Unizor - Physics4Teens - Energy - Kinetic Energy - Introduction
Channel: Zor Shekhtman on UNIZOR Education
Date: 2019-01-14

Unizor - Physics through a Looking Glass of Mathematician

Notes to a video lecture on http://www.unizor.com

Kinetic Energy - Introduction

Kinetic energy is a quantitative characteristic of an object's motion, that signifies that this motion can result in some work, when our object interacts with surrounding environment.

As an example, consider an object of mass m uniformly moving within some inertial frame along a straight line trajectory with speed v.

Assume that at some moment of time there appears a constant force F that acts against its motion. For example, a constant air resistance.

As a result of this interaction with air molecules, our object will slow down because of air resistance acting against its motion until it stops. So, the motion of our object caused some work - moving molecules of air away from the trajectory, after which the motion of our object no longer exists, it stops completely.
Obviously, instead of air resistance, we can consider friction or gravity, or any other force, assumed constant for this experiment.

Let's calculate the work done by this force, as it acts against the motion of our object and causes its deceleration.

First of all, we calculate the deceleration a:
a = F/m
Then, knowing deceleration, we get the time t our force acts until an object stops:
t = v/a = m·v/F
Now the distance S our object travels until a full stop:
S = a·t²/2 = F·t²/(2m) =
= F·m²·v²/(2m·F²) =
= m·v²/(2F)
Finally, the work W performed by our force F during the distance S:
W = F·S = m·v²/2

What's most remarkable about this formula is that the work performed by force F does not depend on this force, but only on the characteristic of an object (mass m) and its motion (speed v).

So, it appears that there is something specific for an object (its mass) and its motion (speed) - the amount of work to bring this object to a state of rest, and this quantity of work equals to m·v²/2.
This quantitative characteristic of an object in motion is called its kinetic energy.