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!