, (b) 7.1 kg kg 1) Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of

30 diameter 60 m. What are the magnitude and direction of her acceleration? Answer: 7.5 m/s2 toward the center of the circle 2) The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m? Answer: 54 m/s 3) The Moon is m from Earth and takes 27.3 days to complete each orbit. What are the magnitude and direction of the acceleration of the Moon, assuming a circular orbit? Answer: m/s2, toward Earth 4) A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s. (a) What are the magnitude and direction of the acceleration of the ball? (b) Find the tension in the string. Answer: (a) 79.0 m/s2 toward the center of the circle (b) 13.8 N 5) A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a) What banking angle should you specify for this curve? (b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed? Answer: (a) 37 (b) 9200 N (normal force), 0 N (friction) 6) What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? (G = N m2/kg2) Answer: N 7) A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (G = N m2/kg2, Mearth = kg) Answer: N Energy 1) Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the following statements is correct? A) Both do positive work, but person X does four times the work of person Y. B) Both do positive work, but person X does twice the work of person Y. C) Both do the same amount of positive work. D) Both do zero work. E) Both do positive work, but person X does one-half the work of person Y. Answer: D

31 2) Two men, Joel and Jerry, push against a car that has stalled, trying unsuccessfully to get it moving. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do on the car. A) Joel does 75% more work than Jerry. B) Joel does 50% more work than Jerry. C) Jerry does 50% more work than Joel. D) Joel does 25% more work than Jerry. E) Neither of them does any work. Answer: E 3) If the force on an object is in the negative direction, the work it does on the object must be A) negative. B) positive. C) The work could be either positive or negative, depending on the direction the object moves. 4) A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position. How much work did gravity do on the bucket during this process? A) 180 J B) 90 J C) 45 J D) 0 J E) 900 J Answer: D

32 5) You throw a baseball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. A) The work is positive on the way up and positive on the way down. B) The work is positive on the way up and negative on the way down. C) The work is negative on the way up and positive on the way down. D) The work is negative on the way up and on the way down because gravity is always downward. 6) Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s? A) The 500-kg object B) The 1000-kg object C) Both have the same kinetic energy. 7) A truck has four times the mass of a car and is moving with twice the speed of the car. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say that A) Kt = 16Kc. B) Kt = 4Kc. C) Kt = 2Kc. D) Kt = Kc. E) Kt = Kc. 8) Three cars (car F, car G, and car H) are moving with the same speed and slam on their brakes. The most massive car is car F, and the least massive is car H. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, which car travels the longest distance to skid to a stop? A) They all travel the same distance in stopping. B) Car F C) Car G D) Car H

33 9) Three cars (car L, car M, and car N) are moving with the same speed and slam on their brakes. The most massive car is car L, and the least massive is car N. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, for which car is the amount of work done by friction in stopping it the greatest? A) The amount of work done by friction is the same for all cars. B) Car L C) Car M D) Car N Answer: B 10) A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? A) the 4.0 kg object B) the 1.0 kg object C) Both objects travel the same distance. D) It cannot be determined from the information given. 11) A stone initially moving at 8.0 m/s on a level surface comes to rest due to friction after it travels 11 m. What is the coefficient of kinetic friction between the stone and the surface? A) 0.13 B) 0.25 C) 0.30 D) 0.43 E) ) A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what was the initial speed of the object? A) 9.8 m/s B) 6.3 m/s C) 3.6 m/s D) 7.2 m/s E) 8.9 m/s Answer: B Var: 5 13) On an alien planet, an object moving at 4.0 m/s on the horizontal ground comes to rest after traveling a distance of 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what is the value of g on that planet? A) 4.0 m/s2

