1. Ramp-n-Roll uDu Basic Idea: Back when you were a mere freshman, you figured out how fast a ball would be moving at the bottom of a hill. But that was based on a cruel lie: namely, that all the potential energy was turned into what we now call translational kinetic energy. That’s just not so. Instead, kinetic energy is partitioned between translational AND rotational parts. It takes energy to roll, so less is available to move forward. So, the rolling ball moves forward more slowly. So, it takes longer to roll to the bottom of a hill than to slide there. ?

2. Ramp-n-Roll uDu Derivation: Let’s enjoy some quality knitting by deriving formulas for the travel times … ? Set U top equal to the translational K bottom Solve the expression for the velocity at the bottom Use that velocity to calculate the time t it will take the ball to travel the length of the ramp L. Repeat the derivation, except include both translational and rotational kinetic energy at the bottom. Solve the new expression for the velocity at the bottom, and then find the time t it will take the ball to travel the length of the ramp L. h L

3. Ramp-n-Roll uDu Derivation: Here’s what I got... Experiment: The two expressions represent a pair of hypotheses. Now, construct a ramp out of a pair of metal rails and a couple of clamps, and measure the actual time as a function on height. Then, plot t 2 versus 1/h (you gotta figure out why) to reject one hypothesis or the other. The slope of your plot is your key to hypothesis happiness. You know enough to use at least 5 heights and some number of repetitions at each height. Think about how you might make the timing as precise as possible, too.

4. Ramp-n-Roll uDu Describe your methods here:

5. Ramp-n-Roll uDu Record your data here:

6. 0246810 1/Height (m -1 ) 10 9 8 7 6 5 4 3 2 1 0 Time 2 (sec 2 ) Show your slope calculations here:

7. Ramp-n-Roll uDu Write a summary and conclusion here: