Question

Please answer all, Thank you.

1. A firework is designed so that when it is fired directly upwards, it explodes and splits into three equal-massed parts at its peak. Someone launches the firework directly upwards and measures the locations of two of the pieces of the firework. They find that one piece landed 2 meters to the left and another piece landed two meters in front of them. Where did the third piece of land?

2. A Newton's cradle is composed of row metal balls, each hung from a string attached to a horizontal rod. So, that when they are at rest, they are nearly touching each other and form a neat line. Explain and prove mathematically why releasing n balls causes the same number of balls on the other side of the cradle to be ejected?

3. Explain the correspondence that lets us easily translate between linear motion and rotational motion. What are the linear analogues of the rotational quantities we have discussed in lecture i.e. angle, angular velocity, angular acceleration and moment of inertia? Where does the correspondence seem to fail?

4. Explain, in words, how we know that a freely spinning asteroid in space is rotating about an axis that passes through its center of mass?

5. You are handed a rod that is three times as dense on one end as it is on the other end. Find the moment of inertia when the axis of rotation is about the heavy end, and find the moment of inertia when the axis of rotation is about the light end.

6. Suppose we have two blocks of masses m1 and m2. The block with mass m1 is moving towards block m2 at speed v. After the collision, we measure the total kinetic energy and find that the total kinetic energy after the collision is m2/(m1+m2) less than the kinetic energy before the collision. Find the final speeds of the two blocks. What type of collision is this?

7. A merry-go-round starts at rest, and begins accelerating clockwise at 0.1 radians per second per second.

a. How long will it take to reach its maximum angular velocity of 5 revolutions per minute?

b. How many times will the merry-go-round have completed a revolution before it reaches its maximum angular velocity? If it's not a whole number of revolutions, include the amount of partial revolutions.

Answer 1