v (m/s) 10 d. displacement from 0-4 s 28 m e. time interval during which the net force is zero 0-2 s f. average velocity from 0-4 s 7 m/s x (m) 20

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1 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 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]

2 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:

3 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:

4 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 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 m/s 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 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:

5 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 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) t (s)

6 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 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

7 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 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

8 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 x1 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 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

9 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 Length of the string and acceleration of gravity 48. Acceleration quadruples and centripetal force quadruples s 52. Total momentum and total energy of the system will remain constant

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