# PHY C6: Kinetic & Potential Energy

Here’s what the topic includes:

• Kinetic Energy
• Derivation of Formula
• Potential Energy
• Potential Energy in a Uniform Field
• Derivation of Formula
• Elastic Potential Energy

Let’s jump in!

What is Kinetic Energy?
Energy due to motion.

Kinetic energy is proportional to HALF of the mass of an object & the SQUARE of the velocity.

As a formula,
Ek = ½ mv2

Every moving object has kinetic energy.

Many are confused by this fact:
Since WORK is Force x Displacement, wouldn’t a constant velocity = 0 acceleration, & thus 0 force?
Wouldn’t an object with no acceleration be doing no work?

The answer is: yes, an object moving at a constant velocity will be doing NO work.
However, it STILL has energy.
Work done is defined as TRANSFORMATION of energy.
If there was an acceleration (& thus increase in kinetic energy), there would be work done.

In this case, W = ΔEk

Derivation of Ek Formula:
Start off with the F = ma formula.
F = ma
a = F/m

From one of the equations of motion,
v2 = u2 + 2as

Combining these equations,
v2 = u2 + 2Fs/m
mv2 = mu2 + 2Fs
Fs = ½ mv2 – ½ mu2

Since Fs = Work = Change in energy,
ΔEk = ½ mv2 – ½ mu2

Thus, at any given moment:
Ek = ½ mv2

Finding Change in Kinetic Energy
If an object experiences a CHANGE in velocity, it will experience a CHANGE in Ek.
As shown above,
ΔEk = ½ mv2 – ½ mu2

Which can be factorised to
ΔEk = ½ m(v2 – u2)

It is a common mistake to calculate (delta)Ek as:
ΔEk = ½ m(v – u)2

Which would yield a WRONG answer.

What is Potential Energy?
Energy due to an object’s position or state.

When an object is in a certain position or state, it has the POTENTIAL to convert that energy into another type.
For example, a ball held above the ground has the POTENTIAL to gain kinetic energy as it falls.

There are 2 main types of potential energy we will explore here:

• Potential Energy in a Uniform Field (due to position)
• Elastic Potential Energy (due to shape)

What is Potential Energy in a Uniform Field?
Potential energy due to the POSITION of an object WITHIN a FIELD.

For example,

• Gravitational Potential Energy: when a mass is in a gravitational field
• Electrostatic Potential Energy: when a charge is in an electric field

Later on, you’ll see the many similarities between the types of potential energy.
For now, the type we will mainly explore is GRAVITATIONAL potential energy.

What is Gravitational Potential Energy?
Energy possessed by a mass due to its position in a gravitational field.

G.P.E. = mass x gravitational acceleration x height of object

As a formula,
Ep = mgh

Derivation of Ep Formula:
Work = Fd

When an object is at a certain height (h), it has the POTENTIAL to fall from that height due to the GRAVITATIONAL FORCE exerted by the Earth onto the mass (weight).

Thus, the work here is a product of weight (force) & height (distance).
Work = Fd
Ep = Wh
Since W = mg
Ep = mgh

What is Elastic Potential Energy?
Energy stored in objects due to the relative position of particles which are at a state of strain.
This is due to a change in the shape of an object.
For example, when a spring is stretched or compressed, it has the POTENTIAL to do work by converting the E.P.E. into kinetic energy.

We will explore this in a later post!