Elastic potential energy - different methods, different results

  • #1
Iamconfused123
66
9
Homework Statement
A car of mass 1000 kg hits the spring with a speed of 10 m/s and condenses it by 1 m. If we disregard the friction, what is the resistance constant of the spring?
Relevant Equations
##E_p=\frac{kx^{2}}{2}##, ##E_k=\frac{mv^2}{2}##
Can someone please tell me where I am wrong?
I tried to solve the problem using velocity equation; ##v_{f}^2= v_{i}^{2} + 2as## and got a= 50m/s^2, F= 50 000N and therefore F=kx -> k=50 000N/m because dx=1.

But it's not correct. When I do it using conservation of energy I get 100 000N/m. Which is correct according to the solutions.
##\frac{mv^2}{2}=\frac{kx^2}{2}## -> k=100 000N/m.

Thank you.
 
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  • #2
Iamconfused123 said:
Can someone please tell me where I am wrong?
Your first calculation is based on assumption of a constant acceleration / constant force. This assumption is incorrect.
 
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  • #3
Hill said:
Your first calculation is based on assumption of a constant acceleration / constant force. This assumption is incorrect.
Thank you very much. Just figured, Ep is proportional to the square of the elongation of the spring.
 

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