Objective
Your task is to design a device that is capable of separating a mixture. The mixture will be provided. The mixture is composed of the following:

• 6 toothpicks (round)
• 6 marbles (small)
• 6 paper clips (small)

Definition of Separation
Your mixture will be considered separated when there are 6 paper clips in one container, 6 marbles in another container, and 6 toothpicks in another container.

Required Energy Changes
You must have at least one mechanical energy change, one potential energy change, one kinetic energy change, and one thermal energy change. You may not count the same procedure as more than one energy change.

Grading
Thirty points of a daily grade are earned by having the four energy changes listed. Your device must have the four energy changes listed and complete the separation successfully to earn forty points of a daily grade. Additional energy changes are worth 5 additional points each, for a maximum of 10 points. A 5 point bonus is earned by having a separate energy change that is not one of the four types listed. There are five problems worth then points each for a total of 50 points of the daily grade.

You must point out your energy changes and state what type of change they are prior to pouring the mixture. This project will be done in lab groups of four.

Problems

1. A 280 kg piano slides 4.3 m down a 30° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. The coefficient of kinetic friction is 0.40. Calculate the force exerted by the man, the work done by the man on the piano, the work done by the frictional force, the work done by the force of gravity, and the net work done on the piano.
2. A spring has k = 88 N/m. Use a graph (or a graphing calculator) to determine the work needed to stretch if from x = 3.8 cm to x = 5.8 cm, where x is the displacement from its unstretched length.
3. A 75 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 5.0 m/s, upward. How fast is he going as he lands on the trampoline, 3.0 m below? If the trampoline behaves like a spring with spring constant of 5.2 x 10⁴ N/m, how far does he depress it?
4. A 17 kg child descends a slide 3.5 m high and reaches the bottom with a speed of 2.5 m/s. How much thermal energy due to friction was generated in this process?
5. An 8 kg stone rests on a vertical spring, compressing it 10 cm. What is the spring constant of the spring? The stone is now pushed down an additional 30 cm and the spring is released. How much potential energy is stored in the spring just before it is released? How high above this new (lowest) position will the stone rise? What will its speed be the instant it is released?