Name: Date: AP Physics B Fall Final Exam Review 1. The first 10 meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity the sprinter had after 2 seconds. (a) Determine the sprinter's constant acceleration during the first 2 seconds. (b) Determine the sprinter's velocity after 2 seconds have elapsed. (c) Determine the total time needed to run the full 100 meters. (d) On the axes provided below, draw the displacement vs. time curve for the sprinter. 2. A woman fell 43.9 m from the top of a building, landing on the top of a metal ventilator box, which she crushed to a depth of 46 cm. She survived without serious injury. What acceleration (assumed uniform) did she experience during the collision? How many g's is this? (936 m/s/s; 96 g s) 3. A ball of moist clay falls to the ground from a height of 15.0 m. It is in contact with the ground for 20.0 ms before coming to rest. What is the average acceleration of the clay during the time it is in contact with the ground? (857 m/s/s) 4. A dart is thrown horizontally toward the bull's-eye of a dartboard with an initial speed of 10 m/s. It hits at a point near the bottom rim, vertically below the bull's-eye, 0.19 s later. (a) How far from the bull's-eye did the dart hit? (b) How far away from the dart board did the thrower stand? (0.18 m; 1.9 m) 5. A rifle is aimed horizontally at a target 30.5 m away. The bullet hits the target 1.9 cm below the aiming point. (a) What is the bullet's time of flight? (b) What is its muzzle velocity? (0.063 s; 484 m/s) 6. You throw a ball with a speed of 25.0 m/s at an angle of 40 above the horizontal directly toward a wall. The wall is 22 m horizontally from the release point of the ball. (a) How long does the ball take to reach the wall? (b) How far above the release point does the ball hit the wall? (c) What are the horizontal and vertical components of its velocity as it hits the wall? (d) When it hits, has it passed the highest point on its trajectory? (1.15 s; 12.0 m; 19.2 m/s and 4.8 m/s; no) 7. A model rocket is fired vertically and ascends with a constant vertical acceleration of 4 m/s/s for 6 s. Its fuel is then exhausted and it continues as a free-fall particle. (a) What is the maximum altitude reached? (b) What is the total time elapsed from takeoff until the rocket strikes the earth? (101 m; 13 s)
Questions i-viii refer to the following set of speed-time graphs. On your answer sheet, write the letter(s) of the graph(s) that represent the kind of motion described. There may be more than one letter for each answer. If there are no graphs for which the description is true, write "none." i. moving at a constant speed ii. increasing speed in either direction iii. moving in the positive direction iv. moving in the negative direction v. standing still vi. decreasing speed in either direction vii. moving in the negative direction at a constant speed viii. moving in the positive direction with a changing speed Questions ix-xv refer to the following set of distance-time graphs. On your answer sheet, write the letter(s) of the graph(s) that represent the kind of motion described. There may be more than one letter for each answer. If there are no graphs for which the description is true, write "none." ix. standing still x. changing speed in either direction xi. increasing speed in either direction xii. moving in the negative direction xiii. moving like a freely-falling object in a vacuum xiv. decreasing speed toward the origin xv. moving with a constant speed
8. A 75 kg person stands on the floor in an elevator at rest. (a) Draw a free body diagram for the person. (b) What is the magnitude of the normal force on the person? (c) The elevator now accelerates upward at 3 m/s/s. What is the new magnitude of the normal force? (d) The elevator turns around and accelerates downward at 1 m/s/s. What is the new magnitude of the normal force? 9. A car is parked on a hill with a constant slope of 25. The car s parking brake is securely set. A tow truck is pulling the car up the hill. The coefficient of friction between the tires and the road is 0.8. (a) Draw a free body diagram for the car. (b) How much force does the tow truck need to pull with in order to move the car up the hill at a constant velocity? (c) The tow truck operator realizes that the car s brake is on and releases it, allowing the car s wheels to roll. The coefficient of friction within the axles is now 0.1. Now how much force does the tow truck need to pull the car up the hill with a constant velocity? 