How does work done affect an object's potential energy?

Work done on an object can increase or decrease its potential energy depending on the direction of the force applied.

When work is done on an object, energy is transferred to or from the object. If the work done is in the direction that opposes gravity, such as lifting an object upwards, the object's gravitational potential energy increases. This is because gravitational potential energy is directly related to the height of the object above the ground. The formula for gravitational potential energy is \( E_p = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height. So, lifting an object higher increases \( h \), and thus \( E_p \).

Conversely, if work is done in the direction of gravity, such as lowering an object, the gravitational potential energy decreases. This is because the height \( h \) is reduced, leading to a decrease in \( E_p \).

In the case of elastic potential energy, work done on an object like stretching or compressing a spring changes its potential energy. The more you stretch or compress the spring, the more work you do, and the more elastic potential energy is stored in the spring. The formula for elastic potential energy is \( E_e = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position.

In summary, the work done on an object affects its potential energy by either increasing it when the object is moved against a force (like gravity or spring tension) or decreasing it when the object moves with the force. Understanding this relationship helps in analysing various physical systems and predicting how energy is transferred and transformed.