Question

A machine displaces a load of 125kgf through a distance of 0.30m while an effort of 12.5kgf acts through a distance of 4.0m. calculate the Efficiency.

Answer 1

Step 1: Given

Load = 125kgf

Load arm = 0.30m

Effort = 12.5kgf

Effort arm = 4.0m

Step 2: Definition & Formula

1. The efficiency of the machine:
2. It is the ratio of mechanical advantage(M.A) to Velocity ratio(V.R).
3. Efficiency(ŋ) = $\frac{M.A}{V.R}$x 100
4. Mechanical advantage:(M.A)
5. It is the ratio of load to effort.
6. Mechanical advantage = $\frac{load}{effort}$
7. Velocity ratio:(V.R)
8. It is the ratio of distance traveled by the effort to the distance traveled by the load in a particular time.
9. Velocity ratio = $\frac{effortarm}{loadarm}$

Step 3: Calculation

Velocity ratio =$\frac{effortarm}{loadarm}$=$\frac{4}{0.3}$=13.33

So the velocity ratio is 13.33

Mechanical advantage = $\frac{load}{effort}$ = $\frac{125}{12.5}$ = 10

So, the mechanical advantage is 10.

Efficiency = $\frac{M.A}{V.R}$x 100 = $\frac{10}{{\displaystyle \frac{40}{3}}}$x 100 = 75 %

Hence , the efficiency of the machine is 75%.