10. A 1200 kg sports car is hurtling toward the bottom of a cliff at 25 m/s. It is stopped by the cliffs in 0.12 seconds. What was the force that the cliff put on the car? 11. Frank, whose mass is 75 kg, jumps from his house s balcony (2 meters high). Foolishly, he holds his body perfectly stiff so that his body strikes the ground like a spear. He jolts to a stop in only 0.016 seconds. The force bringing Frank to a stop is split between each leg. A tibia can withstand a shock of 13200 N without breaking. Can Frank walk away from his jump? 12. You are pulling a 20 kg crate up a 30 incline at constant speed. How large a force parallel to the incline is needed if the coefficient of friction between incline and crate is 0.3? 13. Hercules and Xena are in a boat in serpent infested waters when a demon appears in the boat! Hercules (who has a mass of 75 kg) jumps straight off the front of the boat with a speed of 5 m/s relative to the water. Xena (who has a mass of 71 kg) simultaneously jumps off the back of the boat at 1 m/s relative to the water. If the 100 kg boat was initially traveling forward at 3 m/s, what is its velocity after both heroes jump? 14. If a 1000-kg car is sent toward a cement wall with a speed of 14 m/s and the impact brings it to a stop in 0.08 s, with what average force is it brought to rest? 15. A 300 kg motorboat is turned off as it approaches a dock and it coasts in toward the dock at 0.5 m/s. Isaac, whose mass is 62.0 kg, jumps off the front of the boat with a speed of 3.0 m/s relative to the water. What is the velocity of the boat after Isaac jumps? 16. The ACE towing company tows a disabled 1050-kg automobile off the road at a constant speed. If the tow line makes an angle of 10 with the vertical, what is the tension in the line supporting the car?
17. In the figure below, find the acceleration of the (200 kg) cart that is required to prevent the (5 kg) block from falling. The coefficient of static friction between the block and cart is 0.4. 18. A cup of coffee is sitting on a table in an airplane that is flying at a constant altitude and a constant velocity. The coefficient of static friction between the cup and table is 0.3. Suddenly, the plane accelerates, its altitude remaining constant. What is the maximum acceleration that the plane can have without the cup sliding backward on the table? 19. A student is skateboarding down a ramp that is 6.0 m long and inclined at 18 with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.6 m/s. Neglect friction and find the speed at the bottom of the ramp. 20. A girl is sledding down a slope that is inclined at 30 above the horizontal. A moderate wind is aiding the motion by providing a steady force of 105 N that is parallel to the motion of the sled. The combined mass of the girl and sled is 65.0 kg, and the coefficient of kinetic friction between the sled and the snow is 0.15. How much time is required for the sled to travel down a 175 m slope, starting from rest? 21. A 240 N force is pulling an 85 kg refrigerator across a horizontal surface. The force acts at an angle of 20 above the surface. The coefficient of kinetic friction is 0.2, and the refrigerator moves a distance of 8 m. Find (a) The work done by the pulling force, and (b) the work done by the kinetic frictional force. 22. In screeching to a halt, a car leaves skid marks that are 65 m long. The coefficient of kinetic friction between the tires and the road is 0.71. How fast was the car going before the driver applied the brakes? 23. When a 0.045 kg golf ball takes off after being hit, its speed is 41 m/s. (a) How much work is done on the ball by the club? (b) Assume that the force of the golf club acts parallel to the motion of the ball and that the club is in contact with the ball for a distance of 0.01 m. Ignore the weight of the ball and determine the average force applied to the ball by the club. 24. A cyclist approaches the bottom of a gradual hill at a speed of 11 m/s. The hill is 5.0 m high, and the cyclist estimates that she is going fast enough to coast up and over it without peddling. Ignoring air resistance and friction, find the speed at which the cyclist crests the hill. 25. A swing is made from a rope that will tolerate a maximum tension of 800 N without breaking. Initially, the swing hangs vertically. The swing is then pulled back at an angle of 60 with respect to the vertical and released from rest. What is the mass of the heaviest person who can ride the swing? 26. A wrecking ball swings at the end of a 10 m cable on a vertical circular arc. The crane operator manages to give the ball a speed of 6 m/s as the ball passes through the lowest