34 B) 6.0 m/s2 C) 8.0 m/s2 D) 10 m/s2 E) 12 m/s2 14) A driver, traveling at 22 m/s, slows down her 2000 kg truck to stop for a red light. What work is done on the truck by the friction force of the road? A) J B) J C) J D) J 15) The kinetic friction force that a horizontal surface exerts on a 60.0-kg object is 50.0 N. If the initial speed of the object is 25.0 m/s, what distance will it slide before coming to a stop? A) 15.0 m B) 30.0 m C) 375 m D) 750 m 16) A stone is moving on a rough level surface. It has 24 J of kinetic energy, and the friction force on it is a constant 0.50 N. What is the maximum distance it can slide? A) 2.0 m B) 12 m C) 24 m D) 48 m Answer: D 17) In a ballistics test, a 28-g bullet pierces a sand bag that is thick. If the initial bullet velocity was and it emerged from the sandbag moving at what was the magnitude of the friction force (assuming it to be constant) that the bullet experienced while it traveled through the bag? A) 130 N B) 38 N C) 13 N D) 1.3 N Var: 50+

35 18) A certain car traveling at 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car have stopped had it been going mph? A) 279 m B) 158 m C) 90 m D) 51 m E) 29 m Var: ) You do 116 J of work while pulling your sister back on a fritctionless swing, whose chain is long, until the swing makes an angle of 32.0 with the vertical. What is your sister's mass? A) 15.3 kg B) 13.0 kg C) 17.6 kg D) 19.0 kg Var: ) A tennis ball bounces on the floor three times, and each time it loses 23.0% of its energy due to heating. How high does it bounce after the third time, if we released it from the floor? A) 180 cm B) 18 cm C) 180 mm D) 240 cm Var: ) A 10-kg mass, hung by an ideal spring, causes the spring to stretch 2.0 cm. What is the spring constant (force constant) for this spring? A) 5.0 N/cm B) 49 N/cm C) 0.20 N/cm D) 20 N/m E) N/cm Answer: B 22) An ideal spring stretches by 21.0 cm when a 135-N object is hung from it. If instead you hang a fish from this spring, what is the weight of a fish that would stretch the spring by A) 199 N B) 91 N C) 145 N D) 279 N

36 Var: ) An ideal spring has a spring constant (force constant) of 2500 N/m. is stretched 4.0 cm. How much work is required to stretch the spring by 4.0 cm? A) 4.0 J B) 0.00 J C) 1.0 J D) 3.0 J E) 2.0 J Answer: E 1) How high a hill would a 75-kg hiker have to climb to increase her gravitational potential energy by 10,000 J? Answer: 14 m 2) You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5 cm. What should be the force constant (spring constant) of this spring? Answer: m/m 3) A frictionless simple pendulum, with a small but dense 4.4-kg mass at the end and a length of 75 cm, is released from rest at an angle of 50 with the vertical. (a) To what height above its lowest point does the mass swing on the other side? (b) What is the speed of the mass at the bottom of the swing? Answer: (a) 27 cm (b) 2.3 m/s Impulse and Linear Momentum 1) A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The clay sticks to the wall. Which one of these objects experiences the greater momentum change? A) the ball B) the clay C) Both of them experience the same non-zero momentum change. D) Both of them experience zero momentum change. 2) A tiger is running in a straight line. If we double both the mass and speed of the tiger, the magnitude of its momentum will increase by what factor?

37 A) B) 2 C) 4 D) 8 E) 16 3) Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. The person in the front throws a very massive ball toward the back, and the person in the back catches it. After the ball is caught, the canoe is A) moving backward. B) stationary. C) moving forward. Answer: B 4) A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the momentum change during the collision is correct? (There could be more than one correct choice.) A) The truck experiences the greater magnitude momentum change. B) The small car experiences the greater magnitude momentum change. C) The small car and the truck experience the same magnitude momentum change. D) The magnitude of the momentum change experienced by each one is inversely proportional to its mass. E) The magnitude of the momentum change experienced by each one is directly proportional to its mass. 5) Consider two less-than-desirable options. In the first you are driving 30 mph and crash headon into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce back from the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greater impact force on your car? A) hitting the other car B) hitting the brick wall C) The force would be the same in both cases. D) None of the above choices are correct. 6) A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change of the lighter fragment is A) 25 times as great as the momentum change of the heavier fragment. B) The same as the momentum change of the heavier fragment.

