Question

Define the kinetic energy of an object. Show that work done by a force on an object is equal to the change in kinetic energy of the object.

Answer 1

Step 1: Data provided

Let an object of mass $m$ be at rest.

Thus, its initial velocity, $u$ and It is lying on a smooth surface.

A constant force F acts on the object such that the acceleration produced in the body is $a$.

Let the body move with a velocity $v$ after a displacement $S$.

Step 2: Formula used & Theory

$$\begin{gathered} v^2-u^2=2aS...........3rdequationofmotion. \\ F=ma..............Formulaofforce \\ W=F\times S............FormulaofWork \\ K=\frac{1}{2}m{v}^2..............Formulaofkineticenergy \end{gathered}$$

Kinetic energy:

1. The energy possessed by the body by virtue of its motion is called kinetic energy.
2. The kinetic energy of an object of mass $m$ and velocity $v$ is given by,

$K=\frac{1}{2}m{v}^2$

3. The work done by a force on an object is equal to the change in kinetic energy of the object, this principle is called work-energy principle.

Step 3: Calculation

$$\begin{gathered} as,F=ma \\ \Rightarrow a=\frac{F}{m}.......................\left(i\right) \\ now,v^2-u^2=2aS \\ {v}^2-u^2=2\frac{F}{m}S \\ \frac{1}{2}m(v^2-u^2)=F\times S \\ \frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2=W \\ {K}_i-K_f=W \end{gathered}$$

So, we can say that the change in kinetic energy is equal to the work done by an external force.