Exam Krackers 1001 physics 256

[riceguard]

Okay so this is really driving me crazy, problem states:
What is the spring constant k for the spring shown below? The picture shows a spring being compressed on each side by 5cm with 50N of force
a. 0 N/cm
b. 5 N/cm
c. 10N/cm
d. 20N/cm

Answer B

They're reasoning was to add the 5cm and divide the force by the new length, i.e. 50/10= 5.

But what I'm stuck on is there are two forces each acting on one side of the spring, so if they add the distance together should the force be added together i.e. 100/10 = 10 or each side would be 50/5, what am i missing here?

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[NextStepTutor_1]

Without the actual diagram it is hard to alleviate your concern. But, let's say the spring is on the ground - if you put a force on one end of the spring, the spring will theoretically compress at both ends. If that's the situation here, then there is still just one force (you pushing down on the spring, 50N) that is responsible for the compression of the spring. There is a force (normal force) that is pushing back, but this only ensures that the spring is in equilibrium (not accelerating into the ground).

Using the equation F = -kx we must add the total compression (x) and divide 50 by 10.
What the force in this equation is actually stating is the force that the spring can exert after being compressed by a certain distance. The total distance is 10, the force the it can exert is the same as the force that is exerted on the spring itself (50N).
If you decided to take into consideration both forces acting on the spring then they would actually subtract from each other because they are in opposite directions. However, we're not looking for the net force, we're looking for the force that allows the spring to compress.