38 C) 1/25 as great as the momentum change of the heavier fragment. D) 5 times as great as the momentum change of the heavier fragment. E) 1/4 as great as the momentum change of the heavier fragment. Answer: B 7) Which of the following quantities are units of impulse? (There could be more than one correct choice.) A) N m B) kg s/m C) kg m/s D) N s E) kg m2/s2, D 9) During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a very long barrel. What was the reason for using a long barrel in these guns? A) to exert a larger force on the shells B) to reduce frictional losses C) to allow the force of the expanding gases from the gunpowder to act for a longer time D) to increase the force exerted on the bullet due to the expanding gases from the gunpowder E) to reduce the force exerted on the bullet due to the expanding gases from the gunpowder 10) In a collision between two unequal masses, which mass receives a greater magnitude impulse? A) the larger mass B) the smaller mass C) They receive equal impulses. 11) A very light ping-pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision? A) Neither; both experienced the same magnitude impulse. B) the Ping-Pong ball C) the bowling ball D) It is impossible to tell since the actual mass values are not given. E) It is impossible to tell since the velocities after the collision are unknown.

39 12) A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision? A) 14 kg m/s B) 2.0 kg m/s C) 10 kg m/s D) 6.0 kg m/s E) 8.0 kg m/s 13) A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground. What is the magnitude of its momentum just before it hits the ground if we neglect air resistance? A) 0.28 kg m/s B) 0.88 kg m/s C) 0.44 kg m/s D) 0.62 kg m/s E) 1.4 kg m/s Answer: B 14) Three objects are moving along a straight line as shown in the figure. Taking the positive direction to be to the right, what is the total momentum of this system? A) +106 kg m/s B) -106 kg m/s C) kg m/s D) kg m/s E) 0.00 kg m/s Answer: D 15) A 100-g ball falls from a window that is 12 m above ground level and experiences no significant air resistance as it falls. What is its momentum when it strikes the ground? A) 3.3 kg m/s B) 4.8 kg m/s C) 1.8 kg m/s D) 1.5 kg m/s E) 2.4 kg m/s Answer: D 16) A firecracker breaks up into two pieces, one of which has a mass of 200 g and flies off along the +x-axis with a speed of 82.0 m/s. The second piece has a mass of 300 g and flies off along the +y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces? A) 361 kg m/s at 56.3 from the +x-axis

40 B) 93.5 kg m/s at 28.8 from the +x-axis C) 21.2 kg m/s at 39.5 from the +x-axis D) 361 kg m/s at from the +x-axis E) 21.2 kg m/s at 56.3 from the +x-axis 18) A 0.10-kg ball, traveling horizontally at 25 m/s, strikes a wall and rebounds at 19 m/s. What is the magnitude of the change in the momentum of the ball during the rebound? A) 1.2 kg m/s B) 1.8 kg m/s C) 4.4 kg m/s D) 5.4 kg m/s E) 72 kg m/s 19) A 328-kg car moving at 19.1 m/s in the +x direction hits from behind a second car moving at in the same direction. If the second car has a mass of and a speed of right after the collision, what is the velocity of the first car after this sudden collision? A) 14.0 m/s B) 18.2 m/s C) 24.2 m/s D) m/s Var: ) A 1200-kg cannon suddenly fires a cannonball at What is the recoil speed of the cannon? Assume that frictional forces are negligible and the cannon is fired horizontally. A) 2.9 m/s B) 35 m/s C) 3.5 m/s D) 3.2 m/s Var: ) A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320-g piece moves along the +x-axis with a speed of 2.00 m/s and a 355-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction relative to the +x-axis does the third piece move? A) from the +x-axis B) from the +x-axis C) 36.9 from the +x-axis D) 39.9 from the +x-axis E) 39.8 from the +x-axis

