Calculating Machine Efficiency

The efficiency of a machine represents the ratio of useful work output (work done on the load) to the total work input (work done by the effort). It is typically expressed as a percentage.

Given Data:

• Effort Applied = 5 units
• Load = 10 units
• Distance travelled by effort (\(d_e\)) = 50 units
• Distance travelled by load (\(d_l\)) = 20 units

Calculations:

1. Work Done by Effort (\(W_e\)):

The work done by the effort is calculated as the product of the effort applied and the distance it travels.

\( W_e = \text{Effort} \times d_e \)

\( W_e = 5 \text{ units} \times 50 \text{ units} = 250 \text{ units}^2 \)

2. Work Done on Load (\(W_l\)):

The work done on the load is calculated as the product of the load and the distance it moves.

\( W_l = \text{Load} \times d_l \)

\( W_l = 10 \text{ units} \times 20 \text{ units} = 200 \text{ units}^2 \)

3. Efficiency (\(\eta\)):

Efficiency is the ratio of work done on the load to the work done by the effort, multiplied by 100%.

\( \eta = \left( \frac{W_l}{W_e} \right) \times 100\% \)

\( \eta = \left( \frac{200 \text{ units}^2}{250 \text{ units}^2} \right) \times 100\% \)

\( \eta = \left( \frac{4}{5} \right) \times 100\% \)

\( \eta = 0.8 \times 100\% = 80\% \)

Conclusion:

The efficiency of the machine is 80%.