Periodic Motion Question

[SaintJude]

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This is so embarrassing...I got this same question wrong 2x...so I'm gonna introduce it to the forum so this NEVER happens to me again.

When a spring is compressed to its minimum length and NOT permitted to expand:

A. potential energy is at its max and kinetic energy at its min
B. kinetic energy is at its max and potential energy is at its min (Thanks milski for the Edit!)
C. the sum of potential energy and kinetic energy is zero
D. potential energy and kinetic energy are at their minimum.

Highlight here for answer :A

2 Q:
1. Does the fact that it's not permitted to expand have any special consequence?
2. Also, is there any spring-mass scenario where C could hold true? If the spring was at an equilibrium without any external forces, would the total energy equal 0 then?

 

[chiddler]

Regarding C, i don't think so. when is it possible for potential energy of a spring to be negative?

 

[milski]

What is the difference between A and B? Either I can't read today or you made a typo. 😉

A. Not for the energy. It just means that there will be no movement and no change in these energies.

B. It will have to be at equilibrium and not moving. Not having external forces is not enough - you can have an internal for the system force (like the force from the spring) moving it through the equilibrium point and in that case the sum will not be zero.

 

[milski]

Regarding C, i don't think so. when is it possible for potential energy of a spring to be negative?

PE=KE=0 for a spring at rest in equilibrium position.

 

[chiddler]

PE=KE=0 for a spring at rest in equilibrium position.

👍

 

[SaintJude]

Ah, yes at equilibrium this is definitely true. But another Kaplan question suggests that there is yet another point that this could happen!

The question states:

How far way from equilibrium will the kinetic energy be equal to the potential energy of a spring that that has a spring constant k=0.1 N/m, a speed of 3m/s and a 0.4 kg mass attached?

Hint: The answer is not 0m. So this suggests that there must be a moment when PE can equal KE at a point other than the equilibrium. Right?

 

[chiddler]

Ah, yes at equilibrium this is definitely true. But another Kaplan question suggests that there is yet another point that this could happen!

The question states:

How far way from equilibrium will the kinetic energy be equal to the potential energy of a spring that that has a spring constant k=0.1 N/m, a speed of 3m/s and a 0.4 kg mass attached?

Hint: The answer is not 0m. So this suggests that there must be a moment when PE can equal KE at a point other than the equilibrium. Right?

yes there must be. here you can solve it just by solving for x in kx^2 = mv^2.

but this is just when they're equal. their sum is not 0.

oh but if you're looking at milski's conditions, then you're right.

 

[milski]

Careful with the equilibrium point. In general PE != KE there. The PE=KE=0 being the only exception and considering that that implies no motion, that's not a very interesting case.

In all other non-trivial cases you'll get two symmetric points where PE=KE.

 

[milski]

The green is potential energy, the magenta - kinetic, x-axis is displacement.
For PE=KE=0 the whole graph is collapsed to a single point at (0,0).