41 Answer: B Var: 5 22) Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m? A) 9.0 m B) 16 m C) 21 m D) 24 m E) 28 m Answer: E 23) Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship? A) 1000 s B) 750 s C) 500 s D) 250 s E) 2.50 min 24) The graph in the figure shows the x component F of the net force that acts for 10 s on a 100- kg crate. What is the change in the momentum of the crate during the 10 s that this force acts? A) -100 kg m/s B) -25 kg m/s C) 75 kg m/s D) -75 kg m/s E) 25 kg m/s Answer: D 25) A golf club exerts an average horizontal force of 1000 N on a kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball just as it leaves the tee? A) 30 m/s B) 35 m/s C) 40 m/s D) 45 m/s E) 50 m/s

42 26) Calculate the impulse due to a force of that lasts for A) 6.3 kg m/s B) 5.0 kg m/s C) 5.7 kg m/s D) 6.9 kg m/s Var: ) A kg baseball is thrown horizontally with a velocity of 28.9 m/s. It is struck with a constant horizontal force that lasts for 1.85 ms, which results in a velocity of 37.0 m/s in the opposite direction. What was the magnitude of the horizontal force? A) kn B) 2.19 kn C) 2.80 kn D) 4.99 kn Answer: D 28) A 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of If the clay comes to a stop in what is the average horizontal force on the clay due to the wall? A) 42 N B) 26 N C) 35 N D) 51 N 4 29) A block of mass m = 34 kg and speed V is behind a block of mass M = 81 kg and speed of as shown in the figure. The surface is frictionless and the blocks collide and couple. After the collision, the blocks have a common speed of What is the magnitude of the impulse on the 34-kg block due to the collision? A) 32 N s B) 14 N s C) 41 N s D) 57 N s E) 73 N s Var: ) A kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the ground, and it rebounds with an upward speed of 1.00 m/s. The ball is in contact with the ground for s. What is the average force exerted by the ground on the ball during the time of contact? A) 2.00 N upwards B) 2.00 N downwards

43 C) 22.0 N upwards D) 22.0 N downwards E) 0.00 N 31) A block of mass m = 5.6 kg, moving on a frictionless surface with a velocity of to the right, collides with a block of mass M at rest, as shown in the figure. After the collision, the 5.6-kg block recoils with a velocity of to the left. If the blocks are in contact for 0.20 s, what is the magnitude of the average force on the 5.6-kg block, while the two blocks are in contact? A) 202 N B) 192 N C) 182 N D) 0 N E) 0 N Var: ) A 1200-kg car moving at suddenly collides with a stationary car of mass If the two vehicles lock together, what is their combined velocity immediately after the collision? A) 6.9 m/s B) 8.6 m/s C) 12.1 m/s D) 5.5 m/s Var: ) A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the speed of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision. A) 0.00 m/s B) 3.0 m/s C) 4.0 m/s D) 5.0 m/s E) 6.0 m/s Answer: D 34) Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck. A) 11 m/s at 14 with respect to the original direction of the lighter car B) 16 m/s at 76 with respect to the original direction of the lighter car

44 C) 11 m/s at 76 with respect to the original direction of the lighter car D) 26 m/s at 76 with respect to the original direction of the lighter car E) 16 m/s at 14 with respect to the original direction of the lighter car 35) A puck with a mass m1 = 50 g moving at 1.0 m/s approaches a stationary puck with a mass m2 = 100 g on a frictionless air table, and they undergo a sudden two-dimensional elastic collision. After the collision, both pucks have identical speeds, but travel in different directions. What is the angle between the original and final paths of puck with mass m1? A) 30 B) 60 C) 90 D) 120 E) ) A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. In what direction does the wreckage move just after the collision? A) 36.9 N of E B) 42.0 N of E C) 45.0 N of E D) 53.1 N of E E) 48.0 N of E Answer: E 37) A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the speed of the cars after collision? A) 8.3 m/s B) 14 m/s C) 17 m/s D) 22 m/s Answer: B 38) Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of 24 kg. m/s, and Fido runs northward with momentum 10 kg. m/s. They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision? A) 14 kg. m/s B) 26 kg. m/s C) 34 kg. m/s

