What effort is required to raise an 850 kg load with a simple wheel and axle having a wheel diameter of 3 m and an efficiency of 87%?

To determine the effort required to raise an 850 kg load using a simple wheel and axle, we must first calculate the weight of the load being lifted. The weight (force due to gravity) can be found using the formula:

Weight = mass × gravity

Weight = 850 kg × 9.81 m/s² ≈ 8,338.5 N

Next, we need to consider the efficiency of the wheel and axle system. The efficiency is given as 87%, which means that only 87% of the input work is converted to useful work for lifting the load.

To find the effort required, we can use the formula for a machine's efficiency:

Efficiency = (Output Force / Input Force) × 100%

Rearranging this gives:

Input Force = Output Force / (Efficiency / 100%)

In this scenario, the output force is the weight of the load (8,338.5 N), and the efficiency needs to be expressed as a decimal (0.87):

Input Force = 8,338.5 N / 0.87 ≈ 9,573.56 N

However, this value represents the total input force needed, and not the effective effort we must apply through the