How much does a spring compress with 100 N force?

[brake4country]

Homework Statement

A man compresses a 30 cm spring against a wall. If he applies a 100 N force and the wall is rigid, by how much does he shorten the spring? (k = 1000 N/m).

Homework Equations

F_s=-kx

The Attempt at a Solution

Drew a FBD and labeled applied force of 100 N and calculated the force of the spring resisting the applied force = 30N. At this point, I do not know where to go with this problem.

 

[haruspex]

If the force applied is 100N, how can it be that the reaction from the spring is only 30N?

 

[brake4country]

Ok. I think I figured this out I just need my work checked please. So the formula is F = -kx. So 100 = 1000(30-x) and x = 30 cm. How does this look?

 

[haruspex]

F = -kx. So 100 = 1000(30-x) and x = 30 cm.

I don't think you mean x=30. Also, be careful with units. Put all distances in metres.

 

[brake4country]

Can I use 100 N for the F in F = -kx?

 

[haruspex]

Can I use 100 N for the F in F = -kx?

Yes.

 

[brake4country]

If I put everything in meters, I get 40 cm. Here is my calculation:

F = -kx
-100 = -1000(x-0.3)
x = .4 m or x = 40 cm.

Did I set up the math correctly? I am not sure whether it should be x-0.3 or 0.3--x

 

[haruspex]

If I put everything in meters, I get 40 cm. Here is my calculation:

F = -kx
-100 = -1000(x-0.3)
x = .4 m or x = 40 cm.

Did I set up the math correctly? I am not sure whether it should be x-0.3 or 0.3--x

In the equation F = -kx, what does x represent?

 

[brake4country]

Ok, my mistake. It should be -100 = -1000(.3x) = 33 cm. If this is correct then I understand.

 

[haruspex]

Ok, my mistake. It should be -100 = -1000(.3x) = 33 cm. If this is correct then I understand.

No. Please answer my question regarding what x represents in that equation.

 

[brake4country]

X is the change (displacement) from its resting position.

 

[haruspex]

X is the change (displacement) from its resting position.

Right. You are told F and k. Calculate x.