45 D) It cannot be determined without knowing the masses and velocities of the dogs. Answer: B 1) What is the magnitude of the momentum of a kg baseball traveling at 45.0 m/s? Answer: 6.30 kg m/s 2) A 60-kg swimmer suddenly dives horizontally from a 150-kg raft with a speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps if the water has negligible effect on the raft? Answer: 0.60 m/s 3) A 14,000-kg boxcar is coasting at 1.50 m/s along a horizontal track when it suddenly hits and couples with a stationary 10,000-kg boxcar. What is the speed of the cars just after the collision? Answer: m/s 4) A batter applies an average force of 8000 N to a baseball for 1.1 ms. What is the magnitude of the impulse delivered to the baseball by the bat? Answer: 8.8 N s 5) A batter hits a kg baseball that was approaching him at 30 m/s and, as a result, the ball leaves the bat at 40 m/s in the reverse of its original direction. The ball remains in contact with the bat for 2.0 ms. What is the magnitude of the average force exerted by the bat on the ball? Answer: 4900 N 6) A force of 5.3 N is needed to hold on to an umbrella in a strong wind. If the air molecules each have a mass of kg, and each one strikes the umbrella (without rebounding) with a speed of 2.0 m/s in the same direction, how many atoms strike the umbrella each second? Assume that the wind blows horizontally so that the gravity can be neglected. Answer: per second 7) A car (of mass 1500 kg) and a small truck (of mass 2000 kg) collide suddenly at right angles at an icy intersection. The car was originally traveling eastward at 20.0 m/s and the truck was traveling northward at 20.0 m/s just before the collision took place. What is the speed of the combined wreck just after the collision if the vehicles become enmeshed? Answer: 14.3 m/s SHM 1) If we double the frequency of a system undergoing simple harmonic motion, which of the

46 following statements about that system are true? (There could be more than one correct choice.) A) The period is doubled. B) The angular frequency is doubled. C) The amplitude is doubled. D) The period is reduced to one-half of what it was. E) The angular frequency is reduced to one-half of what it was. Answer: B, D 3) In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.) A) when the speed is a maximum B) when the displacement is a zero C) when the magnitude of the displacement is a maximum D) when the potential energy is a maximum E) when the kinetic energy is a minimum, D, E 4) An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could A) double the amplitude of vibration. B) double the force constant (spring constant) of the spring. C) double both the amplitude and force constant (spring constant). D) double the mass. E) double both the mass and amplitude of vibration. Answer: B 5) A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its acceleration is zero. B) Its speed is zero. C) Its elastic potential energy is zero. D) Its kinetic energy is a maximum. E) Its total mechanical energy is zero., C, D 6) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points 7) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum?

47 A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: B 8) Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B? A) T/ B) T C) T D) 2T E) T/2 Answer: B 9) Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.) A) Both systems will have the same period on the Moon as on Earth. B) On the Moon, ball A will take longer to complete one cycle than ball B. C) On the Moon, ball B will take longer to complete one cycle than ball A. D) On the Moon, ball A will execute more vibrations each minute than ball B. E) On the Moon, ball B will execute more vibrations each minute than ball A., D 10) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Raise the weight. B) Lower the weight. C) Add more mass to the weight. D) Remove some mass from the weight. E) Decrease the amplitude of swing by a small amount. Answer: B 11) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration? A) The period does not change. B) The period increases. C) The period decreases. D) The period becomes zero. E) The period increases if the upward acceleration is more than g/2 but decreases if the upward

