The figure below shows the potential energy for an object moving in response to

Question

The figure below shows the potential energy for an object moving in response to conservative forces from a number of other objects that can be treated as fixed, so we can pretend this is the PE of a single object. Never mind the units of either position or PE for now. We can think of this as about a skateboarder rolling back and forth on a curved track.

A. Suppose the skateboarder starts with 0 kinetic energy at the point ?5 and starts to roll. Describe the motion she will go through assuming that whatever resistive forces are acting can be neglected. Describe one full cycle of the motion.

B. The PE curve is shown as going to negative values. Is this a problem? Explain.

C. 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

as total energy remains constant , if PE decreases, then KE increases and vice versa.
hence as she moves from point -5, her PE starts decreasing

hence her KE will start increasing.

after reaching the maxiumum negative PE at -3, her PE starts rising

hence her KE will start decreasing.

B.as PE is relative value and defined relative to a particular point, there is absolutely no

issue with having PE as negative.

C. if she starts t x=4, after that her PE starts increasing
hence her KE goes on decreasing

and as KE=0.5*mass*speed^2,

once KE becomes 0, she will come to rest.
(temporary rest ofcourse, the driving force will make the rollerskater move in oppposite direction)

D.as PE is relative value, it can take negative values.

if PE max> KE max in absolute value,

then total energy=PE+KE will be negative.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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