Derive expression for kinetic energy...
Answers
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Derivation for the equation of Kinetic Energy:
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S = ½a(v2 - u2)
S = ½a(v2 - u2)
We know F = ma. Thus using above equations, we can write the workdone by the force, F as
S = ½a(v2 - u2)
We know F = ma.
Thus using above equations, we can write the workdone by the force, F as W = ma × ½a(v2 - u2)
S = ½a(v2 - u2)
or W=m( v 2 - u 2 ) ½
If object is starting from its stationary position, that is, u = 0, then
S = ½a(v2 - u2)
We know F = ma. Thus using above equations, we can write the workdone by the force, F as W = ma × ½a(v2 - u2) or W =m( v 2 - u 2 ) ½If object is starting from its stationary position, that is, u = 0,
then W = ½mv2
or W =m( v 2 - u 2 ) ½
If object is starting from its stationary position, that is, u = 0, then
S = ½a(v2 - u2)
It is clear that the work done is equal to the change in the kinetic energy of an object.If u = 0, the work done will be W = ½mv2Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek= ½mv2
hope this answer helps you..❤❤✌✌
Expression for Kinetic energy(Ek)-
Consider an object with mass m, moving with initial velocity u.
Let a force F, act on it causing a displacement s, along the direction of force and accelaration.
Let the object attain final velocity v. We know
F = m x a ------------------------ 1
By position velocity relation we have, V2 = u2 + 2as or s = v2 -u2 2a----------------------------- 2
The work done by the force W = F x s -------------------------------------- 3
Substituting 1 and 2 in 3
W = (m x a) x (v2 - u2/2a) W = m/2 (v2 - u2) W = 1/2 mv2 - 1/2 mu2 -------------------- 4
For an object to be at rest in the beggining, u = 0
Therefore, W = 1/2 mv2 W = Ek ( Ek = kinetic energy)
Therefore, Ek = 1/2 mv2