Physics 2010 Fall 2012 Orest Symko REVIEW SET 2 MIDTERM 2 1. In a popular amusement park ride, a rotating cylinder of radius 15.0 m rotates with an angular speed of 8.0 rad/s. The floor of then drops away leaving the rider suspended against the wall in the vertical position. See figure. Let the rider have a mass of 58.0 kg. A. What applied force is responsible for keeping the rider pinned to the wall? Give this answer in words and a free body diagram would help. B. Determine the centripetal force felt by the rider. In words, what is the source of this force? C. What is the coefficient of friction between the wall and the backsides of the rider in contact with the wall? 2. A 2.00 kg mass is attached to a 1.86 m string and is swung in a circle in a horizontal plane. See figure. The radius of the circle is R = 0.560 m. A. Determine the tension in the string? B. Determine the magnitude of the centripetal force associated with the motion of the mass. What is its direction? In words, what is the source of this centripetal force? C. What is the velocity of the mass? D. How long does it take the mass to complete one full rotation? 3. A rather unusual homemaker decides to dry a single damp sock whose weight is 1.00 N. He uses his electric clothes drier. The drier interior is a drum of radius R = 0.450 m and rotates at a constant speed in a vertical circle. See figure. The sock rotates in such a way that it stays against the drum. The picture on the right shows only the drum and 4 positions of the sock as the drum rotates. At point A the net force on the sock is its weight. A. At point B draw arrows representing the velocity and acceleration of the sock. B. At points A and D draw arrows and use labels showing all the actual forces the sock feels. C. At point C draw an arrow showing the net force the sock feels. Label it. D. The point at which the normal force the sock feels is zero. E. The point at which the weight of the sock does not contribute to the centripetal force. F. The point at which the normal force is twice the sock's weight. G. The point at which the normal force on the sock is equal to the weight of the sock. H. Determine the speed of the sock.
4. A 5.00 kg box is sitting next to a 12.0 kg crate on a horizontal surface. A 150 N force is applied horizontally on the 5.00 kg box. See figure. The coefficient of kinetic friction between each mass and the surface is u = 0.600. A. Construct a free body diagram for each mass using the objects shown below. B. Determine the acceleration of the two mass system. C. As the box and crate accelerate together, what is the force the right face of the box exerts on the left face of the crate? D. As the box and crate accelerate together, what is the magnitude of the force exerted by the left face of the crate on the right face of the box? 5. A 0.250 kg ball (m) is tied to a tall pole with a 1.40 rope (L). The ball is then thrown so it rotates in a horizontal circle, i.e., the plane of the circle is parallel to the ground at constant speed. The rope make an angle of 40.0 ( ) with respect to the pole. See figure. A. On the figure to the right, draw all the actual forces the ball feels. B. What is the radius of the circular path in which the ball travels? C. What is the speed of the ball? D. What is the tension in the rope? E. How much work is done by the tension the ball feels during one complete rotation of the ball? 6. A. The planet Nahar has 1/5 the mass of the earth and its radius is 1/5 that of the earth. On Nahar Rose has a mass of 50 kg. 1. What is Rose's mass on earth? 2. What is Rose's weight on earth? 3. What is Rose's weight on Nahar? B. Below are depictions of situations in which the target object is subject to one or more forces. To the right of each picture construct a free body diagram. In that diagram each identified force must be accompanied by an arrow and a label using notation seen in lecture. Assume air resistance plays no role. a. Clown shot out of a cannon b. Block sliding down incline at constant speed c. Patron in amusement park ride: d. Bob on end of pendulum (on way up) rotating steel cylindrical cage
In the following enter a, b, c, d, none, or all of the above situations that best fit the statements made. 1. Those pictures for which. 2. Those pictures for which is due only to the weight on the object. 3. Those pictures for which points vertically straight upward. 4. Those pictures for which weight is not one of the forces felt by the object. 7. At the initial instant a small 6.00 kg case is seen to be traveling to the right along a horizontal surface with a velocity of 10.0 m/s. The case slows down uniformly and after traveling 15.0 m is seen to have a velocity of 5.00 m/s to the right. See figure. A. Use the motion data to determine the acceleration. B. What is the coefficient of kinetic friction between the case and the surface? C. Suppose now when the case arrives at its initial position with a velocity of 10.0 m/s to the right, a constant force of 23.2 N is applied at an angle of 37. What is the velocity of the case after traveling 15.0 m? 8. A 0.500 kg mass is tied to the end of a 1.40 m string and whirled in a circle whose plane is parallel to the floor. As the mass is whirled faster and faster the string suddenly breaks when the angle between the string and the vertical is 86.0. A. What is the maximum tension the string can sustain just before breaking? B. What is the speed of the mass at the maximum tension the string can sustain? C. What is the period of the circular motion at the maximum string tension? 9. A. A 0.0750 kg toy plane is tied to the ceiling with a string. When the airplane s motor is started, it moves with a constant speed of 1.21 m/s in a horizontal circle or radius 0.440 m. See figure. 1. What is the angle of the string makes with the vertical? 2. What is the tension in the string? B. A 3.50 kg block is at rest on a table. A rope is tied to the right side of this block, hung over a frictionless pulley, and tied to a mass m (see figure). For the block on the table = 0.650 and = 0.450. s k 1. What is the largest mass for m such that the 3.50 kg block does not slip? 2. Suppose m = 5.00 kg. What is the acceleration of the 3.50 kg block when the system is allowed to move?
