Understanding Work Done in Lifting a Body to a Height

When a body is lifted to a certain height, the work done on it is stored as potential energy. This concept is fundamental in physics and has significant applications in various fields, including engineering and everyday life.

Introduction to Potential Energy and Work Done

Once a body is lifted, the work done is stored as its potential energy. The reference point for potential energy is typically taken as the surface of the Earth, where potential energy is considered zero. By lifting a body to a different height, we change its potential energy.

Calculation of Work Done Using Potential Energy

In this case, we will calculate the work done on a body of mass 25 kg lifted to a height of 10 meters. We start by considering the reference point for potential energy to be the surface of the Earth.

Calculating Work Done

The formula for potential energy is given by:

PE mgh, where

PE Potential Energy m Mass of the body (25 kg) g Acceleration due to gravity (9.8 m/s2) h Height (10 m)

Substituting the values, the potential energy is:

PE 25 kg × 9.8 m/s2 × 10 m 2450 Joules

Therefore, the work done to lift the body to a height of 10 meters is 2450 Joules.

Calculating Work Done Using Force and Distance

Another way to calculate the work done is by using the force and the distance over which it is applied. The formula for work done is:

W F × d, where

W Work done F Force (mass × acceleration due to gravity) d Distance (height to which the body is lifted)

The force required to lift the body can be calculated as:

F m × g 25 kg × 9.8 m/s2 245 N

The work done is then:

W F × d 245 N × 10 m 2450 Joules

The Relationship Between Work Done and Potential Energy

When a body is lifted, the work done by an external force is stored as potential energy in the body. This energy can be calculated as:

PE mgh

So, the work done to lift the object to a height of 10 meters is:

W mgh 25 kg × 9.8 m/s2 × 10 m 2450 Joules

This work is stored as potential energy, and the body will have 2450 Joules of potential energy after being lifted to the specified height.

Conclusion

Work done and energy are interrelated concepts in physics, with the unit of both being Joules. The amount of work done in lifting a body is equal to the potential energy gained by the body. Understanding this relationship is crucial for various applications, from basic physics problems to engineering calculations.