Answer:
When two springs are compressed by the same amount, the spring with a higher spring constant will have more potential energy. The potential energy stored in a spring is given by the equation:
U = (1/2)kx^2
where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
If we compress two springs by the same amount, x, then the potential energy stored in each spring will be:
U1 = (1/2)k1x^2
U2 = (1/2)k2x^2
where k1 and k2 are the spring constants of the first and second spring, respectively.
Since x is constant for both springs, we can compare U1 and U2 by comparing k1 and k2. The spring with a higher spring constant will have more potential energy because it requires more force to compress it by the same amount.
To justify this answer further, we can use Hooke's Law which states that the force required to compress or stretch a spring is proportional to its spring constant. Therefore, a spring with a higher spring constant will require more force to compress it by the same amount than a spring with a lower spring constant. This means that more work is done on the higher spring constant spring during compression, resulting in more potential energy being stored in it.