Work-Energy Theorem

The work-energy theorem is a very important and useful theorem in physics and here I will show you how we get that specific formula in full understanding.

Energy can help us solve many things however, it is a very abstract concept that we have no clue about. While the change in energy of two objects can be the same as the roll down a ramp and different inclinations, the rate at which the kinetic energy gets converted from potential energy is different and that is what we can start analyzing first.

dK/dt=d(0.5mv2)/dt=2∗0.5mv(dv/dt)=mv(dv/dt)dK/dt = d(0.5mv^2)/dt = 2*0.5mv(dv/dt) = mv(dv/dt)

We let mm be a constant as we assume that the object itself is not moving at any high speeds and has negligible relativistic effects. That final solution can also be written as:

mv(dv/dt)=Fvmv(dv/dt) = Fv

We call this expression power and it is exactly what we have been talking about, the rate at which energy is expended to some object such as a car in order to make it move and do work.

dK/dt=F(dx/dt)dK/dt = F(dx/dt)

We can cancel the dt′sdt's from both sides.

dK=FdxdK = Fdx

∫dK=∫Fdx∫ dK = ∫ Fdx

K(2)−K(1)=∫FdxK(2) - K(1) = ∫ Fdx

And that is the work-energy theorem. It is very important and very useful to use in physics, specifically in areas such as gravitational fields, electric fields, and oscillatory motion.

#Mechanics

Note by Raghu Alluri
1 year, 10 months ago

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