Elastic potential energy - different methods, different results

• Iamconfused123
Iamconfused123
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.

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.

PeroK and Iamconfused123
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.

• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
15
Views
374
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
22
Views
588
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
588
• Introductory Physics Homework Help
Replies
4
Views
944
• Introductory Physics Homework Help
Replies
6
Views
445
• Introductory Physics Homework Help
Replies
55
Views
3K
• Introductory Physics Homework Help
Replies
44
Views
3K