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Expression for Kinetic Energy

Work Energy and Power I - Concepts

Work

Unit of Work

Displacement in the direction of Force

Displacement in the direction opposite to the Force

Displacement in the direction perpendicular to the Force

Displacement at an angle to the Force

Calculation of Work Done

Energy

Expression for Kinetic Energy

Expression of Kinetic Energy in Terms of Momentum

Class - 9th ISO Subjects

Concept Explanation

Expression for Kinetic Energy

Kinetic Energy: The energy of an object because of its motion is called its kinetic energy. Its SI unit is Joule (J). A flying bird, a running man, a moving train and a swinging bat are some examples of bodies with kinetic energy. Kinetic energy of a body moving with certain velocity is equal to the work done on it to make it acquire that velocity. Kinetic energy of an object increases with its speed.

· Due to kinetic energy, a bullet fired from a gun can pierce a target.

· A moving hammer, drives a nail into a wooden block. Due to its motion, it has kinetic energy or ability to do work.

The kinetic energy of a body of mass m moving with a velocity v is

$K.E. = frac{1}{2}mv^2$

Sometimes, a large rock from space hits the earth’s surface at a very high speed. Its huge kinetic energy creates a large crater on the earth’s surface. One such crater was formed thousands of years ago at Lonar in Maharashtra. The diameter of this crater is 1.8 km.

Expression for Kinetic Energy: Suppose a body of mass “m” moving with a uniform velocity “u”. Force “F” starts acting on it in the horizontal direction and displaces it through a distance of “s” and it attains a velocity “v”. Then, work done to increases its velocity from “u” to “v”.

According to equation of motion:

$v^2 - u^2 = 2as$

So, as the object starts from rest and distance travelled is x

$v^2 = 2ax$ (1)

According to the definition of Force

F = ma

Or $a=frac{ F}{m}$

Putting the value of a in the Equation (1), we get

$v^2 =2frac{F}{m} x$

$mv^2 =2Fx$

$Fx= frac{1}{2}mv^2$

But Fx is the work done by the force on the body. It should be equal to the increase in the kinetic energy of the body as it moves from A to B. Also, since the kinetic energy at A was zero, the increase in kinetic energy should be equal to the kinetic energy at B. So, we conclude the following:

The kinetic energy of a body of mass m moving with a speed v is

$KE= frac{1}{2}mv^2$

Example:Find the kinetic energy of a ball of mass 200 g moving at a speed of 20 cm/s.

Solution The kinetic energy is

$KE= frac{1}{2}mv^2$

Given m= 200g = 0.2 Kg

v = 20 cm/s = 0.2m/s

$K.E. = frac{1}{2} (0.200; kg) times (0.20; m/s)^2 = 0.004 ;J$

Q. If a stone of mass 3 kg be thrown with a kinetic energy of 37.5 J, find its velocity.

Solution: Here, mass m = 3 kg, K.E. = 37.5 J, velosity of stone, v = ?

From $KE= frac{1}{2}mv^2 ; =; 37.5 = frac{1}{2}times;3v^2$

$v^2:=;frac{75}{3};=;25Rightarrow v;=;5;m/s$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Kinetic energy possessed by a car, moving at a speed of 5 m/sec is 5000 J. The mass of the car is
A. 400 kg	B. 1250 kg	C. 200 kg	D. 2500 kg
Right Option : A
View Explanation

Question : 2

A body of mass 20 kg is dropped from a height of 2 m. If g is taken to be equal to 10 $m/s^{2}$ , the kinetic energy of the body, just before striking the ground,will be
A. 40 J	B. 4 J	C. 400 J	D. none of these
Right Option : C
View Explanation

Question : 3

A uniform force of 4N acts on a body of mass 8 kg for a distance of 2.0m. The K.E. acquired by the body is
A. 0.8 J	B. 64 J	C. 4 J	D. 8 J
Right Option : D
View Explanation