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:
[tex]F=-kx[/tex]
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
[tex]x=-\frac{F}{k}[/tex]
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
[tex]U=\frac{1}{2}kx^2[/tex]
We can rewrite the displacement x using the equations above
[tex]x=-\frac{F}{k}[/tex]
So, the elastic potential energy becomes
[tex]U=\frac{1}{2}k(\frac{F}{k})^2=\frac{1}{2}\frac{F^2}{k}[/tex]
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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