Understanding Work Done by a Force: A Practical Example

Work is a fundamental concept in physics, often represented by the formula Work Force × Distance × cos(Θ), where Θ is the angle between the force and the direction of motion. In simple scenarios where the force and the motion are in the same direction (Θ 0), the formula simplifies to Work Force × Distance. Let's delve into a practical example involving an applied force and displacement to understand the concept better.

Given Scenario: A Force of 20.5 N Displaces a Body by 45 m

Suppose a force of 20.5 N is applied to a body, causing it to be displaced by 45 meters. We want to calculate the work done by this force.

Since the problem assumes that the force and displacement are in the same direction (Θ 0), we can calculate the work done using the simplified formula:

W F × d

Where:

F 20.5 N (Force) d 45 m (Displacement)

substitute the values into the formula:

W 20.5 N × 45 m 922.5 Nm

Therefore, the work done is 922.5 Nm (or Joules).

Evaluating Energy Expenditure Considering Human Efficiency

In certain applications, it is crucial to consider the human factor. How much energy does the person spend to achieve this work? Human bodies are not 100% efficient, and it’s often around 25%. This means only about a quarter of the total energy spent is converted into useful work.

If the useful work done is 922.5 Joules, then the total energy spent by the person, including inefficiencies, would be:

Total Energy Useful Work / Efficiency

Given that the efficiency is approximately 25% (or 0.25 in decimal form), the total energy spent is:

Total Energy 922.5 J / 0.25 3690 J

To provide a clearer perspective, 3690 Joules is roughly equivalent to 3.69 kJ (kilojoules).

Conclusion

In conclusion, we have calculated both the work done and the total energy expended to achieve the displacement using the force. The key takeaways are that: Work Done: 922.5 Nm (922.5 Joules) Total Energy Expended: Approximately 3690 Joules (3.69 kJ) These calculations can be invaluable in various applications, from mechanical engineering to sports science, to understand the efficiency of human performance and machinery. Understanding these concepts is crucial for optimizing performance and efficiency in both physical and mechanical work scenarios.

Further Reading

For more in-depth understanding and practical examples of work done and energy expenditure, consider exploring the following topics: Work in Physics Work and Energy Work in Thermodynamics