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Old Sep 19th 2013, 05:22 PM   #1
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Spring constant

A 500 g glider sliding on friction-less track with speed 0.2 m/s hits spring bumper a max distance 0.5 cm before rebounding. What's the spring constant?

So, I calculated the kinetic energy first: 0.5*0.5 kg*0.2 m/s= 0.05 J.
Then calculated potential energy: 0.5 kg*9.8 m/s^2*0.005 m = 0.0245 J.
Then subtract each other: 0.05 J-0.0245 J= 0.0255 J.
Then I set up 0.0255 J = 0.5 Ks (spring constant) * (0.005 m)^2 and I solved for Ks and it's 2040 J/m^2.

It turned out wrong, can anyone tell me what is wrong with my logic here?
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Old Sep 19th 2013, 06:01 PM   #2
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Originally Posted by maserati View Post
A 500 g glider sliding on friction-less track with speed 0.2 m/s hits spring bumper a max distance 0.5 cm before rebounding. What's the spring constant?

So, I calculated the kinetic energy first: 0.5*0.5 kg*0.2 m/s= 0.05 J.
Then calculated potential energy: 0.5 kg*9.8 m/s^2*0.005 m = 0.0245 J.
Then subtract each other: 0.05 J-0.0245 J= 0.0255 J.
Then I set up 0.0255 J = 0.5 Ks (spring constant) * (0.005 m)^2 and I solved for Ks and it's 2040 J/m^2.

It turned out wrong, can anyone tell me what is wrong with my logic here?
In your first line you have 0.5 * 0.5 * 0.2. It should be 0.5 * 0.5 * 0.5 * (0.2)^2

Also, the spring potential energy is (1/2) * k * x^2. It has nothing at all to do with g!!!

I'd approach this from the work-energy theorem directly. That is


The work done is work done by the spring on the glider, thus is (1/2)kx^2. The change in kinetic energy of the glider is (1/2)mv^2. Thus we have


Can you finish it from here?

-Dan
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Old Sep 19th 2013, 06:17 PM   #3
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Originally Posted by topsquark View Post
In your first line you have 0.5 * 0.5 * 0.2. It should be 0.5 * 0.5 * 0.5 * (0.2)^2

Also, the spring potential energy is (1/2) * k * x^2. It has nothing at all to do with g!!!

I'd approach this from the work-energy theorem directly. That is


The work done is work done by the spring on the glider, thus is (1/2)kx^2. The change in kinetic energy of the glider is (1/2)mv^2. Thus we have


Can you finish it from here?

-Dan

Thank you so much!! I see where I went wrong!
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