point of its swing and then gives the ball no further assistance. Friction and air resistance are negligible. What speed does the ball have when the cable makes an angle of 30 with respect to the vertical? 27. A square 0.4 m on each side is mounted so that it can rotate about an axis that passes through the center of the square. The axis is perpendicular to the plane of the square. A force of 15 N lies in this plane and is applied to the square. What is the magnitude of the maximum torque that such a force could produce? 28. One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. One force has a magnitude of 2.0 N and is applied perpendicularly to the length of the stick at the free end. The other force has a magnitude of 6.0 N and acts at a 30 angle with respect to the length of the stick. Where along the stick is the 6.0 N force applied? 29. A uniform plank of length 5.0 m and weight 225 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support. To what distance x can a person who weighs 450 N walk on the overhanging part of the plank before it just begins to tip? 30. As a car in the Indy 500 is going through a turn at a speed of 98.8 m/s, an accelerometer measures a centripetal acceleration of 30.0 m/s/s. Determine the radius of the turn. 31. The maximum tension that a 0.5 m string can tolerate is 14 N. A 0.25 kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed that the ball can have (a) at the top of the circle and (b) at the bottom of the circle? 32. In an exercise apparatus, a spring stretches 0.24 m when a bodybuilder exerts a force of 410 N. (a) When used vertically to support a 12-kg object, by how much does this spring compress? (b) If that object is pushed down and allowed to oscillate, what will be the period of oscillation? In preparation for shooting a ball in a pinball machine, a spring (k = 675 N/m) is compressed by 0.065 m. The ball (m = 0.0585 kg) is at rest against the spring at point A. When the spring is released, the ball slides (without rolling) to point B, which is 0.3 m higher than point A. How fast is the ball moving at B? 33. A horizontal spring (k = 360 N/m) is lying on a frictionless surface. One end of the spring is attached to a wall, and the other end is connected to an object of mass 2.8 kg. The spring is then compressed by 0.065 m and released from rest. What is the speed of the object (a) at the instant when the spring is at its equilibrium length and (b) at the instant when the spring is stretched by 0.048 m past its equilibrium length? 34. The shock absorbers in the suspension system of a car are in such bad shape that they have no effect on the behavior of the springs attached to the axles. Each of the identical springs attached to the front axle supports 320 kg. A person pushes down on the middle of the front end of the car and notices that it vibrates through five cycles in 3.0 s. Find the spring constant of either spring. 35. Suppose that an object on a vertical spring oscillates up and down at a frequency of 5.0 Hz. By how much would this object, hanging at rest, stretch the spring?
36. A typical neutron star may have a mass equal to that of the Sun but a radius of only 10 km. (a) What is the gravitational acceleration at the surface of such a star? (b) How fast would an object be moving if it fell from rest through a distance of 1.0 m on such a star? a. 1.3 x 1012 m/s/s; (b) 1.6 x 106 m/s 37. One of the Echo satellites consisted of an inflated spherical aluminum balloon 30 m in diameter and of mass 20 kg. Suppose a meteor having a mass of 7.0 kg passes within 3.0 m of the surface of the satellite. What is the magnitude of the gravitational force on the meteor from the satellite at the closest approach? 2.9 x 10-11 N 38. Compare the gravitational force exerted on a 3 kg baby (a) by a 70 kg obstetrician who is 1 m away (and approximated as a point mass), (b) by the planet Jupiter (2 x 1027 kg) at its closest approach to earth (6 x 1011 m), and (c) by a Sun-like star 10 light-years away. b. 1 x 10-8 N; (b) 1 x 10-6 N; (c) 4.5 x 10-14 N 39. A spaceship is idling at the fringes of our galaxy, 80000 light-years from the galactic center. What is the ship s escape speed from the galaxy? The mass of the galaxy is 1.4 x 1011 times that of our sun. (Assume for simplicity that the matter forming the galaxy is distributed in a uniform sphere.) 157 km/s 40. A satellite is in a circular orbit just above the surface of the moon. (a) What is the acceleration of the satellite? (b) What is the speed of the satellite? (c) What is the period of the satellite orbit? c. 1.55 m/s/s; (b) 1640 m/s; (c) 1.85 hr