**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

- Potential Energy in a Uniform Field

*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,

E_{k} = ½ mv^{2}

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 = ΔE_{k}

** Derivation of E_{k} Formula:**Start off with the F = ma formula.

F = ma

a = F/m

From one of the equations of motion,

v^{2} = u^{2} + 2as

Combining these equations,

v^{2} = u^{2} + 2Fs/m

mv^{2} = mu^{2} + 2Fs

Fs = ½ mv^{2} – ½ mu^{2}

Since Fs = Work = Change in energy,

ΔE_{k} = ½ mv^{2} – ½ mu^{2}

Thus, at any given moment:

*E _{k} = ½ mv^{2}*

** Finding Change in Kinetic Energy**If an object experiences a CHANGE in velocity, it will experience a CHANGE in E

_{k}.

As shown above,

ΔE

_{k}= ½ mv

^{2}– ½ mu

^{2}

Which can be factorised to

ΔE_{k} = ½ m(v^{2} – u^{2})

It is a common mistake to calculate (delta)E_{k} as:

ΔE_{k} = 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,

*E _{p} = mgh*

** Derivation of E_{p} 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

E_{p} = Wh

Since W = mg

*E _{p} = 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!

**⇐ Previous in Physics: Work & Energy**

**⇒ Next in Physics: Power**