Lesson 5
Conservation

1) Let's consider all this work, potential energy, and kinetic energy stuff. Suppose you toss a ball of mass m vertically into the air. Your hand releases it at the elevation marked "1" in the figure, and the ball moves upward. Ignore air resistance. How much work does gravity do as the ball moves from position 1 to position 2? What is an expression for the change in the potential energy DU of the ball (DU is U₂ - U₁)? How is the work done by gravity on the ball related to this change in potential energy? Is the change in kinetic energy of the ball related to any of these quantities? (If so, how?)

2) An observant friend of yours was at a park over the weekend and noticed children playing on one of those playground rotating platforms that can get going pretty quickly if the kids on-board are big and strong enough. Initially, there were three children on the platform, and they were going around about once every 11 seconds. A fourth child took a leap onto the platform while it was spinning, and then they were going around about once every 15 seconds. Your friend wonders about how heavy the platform is. What do you say?

3) Which of the following do you think is the most correct or best statement?

1. Linear momentum, angular momentum, and energy are quantitites that must be conserved.
2. The laws of conservation of momentum, conservation of angular momentum, and conservation of energy should really be called postulates rather than laws.
3. If Newton's Laws are valid, then linear momentum, angular momentum, and energy are conserved.
4. The conservation laws are really just consequences of the scheme that physicists set up to describe how the physical world behaves, and are not really laws at all.

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

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