Physics 2014 JAMB Past Questions - Question 15: A wheel and axle is used to raise a load whose weight is 800N when an effort of 250N is applied.If the radii of the wheel and axle are 800mm and 200mm respectively ,the efficiency of the machine is

Correct Answer

A

Explanation

To calculate the efficiency of the wheel and axle machine, we can use the formula:

Efficiency = (Output work / Input work) * 100

The output work is the work done on the load, and the input work is the work done by the effort applied.

The output work can be calculated as the product of the load weight and the distance it is raised:

Output work = Load weight * Distance raised

The input work can be calculated as the product of the effort applied and the distance it moves:

Input work = Effort applied * Distance moved

In this case, the load weight is 800N, the effort applied is 250N, and the distances raised and moved are related by the ratio of the radii of the wheel and axle:

Distance raised / Distance moved = Radius of wheel / Radius of axle

Plugging in the given values:

Distance raised / Distance moved = 800mm / 200mm = 4

Now we can calculate the output work and input work:

Output work = 800N * Distance raised
Input work = 250N * Distance moved

Since Distance raised = 4 * Distance moved, we can substitute this into the equations:

Output work = 800N * 4 * Distance moved
Input work = 250N * Distance moved

Now we can calculate the efficiency:

Efficiency = (Output work / Input work) * 100
          = (800N * 4 * Distance moved) / (250N * Distance moved) * 100
          = (3200N * Distance moved) / (250N * Distance moved) * 100
          = (3200N / 250N) * 100
          = 12.8 * 100
          = 1280%

Therefore, the efficiency of the wheel and axle machine is 1280%.