1) The spring constant (k) and the displacement (x)
2) The displacement of the spring will increase
3) Direct relationship
Explanation:
1)
The restoring force in a spring is given by Hooke's law:
where
F is the force
k is the spring constant
x is the stretching/compression of the spring with respect to its natural length
The negative sign means that the direction of the restoring force is opposite to the direction of the stretching/compression.
From the equation, we see that the two factors affecting the force in the spring are:
- The spring constant, k
- The displacement of the spring, x
2)
We can solve this part by re-arranging the previous equation as
So we see that:
- The displacement of the spring is directly proportional the force applied
- The displacement of the spring is inversely proportional to the spring constant
In this problem, the force applied to the spring has been increased: therefore, since x is proportional to F, we can conclude that the displacement of the spring (stretching or compression) will increase as well.
3)
The elastic potential energy stored in a spring is given by
We can rewrite the displacement x using the equations above
So, the elastic potential energy becomes
Therefore, we see that the elastic potential energy is directly proportional to the square of the force applied. Therefore, the relationship between the two quantities is a direct relationship.
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