Physics Final Exam Mechanics Review Answers 1. Use the velocity-time graph below to find the: a. velocity at 2 s 6 m/s v (m/s) 1 b. acceleration from -2 s 6 c. acceleration from 2-4 s 2 m/s 2 2 4 t (s) d. displacement from -4 s 28 m e. time interval during which the net force is zero -2 s f. average velocity from -4 s 7 m/s 2. Use the position-time graph below to find the: a. position at 2 s 12 m x (m) 2 b. acceleration from 4-8 s 12 c. velocity from 4-8 s 2 m/s d. displacement from -8 s 8 m 4 8 t (s) e. average velocity from -8 s 1. m/s 3. In what time does a car cover a distance of 1 m, if it is traveling at a constant speed of 14 m/s? 7.1 s 4. A car moving at a velocity of 17. m/s [E] slows down uniformly to a velocity of 6. m/s [E]. If the car undergoes a displacement of 1 m [E], find the: a. Acceleration 1.27 m/s 2 [W]
b. time interval 8.66 s 5. A car with an initial velocity of 5. m/s [S] accelerates at a uniform 3. m/s 2 [S] for 5. seconds. Find the: a. Displacement 63 m [S] b. final velocity 2 m/s [S] 6. A speeding car passes a stationary police car traveling at a constant 2 m/s. If the police car starts accelerating at a uniform 4 m/s 2, just as the speeding car passes the police car, find the: a. time when the police car catches up to the speeding car 1 s b. displacement from the initial position of the police car 2 m 7. A rock is dropped from rest at the top of a building. After free falling for 1.5 seconds, find the: a. Displacement 11. m b. Velocity 14.7 m/s 8. A ball is thrown straight up at a speed of 15 m/s. Find the: a. maximum height 11.5 m b. acceleration at the maximum height 9.8 m/s 2 c. velocity of the ball when it reaches the position from which is was thrown 15 m/s [down] d. total time the ball was in the air 3.6 s 9. A rock is dropped from rest from a height of 1. meters off the ground. Find the: a. speed of the rock just before hitting the ground 14 m/s b. time that the rock was free falling 1.43 s 1. Two students are standing on a 5. m high bridge. One student throws his rock horizontally at a speed of 9. m/s, while the other student drops her rock from rest. Find the:
a. final speed of each rock just before striking the water 13 m/s vs. 9.9 m/s b. time for each rock to hit the water 1.1 s 11. A hiker walks 45 m [W] in a time of 5 minutes, and then walks 3 m [S] in a time of 4 minutes. Find the: a. Average speed of the hiker 83 m/min b. Average velocity of the hiker 6 m/min (4 S of W) 12. Vector A is 3 m [E]. Vector B is 2 m [NE]. Find the: a. resultant vector from adding A + B 463 m (18 N of E) b. resultant vector from subtracting B from A (A B) 213 m (48 E of S) c. resultant vector from adding 2A + B 754 m (11 N of E) 13. A ball is thrown on level ground with an initial velocity of 25. m/s [3 above the horizontal]. Find the: a. components of the initial velocity v x = 21.7 m/s, v y = 12.5 m/s b. maximum height of the ball 7.97 m c. total time the ball is in the air 2.55 s d. range of the ball 55.4 m e. final speed of the ball just before striking the ground 25 m/s 14. A ball rolls off of a horizontal 85 cm high table at a speed of 9 cm/s. Find the: a. time that the ball is in the air.42 s b. horizontal displacement of the ball.37 m c. final velocity of the ball just before striking the ground 4.2 m/s (78 below horizontal) 15. A 2 kg object is sitting on a horizontal table. Find the:
a. weight of the object 196 N b. force of gravity of the object 196 N c. normal force being exerted on the object 196 N 16. A 5. kg mass is pulled across a rough horizontal surface, at a constant speed, by a force of 2 N [R]. Find the: a. force of friction 2 N [L] b. coefficient of kinetic friction.41 c. new force required to accelerate the mass at 2 m/s 2 [R] 3 N 17. A 1 kg box on level ground is being pulled by a string at an angle of 3 above the horizontal. If the tension in the string is 8 N, find the: a. normal force 58 N b. acceleration if the surface is frictionless 6.93 m/s 2 18. A 4. kg mass is released from rest on a 35 inclined plane as shown. Find the: a. acceleration if frictionless 5.62 m/s 2 b. acceleration if the coefficient of kinetic friction is.4 2.41 m/s 2 19. A train of 3 masses is pulled by a force of 2 N on a frictionless horizontal surface as shown. Find the: a. Acceleration 1.67 m/s2 b. tension T 2 1 N c. tension T 1 3.34 N T 1 T 2 2 kg 4 kg 6 kg 2 N 2. A 2 kg mass is attached to a 1 meter long string, which is fixed to the ceiling as shown. Find the:
a. tension in the string when at rest 19.6 N b. maximum speed if the mass is pulled to the side, such that the string makes an angle of 6 with the vertical, and released from rest 3.13 m/s c. tension in the string at the point of maximum speed 39.2 N 21. A string is placed on a frictionless pulley and two masses are fixed at both ends as shown. Find the: a. acceleration 2.45 m/s 2 b. tension in the string 36.8 N c. speed when the 5 kg mass has moved 1 m, if released from rest 2.21 m/s 5 kg 3 kg 22. A string is placed on a frictionless pulley and two masses are fixed at both ends as shown. Find the: a. acceleration if frictionless 3.68 m/s 2 b. acceleration if the coefficient of kinetic friction is.33 1.65 m/s 2 c. tension in the string in case b 24.4 N 5 kg 3 kg 23. A 17 kg car traveling at a constant 15 m/s is rounding a corner on level ground. If the radius of the turn is 5 m, find the: a. Direction of car s acceleration inward and net force inward b. centripetal acceleration 4.5 m/s 2 c. centripetal force 765 N 24. The force exerted on a 1 kg object is shown as a function of time below. Find the: a. acceleration at 2 s.5 m/s 2 F (N) 1 2 4 t (s)
