Block on Spring without Friction

AI Thread Summary
A spring is stretched 40 cm with a 12 kg block on a frictionless surface, requiring a 25 N force to hold it in place. The spring constant can be determined using the relationship between the force and the displacement, as the force equals the restoring force when the spring is stationary. To find the block's speed when the spring returns to its unstretched length, the Work Energy Theorem is applied, utilizing the kinetic energy and elastic potential energy formulas. The same approach is used to calculate the speed when the spring is halfway (20 cm) back to its relaxed state. Understanding the spring constant is crucial for solving both parts of the problem effectively.
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A spring is stretched a distance of Dx = 40 cm beyond its relaxed length. Attached to the end of the spring is an block of mass m = 12 kg, which rests on a horizontal frictionless surface. A force of magnitude 25 N is required to hold the block at this position. The force is then removed.

a) When the spring again returns to its unstretched length, what is the speed of the attached object?

b) When the spring has returned only halfway (20 cm), what is the speed of the attached object?


Relevant equations:
Work Energy Theorem, KE(final) - KE(initial) = W(spring)
Kinetic Energy, (1/2)mv^2
Elastic Potential Energy for spring, (1/2)kx^2

I know i need to use the Work Energy theorem to find the velocity for part a and b, but how do i find the work done by the spring if i don't know the spring constant? Thats where i got stuck.
 
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You can determine the spring constant by what's given to you in the problem. The restoring force of the spring will be -kx. The force given to you in the problem must equal the restoring force because the spring is being held in place and is not moving.

Does that help?
 
That helps out a lot. It makes sense too. Now the rest of the problem is easy i just needed to know that. Thanks!
 
No problem
 

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