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1. A batter hits a 0.140-kg baseball that was approaching him at 30 m/s and, as a result, the ball leaves the bat at 40 m/s in the reverse of its original direction. The ball remains in contact with the bat for 2.0 ms. What is the magnitude of the average force exerted by the bat on the ball? B i U Font Family AVA DE EE . @ 9 2. A 475-gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in milliseconds) was it in contact with the ball? B i U Font Family AAA DE EE .@3. A 2200-kg auto moving northward at 12.0 m/s runs into a 3800-kg truck which is also moving northward, but at 5.00 m/s. If the vehicles lock bumpers, how fast are they moving just after the collision? B U Font Family AAA DE E . E . 9 95 4. An 80-kg man is skating northward and happens to suddenly collide with a 20-kg boy who is ice skating toward the east. Immediately after the collision, the man and boy are seen to be moving together at 2.5 m/s in a direction 60 north of east. How fast was the boy moving just before the collision? Bi U Font Family & D5. In a police rifle test, a 15-g bullet traveling 213 m/s in a vertical direction suddenly buries itself in a 2.4-kg block of wood at rest directly above it. As a result, the bullet-block combination moves vertically upward. (a) Determine the velocity of the bullet-block combination just after the impact. (b) Determine the maximum height reached by the bullet/block combination. (c) Is kinetic energy conserved in this collision? B i U Font Family AVA DEE E 36 6. Three small masses are positioned at the following coordinates: 3.0 kg at (3.0 m, 2.0 m); 4.0 kg at (0.0 m, -1.0 m); and 5.0 kg at (5.0 m, -7.0 m). What are the coordinates of the center of mass (or center of gravity) of this system? B i U Font Family7. A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity) of this system of beads? B i U Font Family AVA DE EE. 8. A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle? B i U Font Family AAA DE EE9. A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest. (a) How long does it take the wood to make 3 complete cycles of vibration? (b) How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block? Bil U Font Family +J 10. A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire B i U Font Family AVA DE EE . @ 9511. When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s. (a) What is her angular speed in rad/s? (b) What is the magnitude of her linear acceleration? B i U Font Family 12. A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration. If it maintains the same acceleration, how long will it take the turntable to make its second complete revolution? B i U Font Family AAA DE E E.13. A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest. (a) What was the magnitude of the angular acceleration of the centrifuge as it slowed down? (d) How long did it take for the centrifuge to come to rest after being turned off? B i U Font Family AVADEE E .@6 14. The figure shows two blocks connected by a light cord over a pulley. This apparatus is known as an Atwood's machine. There is no slipping between the cord and the surface of the pulley. The pulley itself has negligible friction and it has a radius of 0.12 m and a mass of 10.3 kg. We can model this pulley as a solid uniform disk. At the instant that the heavier block has descended 1.5 m starting from rest, what is the speed of the lighter block? 3.0 5.7 B i U Font Family15. A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, (a) what is the angular acceleration of the pulley, and (b) what is the acceleration of the bucket? B i U Font Family A A DE E E 16. A small 355-g box hangs from one end of a thin light string that goes over a frictionless pulley having a moment of inertia of 0.0125 kg . m 2 2 and a radius of 15 cm. A second small package, this one of mass 680 g, hangs from the other end of the string. When the packages are released, the larger one accelerates downward, the lighter one accelerates upward, and the pulley turns without the string slipping. (a) What is the tension in the string on the side of the 355-g package? (b) At what rate do the packages change their speeds? B i U Font Family AAA DE E E .OG