# Explain how force, energy and work are related?

Sep 30, 2015

Force is a push or a pull, and the displacement of an object due to the application of a force on it is work. The ability to do work is called energy.

#### Explanation:

Force is a push or a pull. If an object of mass $m k g$ at rest is pushed, or pulled, such that it has an acceleration of $a \frac{m}{s} ^ 2$, the force is equal to $m \cdot a$. The displacement of the mass due to the force, $F$, being applied is $s$ meters, so the work done is said to be $F \cdot s \cdot \cos A$, where $A$ is the angle of displacement. The ability to do this amount of work is called energy.

Energy can be of different forms. A moving object has Kinetic Energy, K.E, defined by the expression $K E = \frac{1}{2} \cdot m \cdot {v}^{2}$, where $v$ is the speed of the object.

An object at a height of $h$ meters from the ground has a Gravitational Potential Energy, G.P.E, given by the expression $G P E = m \cdot g \cdot h$, where $g$ is the acceleration due to gravity. As you can see, this actually gives you the work done by gravity on the object.

The energy stored in an ideal stretched or compressed spring is given by $F = k \cdot x$ where $k$ is the spring constant and $x$ is the change in the length of the spring. An ideal spring is one in which the change in its length is proportional to the applied force. In case of an spring that is not ideal, the Elastic Potential Energy, E.P.E, stored is given by the expression $E P E = \frac{1}{2} \cdot k \cdot {x}^{2}$.

There is a strong connection between work and energy. You can visualize this as the energy of an object for doing a work.
This is demonstrated by the expression $W = \Delta K E$, where $\Delta K E$ is the change in kinetic energy of the object for doing that work.
This can be rearranged to:
$W = \Delta K E$
$W = K {E}_{\text{final" - KE_"initial}}$
$W = \frac{1}{2} \cdot m \cdot {v}_{\text{final"^2 - 1/2*m*v_"initial}}^{2}$

Mar 16, 2017

Force is the fundamental characteristic nature of interaction, Energy the measure of Inertia, work the amount of change in Inertia the Force has caused

#### Explanation:

To explain it simply without any equations :

Force is like a characteristic of interaction between any set of objects. Let it be two masses, group of masses, group of charges or whatever. Depending upon type, they causes change in motion.

Energy is a measure of Inertia of the system. How much inertia the body already has decides how much he is going to respond to the above mentioned force. Assuming a uniform form - not varying - we can measure strength of force and classify it based on the action it can provide to a given chunk of mass, by moving it across a small distance and checking it. Or conversely checking how much it moved when it is allowed to move for a small time. My force can't be harder than, say undertaker's force. Because a given mass, we can move a longer distance than I do. Energy is also a kind of measure of how much a moving body changes its motion due to the force. It is either way, but is the same energy - scientists call it Potential energy and Kinectic energy respectively.

Now, switch to the perspective of the force. Given a uniform amount of inertia, how much did the force actually cause change. It depends on the mass of the object really. Hence, work done is how much Force actually did something to the object. It is the change in Energy of the system. Energy hence becomes the perspective of the body and not the force (source)