b. impulse on the object from -2 s 5. Ns c. change in momentum of the object from -4 s 2 kgm/s d. speed of the object at 4 s if it started from rest at t= 2. m/s 25. A 1 kg box on level ground is being pulled by a string at an angle of 3 above the horizontal. If the tension in the string is 8 N and the box moves 5 meters to the right, find the: a. work done by the tension in the string 346 J b. work done by the force of gravity J c. final speed of the box if it was initially at rest 8.32 m/s 26. A 7 kg mass is pulled across a rough horizontal surface, at a constant speed, by a force of 2 N [R]. If the mass moves 1 meters to the right, find the: a. work done by the force 2 J b. work done by friction 2 J 27. A 1 kg mass moving at a speed of 1 m/s encounters a frictionless 2 inclined plane as shown. Find the: a. maximum height 5.1 m 1 m/s b. maximum distance along the incline 14.9 m c. maximum distance along the incline if the coefficient of kinetic friction on the incline is.4 7.1 m 28. A ball rolls inside a bowl as shown. If the ball has a maximum speed of 2. m/s at the bottom of bowl, find how high above the bottom of the bowl the ball goes..2 m
29. A frictionless pulley and two masses are arranged as shown. Assuming the system is released from rest, use conservation of energy to find the: a. kinetic energy of the system just before the 5 kg mass strike the floor 19.6 J 5 kg b. final speed of the 5 kg mass just before it strikes the floor 2.21 m/s 1 m 3 kg 3. The behavior of a Hooke s Law spring is shown in the force-spring extension graph below. Find the: F (N) a. spring constant 6 N/m 3 b. work done in compressing the spring.35 m 3.68 J c. potential energy stored in the spring once it is compressed.35 m 3.68 J.25.5 x (m) 31. The same spring as in the previous problem is attached to a wall while a 5 kg mass is placed in front of the compressed spring as shown. The mass is then displaced.35 m to the right and released from rest. Find the maximum speed of the mass. 1.21 m/s 32. A crane lifts a 1 kg object at a slow speed to a height of 6 meters off the ground. If the crane does so in a time of 8 seconds, find the: a. gravitational potential energy of the object at the completion of the lift 588 J b. work done by the crane 588 J c. power of the crane 735 Watts
33. The force of gravity between two stars of identical mass (1 36 kg) is 2.x1 28 N. Find the distance of separation between the stars. G = 6.67x1-11 Nm 2 /kg 2. 5.8x1 16 m 34. An object undergoing uniform circular motion has a period of 1.5 seconds. Find the: a. Frequency.67 Hz b. Speed of the object if the radius is 5 cm 2.1 m/s 35. Kepler s constant for which of the following two cases will be the same: a. Earth s moon orbiting Earth b. Saturn s moon orbiting Saturn c. a weather satellite orbiting Earth d. Earth orbiting the Sun 36. Compared to an outer orbit, as a satellite is moved to a lower circular orbit the speed of the circular orbit must: increase 37. An object is undergoing uniform circular motion with a frequency of 18 Hz. If the radius of the circle is 5 cm, find the speed of the object. 57 Hz 38. A 2 kg car traveling at 6 m/s strikes the rear of a 4 kg truck. If both vehicles stick together after the collision, find the: a. speed of the pair immediately following the collision 2m/s b. % kinetic energy lost during the collision 67% c. Is the collision elastic or inelastic? inelastic 39. Skater A is moving at 3. m/s [S] and collides with skater B moving at 4. m/s [E]. The mass of skater A is 6 kg and the mass of skater B is 4 kg. Find the final velocity of the pair if they undergo a totally inelastic collision and stick together. 2.4 m/s(42 E of S) 4. A 7. kg rifle, initially at rest, fires a 25 g projectile at a muzzle velocity of 5 m/s. Find the recoil velocity of the rifle. 1.79 m/s 41. Two gliders are on a frictionless air-track. A 1 kg glider with an initial velocity of 2 m/s [R] strikes a 3 kg glider at rest. After the collision, the 1 kg glider has a velocity of 1 m/s [L]. Find the: a. final velocity of the 3 kg glider 1 m/s [R] b. Is kinetic energy conserved? yes
c. Is the collision elastic or inelastic? elastic 42. A car travels over a hump in the road at a speed of 15 m/s. If the occupants of the car feel weightless at the crest of the hump, what is the effective radius of the hump in the road? 23 m 43. Find the horizontal displacement of the projectile from the ball s position when the string is cut by the razor blade. The pendulum is released from rest as shown below..7 m 44.. a. 3 J b. 3 J c. 1.7 m/s 45. 46. 47. Length of the string and acceleration of gravity 48. Acceleration quadruples and centripetal force quadruples 49. 4 5. 2 51. 2 s 52. Total momentum and total energy of the system will remain constant