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

AI Thread Summary
The discussion revolves around calculating the total potential energy of a 1.1 kg mass on a vertical spring, given its maximum speed of 3 m/s. The key point is that potential energy (PE) is zero at the midpoint of the mass's motion, while kinetic energy (KE) is maximized there. At the endpoints, all kinetic energy is converted to potential energy. The user initially miscalculated the energy but realized that PE equals KE, leading to the correct approach of using the formula KE = 1/2 mv^2 for calculations. Ultimately, the user gained clarity on the relationship between kinetic and potential energy in simple harmonic motion.
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[SOLVED] [101]Potential energy of mass on a spring with 2 givens

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.


Homework Equations



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

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 can't get any further.

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