Physics 2007 JAMB Past Questions - Question 46: . A machine has a velocity ratio of 4. If it requires 800 N to overcome a load of 1600 N. what is the efficiency of the machine?

Correct Answer

C

Explanation

To find the efficiency of a machine, you can use the following formula:

Efficiency = (Useful work output / Total work input) x 100%

In this case, the useful work output is the work done on the load (1600 N) over a certain distance, and the total work input is the work done by the effort (800 N) over the same distance.

Efficiency = (Useful work output / Total work input) x 100%
Efficiency = [(Force applied on the load) x (Distance moved by the load)] / [(Force applied by the effort) x (Distance moved by the effort)] x 100%

Now, let's plug in the values:

Useful work output = (1600 N) x (distance)
Total work input = (800 N) x (distance)

Efficiency = [(1600 N) x (distance)] / [(800 N) x (distance)] x 100%

Now, the velocity ratio (VR) of the machine is 4, which means the machine multiplies the input force by 4. Therefore:

Efficiency = [(1600 N) x (distance)] / [(800 N x 4) x (distance)] x 100%

Simplify the equation:

Efficiency = (1600 / (800 x 4)) x 100%

Efficiency = (1600 / 3200) x 100%

Efficiency = 0.5 x 100%

Efficiency = 50%

So, the efficiency of the machine is 50%.