Question

Calculate the Kentic energy when the mass is reduced twice and the speed is tripled

Answer 1

Answer:

9mv²/4 J

Explanation:

$\red{\boxed{\rm Solution}}$

Let the intial speed of mass be v and the intial mass of the body be m

We know that Kinectic energy = m∆v²/2, Here ∆v is the change in velocity here the change in velocity is equal to the final velocity of the body as the mass is starting from rest.

Intial KE = mv²/2

After some time,

The mass of the body is reduced by twice, i.e it is it is reduced by half

Final mass = m - m/2 = m/2

The speed of the body is tripled

Final velocity = 3v

Final KE = [(3v)² x (m/2)]/2 = 9mv²/4

${\boxed{\rm Final \: KE \: is \: 9mv²/4 J }}$

$\red{\boxed{\rm Derivation \: of \: formula \: of \: Kinectic \: energy}}$

According to work energy theorem,

The net work done by all the forces on the body is equal to change in kinectic energy.

Therefore,

∆KE = W

We also know that Work done by a force on the body is equal to magnitude of the force times the change in the displacement by the body

∆KE = F∆s

According to Newton's second law of motion,

F = ma

∆KE = ma∆s

According to third equation of motion,

v² - u² = 2a∆s

a∆s = (v² - u²)/2

Therefore,

∆KE = mv²/2 - mu²/2

For a body which has started from rest,

∆KE = mv²/2 - m(0)/2

Therefore,

∆KE = mv²/2