# EXERCISES AND PROBLEMS

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EXERCISES AND PROBLEMS

ssm Solution is in the Student Solutions Manual.

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Impulse and Linear Momentum

1A cue stick strikes a stationary pool ball. with an average force 50 N over a time of 10 ms. If the ball has mass 0.20 kg. what d does it have just after impact?

2A The National Transportation Safety Board is testing the crash sort highness of a new car. The 2300 kg vehicle. moving at 15 mls. allowed to collide with a bridge abutment, which stops it in 6 s. What is the magnitude of the average force that acts on the during the pact?

3A 150 g baseball pitched at a speed of 40 m/s is hit straight k to the pitcher at a speed of 60 m/s. What is the magnitude of average force on the ball from the bat if the bat is in contact the the ball for 5.

4A Until he was in his seventies, Henri LaMothe excited audiences • belly-flopping from a height of 12 min to 30 cm of water.

5P. Assuming that he stops just as he reaches the bottom of the estimating his mass, find the magnitudes of (a) the gave and (b) the average impulse on him from the water. A averages 1200 N is applied to a 0.40 kg steel balling at 14 m/s in a collision lasting.

6E. In February 1955, a paratrooper fell 370 m from an airplane without being able to open his chute but happened to land in snow, suffering only minor injuries. Assume that his speed at impact was 56 mls (terminal speed), that his mass (including gear) was 85 kg, and that the magnitude of the force on him from the snow was at the survivable limit of 1.2 x 105 N. What are (a) the minimum depth of snow that would have stopped him safely and (b) the magnitude of the impulse on him from the snow?

7E. A 1.2 kg ball drops scenically onto a floor, hitting with a speed of 25 mls. It rebounds with an initial speed of 10 m/s. (a) What impulse acts on the ball during the contact? (b) If the ball is in contact with the floor for 0.020 s. what is the magnitude of the average force on the floor from the ball?

8P. It is well known that bullets and other missiles fired at Superman simply bounce off his chest . Suppose that a gangster sprays Superman’s chest with 3 g bullets at the rate of 100 bullets/min. and the speed of each bullet is 500 mls. Suppose too that the bullets rebound straight back with no change in speed. What is the magnitude of the average force on Superman’s chest from the stream of bullets?

9P. A 1400 kg car moving at 5.3 mls is initially traveling north in the positive y direction. After completing a 90· right hand turn to the positive x direction in, the inattentive operator drives into a tree, which stops the car in 350 ms. In unit-vector notation, what is the impulse on the car (a) due to the turn and (b) due to the collision? What is the magnitude of the average force that acts on the car (c) during the turn and (d) during the collision? (e) What is the angle between the average force in (c) and the positive 😡 direction?

lOP. A 0.30 kg softball has a velocity y of 12 mls at an angle of 35· below the horizontal just before making contact with a bat. The ball leaves the bat 2.0 ms later with a venial velocity of magnitude 10 mls as shown in . What is the magnitude of the average force of the bat on the ball during the ball- bat contact?

l1P. The magnitude of an unbalanced force on a 10 kg object increases at a constant rate from zero to 50 N in 4.0 s. causing the initially stationary object to move. What is the object’s speed at the end of the 4.0 s?

12P. During a violent thunderstorm, hail of diameter 1.0 cm falls directly downward at a speed of 25 m/s. There are estimated cubic meter of air. (a) What is the mass of each ·hailstone (density = 0.92 g/cm-‘)? (b) Assuming that the hail does not bounce, find the magnitude of the average force on a flat roof ‘measuring 10 m x 20 m due to the impact of the hail. (Hint: During impact, the force on a hailstone from the roof is approximately equal to the net force on the hailstone, because the gravitational force on it is small.).

13P. A pellet gun fires ten 2.0 g pellets per second with a speed of 500 m/s. The pellets are stopped by a rigid wall. What are (a) the momentum of each pellet. (b) the kinetic energy of each pellet. and (c) the magnitude of the average force on the wall from the stream

of pellets? (d) If each pellet is in contact with the wall for 0.6 ms, what is the magnitude of the average force on the wall from each pellet during contact? (e) Why is this average force so different from the average force calculated in (c)?

14P. Shows an approximate plot of force magnitude versus time during the collision of a 58 g Super ball with a wall. The initial velocity of the ball is 34 mls perpendicular to the wall; it rebounds directly back with approximately the same speed, also perpendicular to the wall. What is max, the maximum magnitude of the force on the ball from the wall during the collision?

15E. A bullet of mass 4.5 g is fired horizontally into a 2.4 kg wooden block at rest on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet stops in the block, which slides straight ahead for 1.8 m (without rotation).

(a) What is the speed of the block immediately after the bullet stops relative to it? (b) At what speed is the bullet fired?

16P. Two cars A and B slide on an icy road as they attempt to stop at a traffic light. The mass of A is 1100 kg, and the mass of B is 1400 kg. The coefficient of kinetic friction between the locked wheels of either car and the road is 0.13. Car A succeeds in stopping

at the light, but car B cannot stop and rear-ends car A. After the collision.

17P. Bullet is fired horizontally at two blocks at rest on a friction less tabletop. The bullet passes through the first block.

18P. A box is put on a scale that is marked in units of mass and adjusted to read zero when the box is empty. A stream of marbles is then poured into the box from a height h above its bottom at a rate of R (marbles per second).

18P. A 5.0 kg block with a speed of 3.0 m/s collides with a 10 kg block that has a speed of 2.0 m/s in the same direction. After the collision.

19P. A railroad freight car of mass 3.1!! x )O’ kg collides with a stationary caboose car.

20P. A 10 g bullet moving directly upward at 1000 m/s strikes and passes through the center of mass.

21P. In fig. 10-34. a ball of mass m is shot with speed I’j into the barrel of a spring gun of mass M initially at rest on a friction less surface. The ball sticks in the barrel at the point of maximum compression.

22P. A 4.0 kg physics book and a 6.0 kg calculus book. connected by a spring are stationary on a horizontal friction less surface. The spring constant is 8000 N/m.

23P. A block of mass ml = 2.0 kg slides along a friction less table with a speed of 10 m/s. Directly in front of it. and moving.

24P. A 1.0 kg block at rest on a horizontal friction less surface is connected to an outstretched spring (k = 200 N/m) whose other end is fixed.

25E. The blocks slide without friction. (a) What is the velocity of the 1.6 kg block after the collision? (b) Is the collision elastic?

26E. An electron undergoes a one-dimensional elastic collision with an initially stationary hydrogen atom. What percentage of the electron’s initial kinetic energy.

27E. A cart with mass 340 g moving on a friction less linear air track at an initial speed of 1.2 m/s undergoes an elastic collision.

28E. Spacecraft Voyager 2 (of mass m and speed v relative to the Sun approaches the planet Jupiter (of mass M and speed VJ relative to the Sun).

29E. An alpha particle (mass 4 u) experiences an elastic head-on collision with a gold nucleus (mass 197 u) that is originally at rest.

30P. A steel ball of mass 0.500 kg is fastened to a cord that is 70.0 cm long and fixed at the far end.