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# Working with the motion of rigid bodies

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1. During a violent thunderstorm, hail of diameter 1.0 cm falls directly downward at speed of 25m/s. There are estimated to be 120 hailstones per cubic meter of air. (a) what is the mass of each hailstone ( density = 0.92 g/cm^3) ? (b) Assuming that the hail does not bounce fine the magnitude of the average force on a flat roof measuring 10m x 20m 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.

2. Figure below shows an approximate plot of force magnitude versus time during the collision of a 58 g Superball with a wall. The initial velocity of the ball is 34 m/s perpendicular to the wall; it rebounds directly back with approximately the same speed, also perpendicular to the wall. What is F max , the maximum magnitude of the force on the ball from the wall during the collision ?

3. A 2500 kg unmanned space probe is moving in a straight line at a constant speed of 300 m/s. Control rockets on the space probe execute a burn in which a thrust of 3000 N acts for 65.0 s. (a) what is the change in the magnitude of the probes linear momentum if the thrust is backward , forward or directly sideways ? (b) what is the change in kinetic energy under the same three conditions ? assume that the mass of the ejected burn products is negligible compared to the mass of the space probe.

4. Two titanium spheres approach each other head on with the same speed and collide elastically. After the collision one of the spheres whose mass is 300 g remains at rest (a) What is the mass of the other sphere ? (b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 2.0 m/s ?

5. A billiard ball moving at a speed of 2.2 m/s strikes an identical stationary ball a glancing blow. After the collision one ball is found to be moving at a speed of 1.1 m/s in a direction making a 60 degree angle with the original line of motion. (a) Fine the velocity of the other ball. ( b) Can the collision be inelastic , given this data ?

6. An object of mass m undergoes a one-dimensional impulse vector J, with the speed changing from v to u without any change in the direction of travel. Show that the work is 1/2 J ( u + v )

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1. During a violent thunderstorm, hail of diameter 1.0 cm falls directly downward at speed of 25m/s. There are estimated to be 120 hailstones per cubic meter of air. (a) What is the mass of each hailstone (density = 0.92 g/cm^3)? (b) Assuming that the hail does not bounce, find the magnitude of the average force on a flat roof measuring 10m x 20m 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.

Mass/ Volume = Density

Hence mass = density * volume = 0.92 * volume

Assuming a spherical shape for each stone, v = (4/3) pi * r^3 = 4.19 cm^3
Mass = 0.92 * 4.19 = 3.85 g

Mass of 120 stones = 3.85 * 120 = 462 g = 0.462 kg (mass per cubic meter of air)

Area of the roof A = 200 m^2; on every meter square of area 0.462 kg of stone will fall. Hence the total mass of the stone falling on the roof of area 200 m^2 is m = 200 * 0.462 = 92.4 kg

We have average force = impulse/time = change in momentum/time = m (v1-v2)/t
Here the stone doesn't bounce, hence v2 = 0

Thus the average force F = 92.4 * 25/t = 2310 Newton/s

2. Figure below shows an approximate plot of force magnitude versus time during the collision of a 58 g Superball with a wall. The initial velocity of the ball is 34 m/s perpendicular to the wall; it rebounds directly back with ...

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