We can think of this as about a skateboarder rolling back and forth on a curved

Question

We can think of this as about a skateboarder rolling back and forth on a curved track. Now assume that she starts instead at the point x = 4 at the point where the black line intersects the red PE curve (at PE = ?5). Now describe one cycle of her motion.

D. The solid black line is supposed to represent her total mechanical energy—kinetic plus potential. This is negative. Is this a problem? Explain.

E. The black line only is shown on the right suggesting that she can't get to the left side given the energy she has. Is this correct? Explain your reasoning.

F. Now assume that she is as in part C, oscillating back and forth between the points 1.5 and 4 when suddenly, she is flipped to the point ?1 by some bit of magical hand-waving—without changing her total mechanical energy. Describe her motion. Will she be going faster or slower than she was on the right?

(This kind of "magical hand-waving" transition is actually possible on the atomic scale, thanks to the laws of quantum physics.)

Explanation / Answer

C)
Now she will start at x = +4 with 0 KE (at rest) and negative PE -- so negative total mechanical energy. She will start to roll to the left, increasing speed as the PE drops and her KE rises. This continues until she reaches x = +3 units. Then she begins to slow as the PE rises and the KE falls. This continues until about x = 1.5 units when the total energy equals the PE again so the KE must be 0 and she must be at rest. There is, however, an unbalanced force on her pushing her back, so she will run through the entire process in reverse until she comes back to her starting point. She'll never get to the left of the well.

D). The solid black line is supposed to represent her total mechanical energy -- kinetic plus potential. This is negative. Is this a problem? Explain.
Nope. It just means we have chosen the 0 of the PE so that it is negative at the bottom of the well. We could have chosen it 0 at the bottom -- or not. The absolute value of the PE is not meaningful unless we have some good reason for where we want to choose our 0. In this case it could be anywhere. Since only changes in PE matter -- and the difference between the PE and the total -- the absolute value and whether it is + or - has no physical consequence

E). The black line only is shown on the right suggesting that she can't get to the left side given the energy she has. Is this correct? Explain your reasoning.
Yes. She won't have enough energy to get to the other side of the well. Her KE will go to 0 before she gets to the peak.

F). Now assume that she is as in part C, oscillating back and forth between the points 1.5 and 4 when suddenly, she is flipped to the point -1 by some bit of magical hand-waving -- without changing her total mechanical energy.
The question is a bit sloppily worded since on the right she goes from 0 to a maximum speed, and when she is on the left she goes from 0 to a maximum speed, but since the KE is the difference between the total energy (solid black line) and the PE (red curve) for most of the motion on the left she will be going faster than she ever did on the right.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.