Assignment:
1) If you drop both a large and a small ball with the large ball beneath the small, then the small ball can bounce higher into the air than if it was to bounce off the floor directly. If you have a large and small ball handy you could try it! Assume the mass of the large ball is 0.1 kg and the mass of the small ball is 0.01 kg. The radius of the large ball is 30 cm and the radius of the small ball is 10 cm. The balls are initially in contact, with the large ball at a height of 1 m (center of the ball). If the balls are released and fall under gravity to the floor, how high will the small ball bounce up in the air? Assume all collisions to be elastic.
i. How far do the balls initially fall? How fast are they traveling when the large ball hits the ground?
ii. The large ball can be assumed to hit the floor first and rebound back up. At this point, the large ball is traveling up and the small ball is traveling down. Both have the same magnitude of velocity found in i, however, as the collision was "elastic". Use conservation of momentum in an elastic collision to find the new velocities of the large and small balls after they collide.
iii. Now the small ball is traveling back up. Given its velocity, how high will it reach?
2) To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 600 g falcon flying at 20 m/s hit a 1.5 kg raven flying at 9 m/s. The falcon hit the raven at right angles to its original path and bounced back at 5 m/s. (These figures are from a research paper and estimated by the author as he watched this attack occur in New Mexico). Find the change in angle of the ravens motion and its final velocity after the collision. Was energy conserved in the collision?
This is a simple case of momentum before the collision equals momentum after the collision.
i. Write an equation for the momentum in the direction of the raven as he flies towards the collision. Put the momentum before the collision equal to the momentum after the collision in this direction.
ii. Do the same analysis for the direction that the falcon was originally flying.
iii. You should have two equations which yield the ravens velocity in both directions after the collision. Use this to find the magnitude and direction.
iv. Was energy conserved? Calculate the energy before collision, knowing the falcon and ravens initial velocities and masses. Calculate the energy after the collision, knowing the falcon and ravens velocities after the collision.
3) A wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 12 rad/s in 3 s. Find the magnitude of the angular acceleration of the wheel and the angle in radians through which it rotates in this time. Use the linear equations of motion but for angular motion and this should be easy.
4) A 50 kg woman stands on a bathroom scale while riding in an elevator descending with decreasing speed (magnitude of acceleration is 2 ms-2). Draw a free body diagram for the woman. What is thereading on the scale?
If you get the free body diagram correct then this is an easy problem. Think about how you feel on an elevator, or better still go and ride the elevator. Does your answer make sense?
5) A fire hose has an opening whose radius is 10 cm. The hose discharges water at a velocity of 20 ms-1. How much force is required by the fireman to hold the nozzle stationary? A fire hose ejects a stream of water with a speed of 20 m s-1, as above. At what angle to the horizontal should the fire hose be directed if it is to remove the civil liberties of protesters 20 m from where the hose is being held?
i. There are two parts to this problem. In the first part you have to calculate the force required to hold the fire hose. To do this go back to the definition of force. Its not necessarily , because this assumes the mass is constant. Here its the opposite the velocity of the water is constant, and acceleration is zero, but the mass changes as more and more water is being ejected. Go back to the definition of force from the momentum section in the notes.
ii. The second part is simply a range equation plug and chug problem.
6) A 20 kg monkey has firm hold on a light rope that passes over a frictionless pulley and is attached to a 20 kg bunch of bananas. The monkey looks up, sees the bananas, and starts to climb the rope to get them.
As the monkey climbs do the bananas move up, down or remain at rest? Explain.
As the monkey climbs, does the distance between the monkey and the bananas increase, decrease, or remain the same? Explain.
The monkey releases her hold on the rope. What happens to the distance between the monkey and the bananas while she is falling?
Before reaching the ground, the monkey grabs the rope to stop her fall. What do the bananas do?