Question

A spring without a spring constant (k) of 199 N/m is initially compressed by a block at a distance (d) of 0.27 m. Which of the following statements is true regarding the potential energy stored in the compressed spring?

A. The potential energy is 199 J.

B. The potential energy is 0.27 J.

C. The potential energy is 1/2 * 199 * (0.27)² J.

D. The potential energy cannot be determined without more information.

Answer 1

The potential energy stored in the compressed spring with a spring constant of 199 N/m and a displacement of 0.27 m is calculated as 7.23615 J, using the formula U = 1/2 * k * x².

Step-by-step explanation:

The potential energy stored in a compressed spring is calculated using the formula U = 1/2 * k * x², where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, the spring constant (k) is 199 N/m and the displacement (d) is 0.27 m. Substituting these values into the formula gives us the potential energy stored in the compressed spring as U = 1/2 * 199 N/m * (0.27 m)² which yields approximately 7.23615 J.

To provide additional context, if we refer to similar examples, the potential energy can be calculated under various scenarios with different spring constants and displacements. Whether it's a block attached to a spring on a frictionless surface or masses connected by a spring undergoing compression, the method for calculating potential energy remains consistent.