Question

How are force, energy and work related?

Answer 1

We need to understand the three physical quantities force, energy and work initially. The proper definition and understanding is required to find the relation between these quantities which will give the solution for the problem as per the requirement.

Complete answer:
We know that the force, energy and the work done are among the important physical quantities in mechanics. We know from Newton's laws of motion that the force is a cause that induces an effect in a body. For an object moving with respect to time with a changing velocity, there exists an external cause which is termed as the force. In a motion, the force produces an acceleration in a body with mass ‘m’ as –
$F=ma$
The work done is the measure of how much effect the force caused in a body. It is the product of the distance travelled by a body under the influence of the force and the force itself. It is the effect of force on the object. The energy is the amount of work done and the both are the same when calculated. The energy is defined as the capability to do work. It is given mathematically as –

& W=E=F.s \\\ & \therefore W=E=Fs\cos \theta \\\ \end{aligned}$$ Where W is the work done, E is the energy, F is the force, m is the mass of the object, $$s\cos \theta $$ is the displacement of the object in the direction of force. From this we understand that the force, work done and the energy are highly interrelated physical quantities. This is the required solution. **Note:** There are many forms of work done which may appear to be independent of any forces. Actually, the forces in nature are due to the energy available in a system and the force is a method by which this energy is transferred from one system to the other.