10. A 12.0 kg block (m) is sliding to the right across a horizontal surface and is subject to a constant force, = 10.0 N (see drawing). At the initial instant t o = 0, the block is traveling to the right at v o = 8.50 m/s. The block comes to rest with uniform acceleration 5.00 s later. A. What is the acceleration of the block, magnitude and direction, during this motion? B. What frictional force does the block feel from the horizontal surface while it is slowing down? C. What is the coefficient of kinetic friction,, between the block and the horizontal surface? k D. ]How long would it take the block to come to rest from the initial 8.50 m/s if the applied force,, were not acting? 11. In the drawing shown the block on the table has a mass of 40.0 kg mass and the hanging block has a mass of 20.0 kg. The coefficient of kinetic friction between the table and the 40.0 kg block is 0.300. A. What is the magnitude of the acceleration of the descending block? B. What is the magnitude of the tension the block on the table feels? C. If the descending block, starting from rest, falls 1.20 m, what is the net work the tension felt by both blocks does? 12 A. The following shows the path of the arrow fired at the opening ceremonies of the Barcelona Olympics that lit the Olympic flame. Assume no air resistance. Do all drawings on graph. 1. Draw the position vector, to location where the flame lights. Include a label. 2. Write out this position vector in two ways: (a) magnitude and direction, and (b) in unit vector form. (a) : (b) 3. At location B draw the velocity vector. Include a label. 4. At location A draw the acceleration vector. Include a label. 5. In unit vector form write down the displacement vector between A and D. Draw it. Label it. = 6. At B draw an arrow to represent the net force the arrow feels. Include a label. 7. List all the external forces the arrow feels when it is at C. 8. At what location (0, A, B, C and/or D) is the speed of the arrow largest? 13. A rock is tossed out of a window that is 18.0 m above the ground at an initial velocity of 20.0 m/s at 37 above the horizontal. See figure. Use the point on the ground directly below window as the origin of the coordinate system. A. After 3.00 s find the position of the rock in its flight. Remember position is a vector. B. At t = 3.00 s determine the velocity of the rock. C. What is the instantaneous speed of the rock at 3.00 s? D. At t = 3.00 s, draw on the picture above, the position, velocity and acceleration vectors for the rock.
14. A rock is hurled from the top of a three-story building (h = 12.0 m) with a velocity ( ) of 26.0 m/s at an angle of 37.0 ( ) above the horizontal (see drawing). Find the horizontal distance (R) of the rock just as it hits the ground. 15. A. Two large crates (m 1 = 120. kg, m 2 = 180. kg) are hung by strong massless cables as shown in the drawing. A tension applied to the upper cable of T = 3.60 10 3 N accelerates this load upward. Find (1) the upward acceleration of the two-crate load, and (2) the tension in the cable between the upper and lower crates. B. A youngster is twirling a 0.110 kg ball on a string in a horizontal circle of radius 0.360 m. The ball travels once around the circle in 1.24 s. 1. What is the constant speed of the ball as it travels around the circle? 2. Find the centripetal force on the ball. 3. What is the tension on the string? 16. A vandal hurls a small rock at an initial speed of v o = 23.0 m/s at an angle = 40.0 above the horizontal. The vandal is standing at a distance of 30.0 m from the building. A. At what vertical distance above the point where the rock leaves the vandal s hand does the it strike the left wall of the building? B. What is the speed of the rock just before striking the building? C. Is the rock on the way up or on the way down when it hits the building? 17. A. A 10.0 kg block and a 20.0 kg block are sitting on a horizontal surface and are connected by a massless string as shown in the drawing. The coefficient of kinetic friction between both blocks and the surface is k = 0.650. A force of = 238.0 N is applied to the right block as shown.. 1. What is the acceleration of this two-body system? 2. What tension exists in the string connecting the two block? B. A swing ride at Lagoon consists of chairs that are swinging in a circle by 15.0 m cables which are attached to a vertical rotating pole. Take the mass of the chair and its contents to be 88.0 kg. 1. What is the tension in the cable? 2. What is the speed of the chair?
