1. The age of the universe is about 14 billion years. Assuming two significant figures, in powers of ten in seconds this corresponds to

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1 1. The age of the universe is about 14 billion years. Assuming two significant figures, in powers of ten in seconds this corresponds to A) s B) s C) s D) s E) s ( yr) s 1 yr = s 2. A car traveling at 24.2 m/s is 280 m behind a truck traveling at 19.2 m/s. How long will it take the car to reach the truck? A) 11 s B) 26 s C) 32 s D) 41 s E) 56 s v ct = v cg v tg = 24.2 m/s 19.2 m/s = 5.0 m/s t = d / c ct = (280 m) / ( 5.0 m/s) = 56 s 3. A 10-kg rock and a 20-kg rock are thrown upward with the same initial speed v0 and experience no significant air resistance. If the 10-kg rock reaches a maximum height h, what maximum height will the 20-kg ball reach? A) 4h B) h/2 C) 2h D) h/4 E) h The height reached does not depend on the mass of the ball. v = 0; v 2 v 0 2 = 2aΔy = 2gh v 0 2 = 2gh h = v 0 2 2g

2 4. An airplane travels at 300 mi/h south for 2.00 h and then at 250 mi/h north for 750 miles. What is the average speed for the trip? A) 275 mi/h B) 270 mi/h C) 280 mi/h D) 260 mi/h E) 30 mi/h t 1 = 2.0 h, d 1 = 300 m/h ( ) 2.0 h ( ) = 600 mi; t 2 = 750 mi ( ) / 250 mi/h ( ) = 3.0 h v = d 1 + d 2 t 1 + t mi = = 270 mi/h 5 h 5. The figure shows four vectors M, N, S and T. Vector S can be expressed by the other vectors as A) M N B) M + N C) N M D) N M + T E) T N M ( N) starts at the tail of S and ends at the tail of M. M ends at the head of S. M and ( N) add up to S. 6. A ball is thrown with a velocity of magnitude 20.0 m/s at an angle of 25.0 above the horizontal. What is the vertical component of the ball's velocity immediately after the kick? A) 15.6 m/s B) 9.33 m/s C) 12.6 m/s D) 8.45 m/s E) 18.1 m/s v x = ( 20.0 m/s)sin 25.0 o ( ) = 8.45 m/s

3 7. James and John dive from an overhang into the lake 5.0 meters below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below A) the splashdown speed of John is 17 m/s larger than that of James. B) the splashdown speed of James is 9.8 m/s larger than that of John. C) they will both have the same splashdown speed. D) the splashdown speed of James is 17 m/s larger than that of John. E) the splashdown speed of John is 25 m/s larger than that of James. v 2 2 y = v y,0 v James = v John = ( ) 5.0 m 2gΔy = m/s 2 v 2 2 y + v x,james v 2 2 y + v x,john ( ) = 98 (m/s) 2 v y = 9.9 m/s. = ( 9.9 m/s) = 9.9 m/s = ( 9.9 m/s) 2 + ( 25 m/s) 2 = 26.9 m/s v John v James = 26.9 m/s 9.9 m/s = 17.0 m/s 8. 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) 17 m/s B) 20 m/s C) zero D) 10 m/s E) 6.8 m/s The horizontal acceleration is zero and therefore the horizontal velocity at the top of the trajectory is the same as the initial horizontal velocity. v x,top = v x,0 = ( 20 m/s)cos 60 o ( ) = 10 m/s

4 9. A certain aircraft has a mass of 300,000 kg. At a certain instant during its landing, its speed is 27.0 m/s. If the braking force is a constant 445,000 N, what is the speed of the airplane 10.0 s later? A) 20.0 m/s B) 14.0 m/s C) 10.0 m/s D) 12.2 m/s E) 18.0 m/s F = ma a = F m = 445,000 N =1.48 m/s2 300,000 kg ( ) 10.0 s v = v 0 + a( Δt) = 27 m/s 1.48 m/s 2 ( ) = 12.2 m/s 10. A 50.0-kg crate is being pulled along a horizontal frictionless surface. The pulling force is 10.0 N and is directed 20.0 above the horizontal. What is the magnitude of the acceleration of the crate? A) m/s 2 B) m/s 2 C) m/s 2 D) m/s 2 E) m/s 2 F x = ma x a x = F x m = F cosq ( m = 10.0 N )cos 20.0 o 50.0 kg ( ) ( ) = m/s The motion of a block sliding down a frictionless ramp can be described as motion with A) a constant speed, independent of the slope of the ramp. B) a constant speed that depends on the slope of the ramp. C) an acceleration which increases as the block slides. D) a constant acceleration less than 10 m/s 2. E) a constant acceleration greater than 10 m/s 2.

