A clever engineer designs a "sprong" that obeys the force law fx =−q(x−xe)3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. for simplicity, we'll let xe =0m. then fx =−qx3.

The objective of this question is to compute the units of q and calculate the expression for the P.E of the compressed spring

q = N/m³

Explanation:

Given that:

The equation for the force law is:

where;

e = equilibrium position of the end of the spring

i.e. = 0

q = is the spring constant

Also;

From above the units of q can be calculated by making q the subject of the formula :

where x is in meters and F is in Netwon;

Then :

q = N/m³

The Potential energy P.E of the compressed spring can be calculated by using the integral: