# Potential and Kinetic Energy

## Energy

Energy is the capacity to do work.

The unit of energy is J (Joule) which is also kg m2/s2 (kilogram meter squared per second squared)

Energy can be in many forms! Here we look at Potential Energy (PE) and Kinetic Energy (KE).

## Potential Energy and Kinetic Energy A hammer:

• when raised up has potential energy (the energy of position or state)
• when falling down has kinetic energy (the energy of motion)

### Potential energy (PE) is stored energy due to position or state • a raised hammer has PE due to gravity.
• fuel and explosives have Chemical PE
• a coiled spring or a drawn bow also have PE due to their state

### Kinetic energy (KE) is energy of motion A moving car has a lot of kinetic energy

### From PE to KE These skydivers have potential energy due to being high up.
After they jump this potential energy gets
converted into kinetic energy (and heat) as they speed up.

## Gravitational Potential Energy

When the PE is due to an objects height then:

PE due to gravity = m g h

Where:

• m is the objects mass (kg)
• g is the "gravitational field strength" of 9.8 m/s2 near the Earth's surface
• h is height (m) ### Example: This 2 kg hammer is 0.4 m up. What is it's PE?

PE = m g h
= 2 kg × 9.8 m/s2 × 0.4 m
= 7.84 kg m2/s2
= 7.84 J

## Kinetic Energy

The formula is:

KE = ½ m v2

Where

• m is the object's mass (kg)
• v is the object's speed (m/s) ### Example: What is the KE of a 1500 kg car going at suburban speed of 14 m/s (about 50 km/h or 30 mph)?

KE = ½ m v2

KE = ½ × 1500 kg × (14 m/s)2

KE = 147,000 kg m2/s2

KE = 147 kJ

Let's double the speed! ### Example: The same car is now going at highway speed of 28 m/s (about 100 km/h or 60 mph)?

KE = ½ m v2

KE = ½ × 1500 kg × (28 m/s)2

KE = 588,000 kg m2/s2

KE = 588 kJ

Wow! that is a big increase in energy! Highway speed is way more dangerous.

Double the speed and the KE increases by four times. Very important to know ### A 1 kg meteorite strikes the Moon at 11 km/s. How much KE is that?

KE = ½ m v2

KE = ½ × 1 kg × (11,000 m/s)2

KE = 60,500,000 J

KE = 60.5 MJ

That is 100 times the energy of a car going at highway speed.

## From PE to KE

When falling, an object's PE due to gravity converts into KE and also heat due to air resistance.

Let's drop something! ### Example: We drop this 0.1 kg apple 1 m. What speed does it hit the ground with?

At 1 m above the ground it's Potential Energy is

PE = m g h

PE = 0.1 kg × 9.8 m/s2 × 1 m

PE = 0.98 kg m2/s2

Ignoring air resistance (which is small for this little drop anyway) that PE gets converted into KE:

KE = ½ m v2

Swap sides and rearrange:

½ m v2 = KE

v2 = 2 × KE / m

v = √( 2 × KE / m )

Now put PE into KE and we get:

v = √( 2 × 0.98 kg m2/s2 / 0.1 kg )

v = √( 19.6 m2/s2 )

v = 4.427... m/s

Note: for velocity we can combine the formulas like this:

 Velocity from KE: v = √( 2 × KE / m ) Put in formula for PE: v = √( 2 × mgh / m ) Cancel m/m: v = √( 2gh )

The mass does not matter! It is all about height and gravity. For our earlier example:

v = √( 2gh )

v = √( 2 × 9.8 m/s2 × 1 m )

v = 4.427... m/s

## Summary

• Energy is the ability to do work
• Potential Energy (PE) is stored energy due to position or state
• PE due to gravity = m g h

• Kinetic Energy (KE) is energy of motion
• KE = ½ m v2