18. A. The drawing shows the flight of a golf ball (no air resistance) from an elevated tee to a distant green. A, B, C, and D indicate points along the flight of the ball on the way to the green. 1. At point A draw a vector to represent the instantaneous velocity. Label it. 2. At B draw a vector to represent the acceleration of the ball. Label it. 3. At C draw a vector to represent the net force the ball feels. Label it. 4. At which point is the speed least? 5. At which point is the speed greatest? 6. At which two points is the speed the same? 7. At which point is the magnitude of v greatest? B. Below are pictures of physical situations in which a target object is subject to one or more forces. To the right of each picture construct a free body diagram. Only the target object is shown at the right Each force identified must be accompanied by an arrow and a label using notation developed in lecture. 1. The large wooden bullet shot out of an air cannon (no air resistance). y 2. A pair of blocks accelerating to the right on a frictionless surface in such a way that m 2 does not slip. 3. A tennis ball attached to a string swinging in a horizontal circle. 19. Two forces, and, act on a 5.00 kg block as shown in the drawing. The coefficient of kinetic friction between the table and the bottom of the block is k = 0.200. The magnitudes of the forces are F = 50.0 N and F = 45.0 N. 1 2 A. What is the magnitude of the kinetic frictional force the block feels? B. What is the acceleration (magnitude and direction) of the 5.00 kg block? 20. The drawing shows a 1.20 kg ball attached to a vertical post by strings of length 1.20 m and 1.60 m. The ball is set whirling in a horizontal circle such that the ball completes a full rotation every 0.754 s. A. What is the speed of the ball? B. What centripetal force (magnitude only) does the ball feel as it rotates around the post? C. What are the tensions in the 1.20 m and 1.60 m strings?
21. A. The following drawings depict a number of physical situations. Next to each picture is one of the objects in the figure. For that object construct a complete free body diagram. Draw arrows to represent forces and label them. 1. Block 2 (m 2) is dropping with constant velocity. The object of interest is m1. 2. The horizontal force is large enough that m 2 does not slide down the right face of m 1. There is no friction between m and the table. The object of interest is m. 1 1 3. A small block is being held against the inside wall of a circular plexiglass drum due to the rotating motion of the drum. At the instant shown, the object is on the far right of the drum as it moves counter clockwise. The object of interest is the block. B. The figures below are 4 views from above of various particles on a string moving in a horizontal circle on a table top. All the particles are moving at the speeds shown. 1 2 3 4 1. Which of the pictures displays the largest centripetal force on the mass shown? 2. Which of the pictures displays the least centripetal force on the mass shown. 3. Which mass has the largest centripetal acceleration? 4. Which mass has the smallest centripetal acceleration? 5. Which mass feels the greatest tension?
22. A. In the movie King Kong the blonde damsel escapes from the love struck ape with the help of a close friend by climbing down a vine from King Kong s mountain lair. King Kong awakens and notices his love interest descending down the vine. He quickly grabs the vine and begins pulling the pair upward with a constant tension of 1510 N. See drawing. The damsel hangs from the end of the vine while her friend hangs from the vine a few meters above her. 1. What is the acceleration of the fleeing friends as King Kong pulls them towards him? 2. What is the tension on the vine exerted on the damsel? The tension is not 1510 N. B. A 125 N force is applied to a 28.0 kg trunk at an angle of 37.0 with respect to the horizontal as shown in the drawing. The coefficient of kinetic friction is = 0.240. Calculate the acceleration, magnitude and direction, of the trunk. k 23. A hockey puck of mass 0.100 kg is attached to a string. The string passes through a hole in the center of a table. The puck travels without friction at a constant speed on the top of the table in a circular path of radius 0.500 m. Initially you do not peer below the top of the table to see what is attached to the other end of the string. See drawing. A. If the period with which the puck travels in a circular loop is 0.250 s, what is the tension in the string attached to the puck? B. You now look under the table and see a mass M attached to the other end of the string. What is the mass of M (in kg) which is supported by the string?