Spring Question

[mspeedwagon]

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A block is resting on a spring, which is sitting on a table. What would change in if this spring were replaced by a stiffer string?

I'm assuming this question is asking for some application of Hooke's law. I would think that the FBD of the spring and block consist of a Fspring vector pointing up and a Fgravity pointing down. If you put in a stiffer string you'd still have the same FBD. But, I know the stiffer spring has a different spring constant. What changes? Help.

 

[maybemed2013]

I believe a stiffer string would have a larger constant in the equation F=-kx. If you have a stiffer string it takes more force to move it.

 

[milski]

Correct about larger k in F=-kx

The new spring will be harder to compress - the equilibrium point where the block rests will be higher (with less displacement of the spring).

 

[MD Odyssey]

A more intuitive way to look at the problem would be to consider the meaning of the spring constant. The spring constant, given in Newtons per meter, is really telling you about the force required per unit distance of displacement. Another way to look at it is how many Newtons of force is required to compress the spring a meter. Stiffer springs require a greater force to compress the spring the same distance. Since the force due to gravity hasn't changed, the restoring force of the spring is going to be the same, but the necessary distance is less for a stiffer spring.