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[101]Potential energy of mass on a spring with 2 givens

[SOLVED] [101]Potential energy of mass on a spring with 2 givens

1. Homework Statement

A 1.1 kg mass vibrating up and down on the end of a vertical spring has a maximum speed of 3 m/s. What is the total potential energy of the mass on the spring when the mass is at either endpoint of its motion? NOTE: Assume that the potential energy of the mass on the vertical spring is zero when the mass is at the midpoint of its motion.


2. Homework Equations

ME=KE+PE?
PE(tot)=PE(g)+PE(e)?

3. The Attempt at a Solution

I am having a hard time figuring out how to attack this one... I have a graph of energy of a simple harmonic motion, which I understand. It makes sense to me that KE will be greatest and PE will be zero at its midpoint, and vice versa at the uppermost and lowermost part of its the motion. But without the spring constant or its length of travel, I cant get any further.

Can someone "light bulb" me?=P
Thank you so much for your help!
 

Answers and Replies

458
0
Well, the velocity is the fastest at the midpoint of the oscillation, where the potential energy is zero. When the velocity is zero, the spring is stretched at its maximum, the amplitude, so all of that kinetic energy that you had at the midpoint is now transferred into potential energy at the endpoints.
 
Thanks for the reply, I think I am getting warmer.

I figured the KE at the mid point would be the mass times its velocity (1.1kg * 3m/s = 3.3J), which much equal the PE. However, the 3.3J is incorrect...

and.. ah hah. I was trying to make things too difficult.
I should have just remembered PE=KE and KE=1/2mv^2

Thanks for the help!
 

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