Question

An archer pulls back the string on her bow to a distance of 70 cm from its equilibrium position. to hold the string at this position takes a force of 140 n. how much elastic potential energy is storied in the bow?

Answer 1

The amount of elastic potential energy stored in the bow is calculated using the spring formula E = 1/2 k x^2, where k is the spring constant and x is the displacement. First, the spring constant is deduced using the provided force and displacement, and then the energy is calculated.

Step-by-step explanation:

The question concerns the amount of elastic potential energy stored in a bow when an archer pulls back the string. This type of energy is associated with objects that can be stretched or compressed, like a bowstring. The elastic potential energy can be calculated using the formula for springs: E = 1/2 k x^2, where E is the elastic potential energy, k is the spring constant, and x is the displacement from equilibrium.

While we do not have the spring constant (k) given directly, we can deduce it from the provided force and displacement since the force exerted by a spring is also described by Hooke's Law: F = k x. Given the force (140 N) and displacement (70 cm or 0.7 m), we can find k. After that, we can plug k and x back into the elastic potential energy formula to find the energy stored in the bow.