To calculate the energy used in overcoming friction when a machine does work, we can use the concept of efficiency. The efficiency of a machine is defined as the ratio of useful work output to the total energy input, expressed as a percentage.
The efficiency (\( \eta \)) is given by:
\[ \eta = \frac{\text{Useful Work Output}}{\text{Total Energy Input}} \times 100 \]
In this case, we know:
- Efficiency (\( \eta \)) = 75%
- Useful Work Output = 2500 J
First, we can rearrange the efficiency formula to solve for the total energy input:
\[ \text{Total Energy Input} = \frac{\text{Useful Work Output}}{\eta / 100} \]
Substituting the known values:
\[ \text{Total Energy Input} = \frac{2500 , \text{J}}{0.75} = \frac{2500}{0.75} = 3333.33 , \text{J} \]
Now that we have the total energy input, we can calculate the energy used in overcoming friction. The energy used to overcome friction is the difference between total energy input and useful work output:
\[ \text{Energy used to overcome friction} = \text{Total Energy Input} - \text{Useful Work Output} \]
Substituting the values:
\[ \text{Energy used to overcome friction} = 3333.33 , \text{J} - 2500 , \text{J} = 833.33 , \text{J} \]
Thus, the energy used in overcoming friction is approximately 833.33 J.