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### 2.4 Energy

We hear the term "Energy" a lot in physics. Here we'll discuss about the notion about energy.

When we talk about energy in physics we're basically refering to the "capacity for doing work." It is a scalar quantity. One of the important concept related to the energy is the "Law of conservation of energy."

Law of conservation of energy: "It states for an isolated system, the total energy remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another."

Some form energy that we know are,
• Mechanical energy, Chemical energy, Electrical energy, Nuclear energy, Radiation energy, Sound energy, Internal and Thermal energy. (click here)
Let's study the kinetic energy. We have learned that the kinetic energy/mechanical energy is equal to the following, $E_{k}=\frac{1}{2}mv^{2}$, where $m=$ mass of an object in kg, $v=$velocity of an object in $ms^{-1}$. Kinetic energy of a body is its capacity to do work due to its motion. Consider the following situation where, a ball starts with initial velocity $u=0$ is pushed with a force $F$ and covers a displacement $d$. How do we calculate the total kinetic energy transfered to the ball.

We'll derive the formula for the kinetic energy. From the kinematics we know,
$$v^{2}=u^{2}+2ad$$
and from Newtons second law
$$F=ma$$
If we start an object at rest then the initial velocity is zero (i.e. $u=0$). Then from the definition of work,
\begin{align*} W&=F\times d\\ &=m\times a\times d\\ &=m\times \frac{v^{2}}{2d}\times d \\ &=\frac{1}{2}mv^{2}\end{align*}
Thus,
$$W=E=\frac{1}{2}mv^{2}$$

$Ex.$ An object of mass $4kg$ is moving at a speed of $30ms^{-1}$. Calculate the Kinetic energy of an object?
$sol^{n}$=1800$J$