Solving Hooke's Law Problem: Find Position of Block

[Amy Marie]

A block attached to a spring (which is attached to a wall) lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 3.0 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. When that stopping point is reached, what is the position of the block?

I tried using Hooke's Law:

3.0 = 50x

x = 3.0/50

x = 0.06 m

However, when I checked my answer, it said x = 0.12 m.

Does anyone know what I did wrong? Thank you!

 

[Doc Al]

Hooke's law tells you what force the spring exerts for any given extension. You found the extension that gives a restoring force equal to the applied force. But that just means the net force is zero at that point, not that it stops.

Hint: Think work and energy, not force.

 

[nil1996]

The work done by the force=the potential energy of the block.

 

[Amy Marie]

Thank you for your help!

 

[Nickie]

Your calculation is correct. However, the problem description may be misleading. It states that the block is pulled until it stops, but does not specify whether the block stops due to the applied force or due to the spring reaching its maximum extension. If the block stops due to the applied force, then your answer is correct. However, if the block stops due to the spring reaching its maximum extension, then the position of the block would be twice the value you calculated, i.e. x = 0.12 m. It would be helpful to clarify this in the problem statement.