Question

A weight of 719 N is raised by a two-pulley arrangement as shown. How much work is done by the agent (force f) to raise the weight by a vertical distance of 19 m? Assume the pulleys are weightless, the rope does not stretch, and the system moves at a constant speed, which is slow enough that the kinetic energy is negligible. Answer in units of J. What is the change in potential energy?

Answer 1

The work done by the agent to raise the weight by 19 m is 6830.5 J. The change in potential energy is also 6830.5 J.

Step-by-step explanation:

To calculate the work done by the agent (force f) to raise the weight, we need to determine the force applied and the distance over which it is applied.

In this case, the force applied is the tension in the rope, which is equal to half the weight of the weight being lifted (since it is a 2-pulley system).

So the force is 719 N / 2 = 359.5 N. The distance over which the force is applied is the vertical distance the weight is raised, which is given as 19 m.

The work done is calculated using the formula:

Work = Force × Distance × cos(θ)

In this case, θ = 0 degrees since the force and displacement are in the same direction.

Therefore, the work done by the agent is:

Work = 359.5 N × 19 m × cos(0°) = 6830.5 J

The change in potential energy is equal to the work done by the agent. So the change in potential energy is 6830.5 J.