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
\( \eta = \left( \frac{\text{Work Output}}{\text{Work Input}} \right) \times 100\% = \left( \frac{200}{250} \right) \times 100\% = 0.8 \times 100\% = 80\% \)
Similar Questions
- The force applied to overcome a load is called _____.
Important Questions from Mechanical Advantage
Which of the following mechanical devices efficiently distributes or multiplies loads with little effort?
- The force applied to overcome a load is called _____.
