Hooke's Law / Spring Q

[amusedtodeath24]

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Hello all,

It might be easier to describe the problem then ask my Q -

A 50 N force is applied to both ends of a spring, compressing each end by 5 cm. The problem is asking for the spring constant.

When I did the problem, I thought it was k = 100 N / 10 cm = 10 N/cm.

The answer, however, is 5 N/cm which is obtained by k = 50 N / 10 cm.

Why is it that when you set up F = k * x, the x is 10 cm (total displacement) but the F is NOT 100N but rather 50N?

Thank you, as always.

 

[HawkeyePostOp]

Imagine you have a spring attached to a wall. If you apply 50 N of force to one end of the spring, 50 N of force is reacting at the other side. If you look at it from the point of view of the middle of the spring, it seems that 50 N is pushing on both sides, and each half is compressing by 5 cm.

When discussing compression, forces applied to a spring are assumed to be counteracted by another equal but opposite force (at least on the MCAT). You only count the magnitude of one uncoupled force.

 

[minhaj]

In questions that have to do with springs or massless ropes, remember that the spring or the rope only transfer the force.

Think of the question this way, if the spring was attached to a wall on one end and you compress it with a force of 50 N the wall pushes back with a force of 50 N (newtons third law). However, you dont say that the total force was 100N its only 50N. The spring only transferred the force from your hand to the wall and from the wall to your hand.

I hope thats not confusing

 

[amar21]

i dont think you will encounter a question like this on the mcat

its poorly worded to say that a 50N force is applied at both ends of the spring.. it can be interpreted in many different ways

i dont know if you can say that 50N force being applied one way is REACTED 50N the other way as a reaction force... because its not a reaction force, its a seperate external force that is being applied... (at least how the question states it...

the examples provided do make sense, but they are not the same scenario as teh question states. For example, if the spring was attached to a wall then there would only be 1 external force being applied to the end of the spring and the reaction force would be the wall... but that is not the case, there is no wall in this example

where did you get this from? im curious to know, because it has confused the hell out of me