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=20.5mv(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 dtsdt'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.

Note by Raghu Alluri
11 months, 3 weeks ago

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