derive the expression for kinetic energy (ke)
Answers
Answer:
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Let a body of mass ‘m’ is moving with a velocity ‘v’.A force ‘F’ is applied on it to stop its motion for which the retardation ‘h’ is produce in the body and the body covers a distance ‘s’ before coming rest.
Work done by the force to stop the motion of the body is the measure of kinetic energy .
Here,
Initial velocity = v
Final velocity = 0(zero)
From Newton’s 2nd law
F = ma
or, a = F/m
From 3rd equation of motion
0=v^2 - 2as
or, 2as = v^2
or, 2 × F/m × s = v^2
or, s = (mv^2) /2F
Therefore , workdone by the force,
W = Fs
or, W = F ( mv^2 )/2F
or, W = 1/2 mv^2
Hence,
Kinetic energy = 1/2mv^2.
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Explanation:
Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Derivation:
Let us consider an object of m which is at rest lying on a table.
Let A force F acts on the object which moves the object through a distance S.
The workdone=F×S
W=Fnet ×S-------(1)
Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration.
From Third equation of motion:
V²−u²=2as
s=V²−u²/2a----------(2)
By Newton's Second law:
F=ma------(3)
From equation (1), (2) and (3)
W=ma×(V² −u²/2a)=(1/2)m(V² −u²)
As we assumed object at rest, u=0
W=(1/2)mV²
we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.