Question

A machine has a velocity ratio of 4. If it is used to raise a load of 400 N by 4 m using an effort of 200 N, find the work done on the machine. Take g = 10 m/s${}^2$.

• A. 1600 J
• B. 3200 J
• C. 6400 J
• D. 2000 J

Answer 1

The correct option is B

3200 J

Given, velocity ratio = 4
Load = 400 N
Effort = 200 N

The mechanical advantage (MA) of a machine is the ratio of the load overcome to the effort applied.
So, $MA=\frac{\text{load}}{\text{effort}}=\frac{400}{200}=2$

Also, efficiency of the machine is the ratio of mechanical advantage (MA) to the velocity ratio (VR).
So, Efficiency $\left(\eta \right)$ = $\frac{\text{MA}}{\text{VR}}=\frac{2}{4}=\frac{1}{2},$

Percentage efficiency = $\frac{1}{2}\times 100$

Output work = Force x Distance
= 400 N x 4 m = 1600 J.

So, work done on the machine (input) = $\frac{\text{output}}{\text{efficiency}}=\frac{1600}{\left(1/2\right)}=3200J$