Calculating Work Done in Lifting a Body

When a body of mass 10 kg is lifted to a height of 5 meters from the ground, it's important to understand how to calculate the work done in this process. This article will guide you through the steps to find the work done, emphasizing the role of gravitational potential energy and the formula used for such calculations.

Understanding the Formula for Work Done

The work done in lifting a body against gravity can be calculated using the formula for gravitational potential energy:

Work Done Mass × Gravity × Height

Where:

Mass (m) is the mass of the body in kilograms (kg). Gravity (g) is the acceleration due to gravity, which is approximately 9.81 m/s2 on the Earth's surface. Height (h) is the distance in meters to which the body is lifted from the ground.

Example Calculation

Given the following parameters:

Mass (m) 10 kg Height (h) 5 m Acceleration due to gravity (g) 9.81 m/s2

To find the work done, we use the formula:

Work Done Mass × Gravity × Height

Substituting the values, we get:

Work Done 10 kg × 9.81 m/s2 × 5 m

Now, performing the calculation:

Work Done 10 × 9.81 × 5 490.5 joules

Therefore, the work done in lifting the body is 490.5 joules.

Discussion on Work Done and Potential Energy

The work done on an object is equivalent to the gain in its potential energy. This can be derived from the formula:

Work Mass × Acceleration due to gravity × Height

Using the same example:

Given:

Mass (m) 10 kg Gravity (g) 9.81 m/s2 Height (h) 5 m

The work done is calculated as:

Work 10 kg × 9.81 m/s2 × 5 m 490.5 joules

This demonstrates that the work done in lifting the body is indeed 490.5 joules.

Additional Considerations

It's important to note that the force required to lift the body is equal to its weight:

Force Mass × Gravity 10 kg × 9.81 m/s2 98.1 N (Newtons)

Work is then calculated as:

Work Force × Distance 98.1 N × 5 m 490.5 joules

This confirms the initial calculation. Additionally, when the body is raised to a height of 8 meters, the work done would be:

Work 10 kg × 9.81 m/s2 × 8 m 784.8 joules

This shows a higher amount of work is required when the height is increased.

Conclusion

In summary, the work done in lifting a body against gravity can be calculated using the formula for gravitational potential energy. The calculations illustrate the importance of correctly applying the formula and understanding the concepts of work and potential energy.