Calculate the Mechanical Advantage of a Pulley System

What is the mechanical advantage of the pulley system?

A farmer uses a pulley system to raise a 225 N bale 16.5 m. A 129 N force is applied by pulling the rope 33.0 m. What is the mechanical advantage of the pulley system?

Answer:

The mechanical advantage of the pulley system is 2, meaning that the output force is twice the input force.

The mechanical advantage of the pulley system can be calculated by dividing the output force (225 N) by the input force (129 N). However, since the input force is applied over a distance (33.0 m), while the output force is applied over a different distance (16.5 m), we also need to take into account the effect of the pulley system on distance.

Since the force and distance are both perpendicular to the direction of motion, we can assume that the work done is the same on both sides of the pulley system. Therefore, the work done by the input force (W1) is equal to the work done by the output force (W2), and we can set up the following equation:

W1 = F1 x d1 = F2 x d2 = W2

where F1 is the input force (129 N), d1 is the distance over which it is applied (33.0 m), F2 is the output force (225 N), and d2 is the distance over which it is applied (16.5 m).

Solving for the output force, we get:

F2 = F1 x d1 / d2 = 129 N x 33.0 m / 16.5 m = 258 N

Now we can calculate the mechanical advantage:

MA = F2 / F1 = 258 N / 129 N = 2

Therefore, the mechanical advantage of the pulley system is 2, meaning that the output force is twice the input force.