Question

What is the relation between work and Energy?

Answer 1

Step 1: Find the equation for work done.

Work is said to be done if a body moves through a certain distance under the application of force. The work done is equal to the product of force and the distance travelled in the direction of the force. The capacity of a body to do work is called its energy. Work is directly proportional to the energy.

Work done in terms of velocity of an object can be mathematically expressed as:

$W=\frac{1}{2}m{v}_f^2-\frac{1}{2}m{v}_i^2$

Where, $W$ is the work done by the object measured using Joules.

$m$ is the mass of the object measured in kgs.

$v_i$ is the initial velocity of an object measured using m/s.

$v_f$ is the final velocity of an object measured using m/s.

Step 2: Find the relationship between work and energy.

The work-energy theorem states that ‘the net work done by the force on an object is equal to change in its kinetic energy.’

Therefore,

$$\begin{gathered} W=K_i–K_f \\ \Rightarrow W=\Delta K \end{gathered}$$

Where, $W$ is the work done by the object measured using Joules.

$K_i=$ initial Kinetic Energy.

$K_f=$ Final Kinetic Energy.

$\Delta K=$ Difference in Kinetic Energy.