Machine Efficiency Calculation

To find the efficiency of the machine, we need to calculate the Mechanical Advantage (MA), the Velocity Ratio (VR), and then use the formula for efficiency.

Mechanical Advantage (MA)

Mechanical Advantage is the ratio of the load to the effort applied.

Given:

• Load = 10 units
• Effort = 5 units

The formula for MA is:

\( \text{MA} = \frac{\text{Load}}{\text{Effort}} \)

Substituting the values:

\( \text{MA} = \frac{10}{5} = 2 \)

Velocity Ratio (VR)

Velocity Ratio is the ratio of the distance travelled by the effort to the distance travelled by the load.

Given:

• Distance travelled by effort = 50 units
• Distance travelled by load = 20 units

The formula for VR is:

\( \text{VR} = \frac{\text{Distance travelled by effort}}{\text{Distance travelled by load}} \)

Substituting the values:

\( \text{VR} = \frac{50}{20} = 2.5 \)

Machine Efficiency

Efficiency is the ratio of Mechanical Advantage to Velocity Ratio, expressed as a percentage.

The formula for efficiency (\(\eta\)) is:

\( \eta = \left( \frac{\text{MA}}{\text{VR}} \right) \times 100\% \)

Substituting the calculated MA and VR:

\( \eta = \left( \frac{2}{2.5} \right) \times 100\% \)

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

\( \eta = 80\% \)

Alternatively, efficiency can be calculated as the ratio of work output to work input.

Work Input = Effort \(\times\) Distance travelled by effort = \(5 \times 50 = 250\) units

Work Output = Load \(\times\) Distance travelled by load = \(10 \times 20 = 200\) units

\( \eta = \left( \frac{\text{Work Output}}{\text{Work Input}} \right) \times 100\% = \left( \frac{200}{250} \right) \times 100\% = 0.8 \times 100\% = 80\% \)