48 acceleration is less than g/2. Answer: B 12) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall? A) The period does not change. B) The period increases slightly. C) The period decreases slightly. D) The period becomes zero. E) The period becomes infinite because the pendulum would not swing. Answer: E 13) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems? A) Both periods would remain the same. B) Both periods would increase. C) Both periods would decrease. D) The period of the pendulum would increase but the period of the spring would stay the same. E) The period of the pendulum would decrease but the period of the spring would stay the same. 14) A leaky faucet drips 40 times in What is the frequency of the dripping? A) 1.3 Hz B) 0.75 Hz C) 1.6 Hz D) 0.63 Hz 15) If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz? A) 4560 Hz B) 1450 Hz C) 3.98 Hz D) 2.54 Hz E) 1.27 Hz Answer: E 16) If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change? A) 4 B) 2 C) D) 2/π

49 17) The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm? A) 4.34 s B) s C) s D) 7.39 s E) 7.75 s 18) An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s? A) 1.33 cm/s2 B) cm/s2 C) 11.5 cm/s2 D) 14.9 cm/s2 E) 0.00 cm/s2 Answer: D 19) If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4 20) A kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of s. What is the force constant (spring constant) of the spring? A) 2.45 N/m B) 12.1 N/m C) 24.1 N/m D) N/m E) N/m 21) When a kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations? A) s B) s C) s D) s E) 1.44 s

50 22) A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is The block is pulled from its equilibrium position at x = m to a displacement x = m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is its kinetic energy is closest to A) 0.90 J. B) 0.84 J. C) 0.95 J. D) 1.0 J. E) 1.1 J. 23) How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz? A) 39.5 kg B) 2.00 kg C) 1.00 kg D) 1.56 kg E) 6.29 kg 24) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same? A) m B) m C) 0.12 m D) 0.17 m Answer: D 25) A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position? A) 0.00 J B) 0.22 J C) 0.45 J D) 0.90 J E) 1.4 J 26) A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to

51 the length of the cables. A) 4.4 s B) 4.8 s C) 5.3 s D) 5.7 s 27) On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? A) T B) T/ C) T/6 D) 6T E) T/3 28) A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period? A) 2T B) T C) T D) T/ E) T/2 29) A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing? A) 6.00 s B) 3.46 s C) 2.00 s D) 1.15 s E) s Answer: B 30) An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N- 40? A) 4.85 m/s2 B) 1.66 m/s2 C) 3.74 m/s2 D) 2.39 m/s2 E) 9.81 m/s2 1) If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

52 Answer: 0.25 Hz, 4.0 s 2) A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b) How long does it take the needle tip to travel a total distance of cm? Answer: (a) 0.20 s (b) 0.90 s 3) A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a) What is the maximum speed of that point in SI units? (b) What is the maximum acceleration of the point in SI units? Answer: (a) 6.82 m/s (b) m/s2 4) A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time t, if x is equal to 8.3 cm at t = 0.0 s. Use the cosine function. Answer: x = (8.3 cm) cos[2πt/(4.6 s)] or x = (8.3 cm) cos[(1.4 s-1)t] 5) An object oscillates such that its position x as a function of time t obeys the equation x = (0.222 m) sin(314 s-1 t), where t is in seconds. (a) In one period, what total distance does the object move? (b) What is the frequency of the motion? (c) What is the position of the object when t = 1.00 s? Answer: (a) m (b) 50.0 Hz (c) m 6) When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (spring constant) of 467 N/m, the system obeys the equation y = (4.4 cm) cos(33.3 s-1 t). What is the mass of this laboratory sample? Answer: kg 7) An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant) 1720 N/m. The object is set into simple harmonic motion, with an initial velocity of and an initial displacement of Calculate the maximum speed the object raches during its motion. Answer: 4.5 m/s 8) A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what distance from the equilibrium position are the kinetic energy and the potential energy the same? Answer: (a) 0.24 m (b) 0.17 m

53 9) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system? Answer: (a) 0.56 J (b) 0.24 m Rotational Motion 1) The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P? A) A B) B C) C D) D E) The moment of inertia is the same for all of these objects. Answer: B 2) A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is A) more than the total kinetic energy of the cylinder. B) less than the total kinetic energy of the cylinder. C) equal to the total kinetic energy of the cylinder. Answer: B 3) The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, A) the block at the left lands first. B) the block at the right lands first.