Question

Assume that the system has zero gravitational potential energy at the lowest point of the motion. Derive an expression for the total mechanical energy, Eequilibrium, of the system as the monkey passes through the equilibrium position in terms of m, x, d, g, k, and the speed of the monkey,Ve

Answer 1

Answer:

See explanation

Explanation:

From what I can see in the question, there is a monkey of mass m suspened at the end of a spring which constant is k and this monkey has moved a distance d.

The mechanical energy for the situation will be composed of elastic potential energy from the spring, kinetic energy from the monkey and potential gravitational energy from the monkey as well.

$E = K_{monkey} + U_{monkey} + U_{spring}\\E= \frac{mv_{e}^2}{2} + mgd + \frac{kx^2}{2}$

where m is the monkey's mass, $v_{e}$ is the speed of the monkey, d is the distance that the monkey has moved, k is the spring constant and x is the distance that the spring has stretched