5 The constant acceleration of a block sliding down a frictionless ramp is a = g sinθ, where g is the acceleration of gravity of 9.8 m/s 2 and θ is the angle of the ramp with the horizontal. 12. A 4.0-kg object is placed on a scale in an elevator. The scale shows an apparent weight of the object of 44 N. What is the acceleration of the elevator? A) 11 m/s 2 upward B) 1.2 m/s 2 upward C) 1.2 m/s 2 downward D) 10 m/s 2 upward E) 2.4 m/s 2 downward Choose +y to point upward: F N mg = ma a = F N m g = 44 N 9.8 m/s 2 = 1.2 m/s 2, upward. 4.0 kg 13. 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) 32.9 m/s B) 12.8 m/s C) 10.7 m/s D) 45.7 m/s E) 21.4 m/s f k = ma a = f k m = m F k N m = m k mg m = m k g v 2 v 2 0 = 2aΔx v 2 0 = v 2 2aΔx = 0 2( m k g)δx v 0 = 2m k gδx = 2( 0.300) ( 9.81 m/s 2 )( 28.0 m) = 12.8 m/s

6 14. Which of the following is true about the mass and weight of an astronaut on the Moon's surface, compared to Earth s surface? A) Mass is less, weight is same. B) Mass is same, weight is less. C) Both mass and weight are less. D) Both mass and weight are the same. C) Both mass and weight are more. The mass of an astronaut doesn t change. Mass is a measure of the astronaut s inertia i.e. his resistance to acceleration. Weight is mass times the acceleration of gravity. Gravity is about one sixth on the Moon compared to Earth. Thus, the astronaut s weight is also one sixth on the Moon compared to Earth. 15. A sheet of paper and a book fell at different rates in a physics lecture demo until the paper was wadded up into a ball. The lecturer then claimed that if the air resistance could be neglected, all objects would fall at A) the same constant speed regardless of the type of material. B) the same constant speed regardless of how much they weigh. C) different constant speed depending on the type of material. D) the same constant acceleration. E) different accelerations proportional to their masses. If air resistance can be neglected, all free-falling objects, regardless of mass, weight, or material, experience the same constant acceleration of gravity of 9.8 m/s 2.

7 16. The graphs above represent the position x, velocity v, and acceleration a as a function of time t for an object moving in one dimension. Which of the following could be the scenario described by the graphs? A) A car breaking for a red light. B) A rock being dropped from a bridge into the water below. C) A rock being thrown straight up and coming back down. D) A plane flying at 400 miles per hour. E) An astronaut on the International Space Station. The motion shown is for constant positive acceleration with increasing positive velocity. This scenario is true for the rock being dropped. 17. A cart with weight of 40 N is moving on a ramp with an incline of 50 o with respect to the horizontal. Assuming no friction, what is the magnitude of the net force acting on the cart? A) 25.7 N B) 30.6 N C) 32.1 N D) 38.3 N E) 28.2 N Choose the +x-axis to point down the incline and the +y-axis in the direction of the normal force by the incline on the cart. The net force on the cart is the x-component of the weight of the cart. F net =W sinq = ( 40 N)sin 50 0 ( ) = 30.6 N

8 18. As shown in the figure, a force F pushes three boxes with masses m1 = 1.3 kg, m2 = 3.2 kg, and m3 = 4.3 kg across a frictionless, level surface. Find the magnitude of the contact force between boxes 2 and 3. A) 0.23 F B) 0.49 F C) 0.88 F D) 1.23 F E) 1.44 F Since all boxes are in contact, they will all have the same acceleration. F ( 4.3 kg) a = = m 1 + m 2 + m 3 m 1 + m 2 + m kg ( ) F = m a = m 3 F 32 3 ( ) ( ) F = 0.49F

9 19. An object of mass m is at rest on an inclined plane as shown in the figure. The inclined plane forms an angle θ with the horizontal. The coefficient of static friction between the object and the plane is μs. Which of the following diagrams correctly shows the forces acting on the object? d) correctly shows the forces. Weight always pulls an object straight down, a normal force is always perpendicular to the surface, and friction is always parallel to the surface. In this case, friction points up the ramp because it opposes the motion of the object sliding down the ramp.

10 20. A race car moving to the left in the sketch begins to slow down from a velocity v0 after crossing a finish line to a velocity vf. Which of the following is the correct direction of the car s acceleration when slowing down? A. B. C. D. E. The acceleration is proportional to the change in velocity vf v0, which points to the right. 21. As a ball falls, the action force is the gravitational pull of the Earth s mass on the ball. What is the reaction force to this action force? A) Air resistance acting against the ball. B) The acceleration of the ball. C) The gravitational pull of the ball s mass on Earth. D) Non-existent in this case. E) None of the above. According to Newton s law of gravity, the ball s mass exerts a gravitational pull on Earth of the same magnitude and opposite direction of the gravitational pull of the Earth s mass on the ball. These two forces form a Newton s third law action reaction pair.