Question

The two springs shown in the figure below are 10.0 cm long when uncompressed (as in the figure on the left). The spring constant of the spring on the left is 5.29 N/cm. The spring constant of the spring on the right is 15.89 N/cm. The springs are then compressed and an 8.00 cm long block is inserted between them.

How much potential energy is stored in the springs in the new position?
1.21 J
1.27 J
1.25 J
1.23 J

Answer 1

The subject in question is physics, focusing on Hooke's Law and how to calculate the force needed to either compress or expand a spring based on its spring constant and the distance of compression or expansion.

Step-by-step explanation:

The question is related to physics, specifically the topic of Hooke's Law and spring constants. Hooke's Law states that the force required to compress or extend a spring by some distance is directly proportional to that distance. The formula to calculate this force is F = kx, where F is the force in Newtons, k is the spring constant in Newtons per meter (N/m), and x is the displacement of the spring from its equilibrium position in meters.

1. To find the force required to compress a spring with a constant of 80 N/m by 5 cm (or 0.05 m), we use the formula F = (80 N/m)(0.05 m) which equals 4 N.
2. Similarly, to determine the force to expand the same spring by 15 cm (or 0.15 m), we apply F = (80 N/m)(0.15 m) to get 12 N.

These example calculations demonstrate the direct relationship between force, spring constant, and displacement as per Hooke's Law in physics.