John is using a pulley to lift the sail on his sailboat. The sail weighs 150 N, and he must lift it 4.0 m.

A. How much work must be done on the sail?
B. If the pulley is 50% efficient, how much work must John do on the rope to lift the sail?

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To calculate the work done in lifting the sail, we can use the formula:

Work = Force × Distance × cos(θ)

where:
- Work is the amount of work done (in Joules),
- Force is the applied force (in Newtons),
- Distance is the distance over which the force is applied (in meters),
- θ is the angle between the applied force and the direction of motion (in degrees).

A. How much work must be done on the sail?
In this case, the force used to lift the sail is equal to its weight, which is 150 N. The distance over which the force is applied is 4.0 m. And since the force is acting in the same direction as the motion, the angle θ is 0°. Therefore, we can calculate the work as follows:

Work = 150 N × 4.0 m × cos(0°)

The cosine of 0° is 1, so the equation simplifies to:

Work = 150 N × 4.0 m × 1

Work = 600 Joules

So, the amount of work that must be done on the sail is 600 Joules.

B. If the pulley is 50% efficient, how much work must John do on the rope to lift the sail?
To calculate the work that John must do on the rope, we need to consider the efficiency of the pulley system. Efficiency is defined as the ratio of the useful work done to the total work done.

Efficiency = Useful Work / Total Work

In this case, the useful work done is the work done on the sail, which we calculated to be 600 Joules. The total work done is the work done on the rope.

To find the total work done, we can use the formula:

Total Work = Useful Work / Efficiency

Since the pulley is 50% efficient, the efficiency is 0.5. Plugging in the values, we get:

Total Work = 600 Joules / 0.5

Total Work = 1200 Joules

Therefore, John must do 1200 Joules of work on the rope to lift the sail.