Write detailed answer 1) derive the formula for kinetic energy of an object od mass m, moving with velocity v
Answers
Kinetic Energy:
The energy possessed by an object due to its motion is called as kinetic Energy.
Derivation:
Let us consider an object of mass " m " which is at rest on smooth horizontal plane.
Let a Force , F acts on the object and let the object from rest moves from point A to point B and covers a displacement S.
The WORK Done by Force on the object is :
Workdone = Force x displacement.
W= FxS ____(1).
From third equation of motion;
V^2 -U^2 =2aS
S= V^2 -U^2/2a ______(2)
By Newtons second law of motion:
F= ma
From equation 1 and 2
W= m*a* (V^2- U^2)/2a
As we have assumed object is at rest, u=0
W=m*V^2/2
The WORK Done appears as kinetic energy of the body.
Therefore,
K.E = (1/2 )mv^2
Answer:
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=FxS
W=FnetXS-------(1)
Let the workdone 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 certain velocity is equal to workdone on the object to acquire that velocity from rest.
∴K.E=1/2 mV²