To calculate the efficiency of a four-wheeled pulley system where a load of 50 N is lifted using an effort of 30 N, follow these steps:
1. Understand the concept of efficiency:
Efficiency in a mechanical system is defined as the ratio of the useful output (load lifted) to the input effort, expressed as a percentage.
2. Identify given values:
- Load (useful output): 50 N
- Effort (input): 30 N
3. Use the formula for efficiency:
Efficiency ([tex]\( \eta \)[/tex]) is calculated by the formula:
[tex]\[
\eta = \left( \frac{\text{Load}}{\text{Effort}} \right) \times 100
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
\eta = \left( \frac{50 \, \text{N}}{30 \, \text{N}} \right) \times 100
\][/tex]
5. Perform the division:
[tex]\[
\eta = \left( \frac{50}{30} \right) \times 100
\][/tex]
6. Calculate the efficiency:
[tex]\[
\eta = 1.6666666666666667 \times 100
\][/tex]
7. Express the result as a percentage:
[tex]\[
\eta = 166.67\%
\][/tex]
Therefore, the efficiency of the four-wheeled pulley system is 166.67%.
