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# Mechanics: Force, energy and momentum.

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1. A 0.25 kg ball is thrown straight up into the air with an initial speed of 19 m/s. Find the momentum of the ball at the following locations.
(a) at its maximum height
(b) halfway to its maximum height

2. A 2.75 kg steel ball strikes a wall with a speed of 10.0 m/s at an angle of 60.0° with the surface. It bounces off with the same speed and angle (Fig. P6.14). If the ball is in contact with the wall for 0.225 s, what is the average force exerted on the ball by the wall?

3. A 70.0 kg person throws a 0.0430 kg snowball forward with a ground speed of 33.0 m/s. A second person, with a mass of 55.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.10 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard the friction between the skates and the ice.

4. A 7.0 g bullet is fired into a 1.5 kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 13 cm. Find the initial speed of the bullet.

5. In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person's heart in one stroke. This information can be obtained by means of a Ballisto-cardiograph. The instrument works as follows: The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood can be determined independently (for example, by observing an ultrasound Doppler shift). Assume that the blood's speed is 44.5 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 6.90 10-5 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplified example illustrates the principle of Ballisto-cardiography, but in practice a more sophisticated model of heart function is used.

6. Consider a frictionless track as shown in Figure P6.48. A block of mass m1 = 4.55 kg is released from A. It makes a head on elastic collision at B with a block of mass m2 = 9.50 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

7.A bullet of mass m and speed v passes completely through a pendulum bob of mass M as shown in Figure P6.50. The bullet emerges with a speed v/2. The pendulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? (Use M for M, m for m, l for , and g for gravity, as necessary.)

8. Two carts of equal mass, m = 0.250 kg, are placed on a frictionless track that has a light spring of force constant k = 47.0 N/m attached to one end of it, as in Figure P6.60. The red cart is given an initial velocity of 0 = 2.60 m/s to the right, and the blue cart is initially at rest.
(a) If the carts collide elastically, find the velocity of the carts just after the first collision.
(b) If the carts collide elastically, find the maximum compression in the spring.