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,
and from Newtons second law
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*}

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

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