**Units Used This Topic:**

**energy** Joule (J)

**extension** metre (m)

**gravitational field strength** Newton/kilogram (N/kg)

**height** metre (m)

**mass** kilogram (kg)

**powe**r Watt (W)

**specific heat capacity** Joule/kilogram x degrees celsius (J/kg℃)

**spring constant **Newton/metre (N/m)

**temperature** degrees celsius (℃)

**time** second (s)

**velocity** metre/second (m/s)**Force **Newton (N)

A** system** is an object or group of objects.

Energy can be stored in different Energy Stores:

**kinetic energy store**: The energy store of a moving object**chemical energy store**: The energy stored in chemical bonds, such as those between molecules**gravitational potential****energy store**: The energy stored in an object due to its height**elastic potential****energy store**: The energy stored in a stretched or compressed object**thermal****energy store**: The energy stored in an object due to its temperature**magnetic****energy store**: The energy stored due to the poles of a magnet being near each other but not touching**nuclear energy store**: The energy stored in the nucleus of an atom**electrostatic****energy store**: the energy stored when electric charges are near each other but not touching

Energy can be transferred between stores in only 4 ways:

**by heating****by waves**(e.g. light)**mechanically**(e.g. gravity)**electrically**

When a system changes, there are changes to the way energy is stored. For example when an object is projected upwards the initial kinetic energy store of the object is transferred mechanically to the gravitational potential energy store of the object

**Question: **Describe the change in the way energy is stored when a moving object hits an obstacle:

The initial **kinetic energy store of object** is transferred mechanically to the **thermal energy store of the obstacle**

**Question: **Describe the change in the way energy is stored when a car is accelerated by a constant force:

The initial **chemical energy store of the fuel** is transferred to the **kinetic energy store of the car**

**Question: **Describe the change in the way energy is stored when a car slows down:

The initial **kinetic energy store of the car** is transferred to the **thermal energy store of the brakes**

**Question: **Describe the change in the way energy is stored when water is boiled in an electric kettle

The initial** thermal energy store of the heating element** is transferred to the **thermal energy store of the water**

When the Underground was first built, the clay walls were around 14C.

Nowadays they are anywhere between 19C and 26C, with air temperatures often reaching 30C.

The thermal energy transferred to the brakes as the trains slow down has been absorbed by the walls of the underground causing the temperature rise.

This is why the underground is always so hot!

You can find the quantity of energy stored for a number of different type of energy store.

The kinetic energy of a moving object can be calculated using the equation:

**kinetic energy = ½ × mass × speed ²**

**Question: ** What is the kinetic energy of a 4kg cat moving at 14m/s:

**kinetic energy = ½ × mass × speed ²**

k.e = **½** x 4 x 14**²**

k.e = **½** x 4 x 196

The kinetic energy of the cat is **392 Joules**

**Question: ** What is the mass of a snowball with 5,000 J kinetic energy which is moving at 5m/s?

**kinetic energy = ½ × mass × speed ²**

5000 ** =** ½ × mass × 5²

mass = (2 x 5000) / 5² = 10000/25

The mass of the snowball is **400 kg**

The amount of elastic potential energy stored in a stretched spring can be calculated using the equation:

**elastic potential energy = ½** **× spring constant × extension ² **

**Question: **How much elastic potential energy is stored when a spring (spring constant = 14 N/m) is extended by 0.4m?

**elastic potential energy = ½ × spring constant × extension ² **

epe = ½ x 14 x 0.4^{2}

epe = ½ x 14 x 0.16

There is **1.12 Joules** stored in the stretched spring

**Question:** Find the spring constant of a spring which has 240J elastic potential energy when it is compressed by 250cm

**elastic potential energy = ½ × spring constant × extension ² **

240 = ½** **x spring constant x 0.25^{2}

240 = ½** **x spring constant x 0.0625

spring constant = (2 x 240) / 0.0625

The spring constant is **7680 N/m**

On earth the gravitational field strength is 9.8 N/kg

The change in gravitational potential energy of an object when its height is changed can be calculated using the equation:

**g.p.e. = mass × gravitational field strength × change in height**

**Question:**What is the change in gravitational potential energy of a 6kg object when it is raised by 2m?

**g.p.e. = mass × gravitational field strength × change in height**

g.p.e = 6 x 9.8 x 2

The change in gravitational potential energy is **117.6 Joules**

**Question**: An object gains 200J gravitational potential energy when it is lifted by 50cm. What is the mass of the object?

**g.p.e. = mass × gravitational field strength × change in height**

200 = mass x 9.8 x 0.5

mass = 200 / (9.8 x 0.5)

The object has a mass of **40.8kg**

**Power** is defined as the rate at which energy is transferred or the rate at which work is done.** ** The faster a device transfers energy the more powerful it is.

**power = energy transferred / time**

An energy transfer of **1 joule per second** is equal to a power of 1 watt.

**Question:** A hairdryer transfers 6000J in 2s. How powerful is it?

**power = energy transferred / time**

= 6000 / 2

The hairdryer has a power of **3000W**

**Question**: How much energy does a 3500W kettle transfer in 30s?

**power = energy transferred / time**

3500 = energy transferred / 30

energy transferred = 3500 x 30

The kettle transfers **105000 Joules**

**Conservation of Energy:**

Energy can be transferred usefully, stored or dissipated (spread out so it becomes less useful), but cannot be created or destroyed.

Where there are energy transfers in a **closed system**, that there is no net change to the total energy. This means that all the energy you put in, is the same amount as comes out.

**Question:** A 50kg rocket is launched at 25m/s. How high does the rocket climb? (g = 9.8N/kg)

- Calculate initial Kinetic Energy
**kinetic energy = ½ × mass × speed ²**- = ½ x 50 x 25
^{2} - = ½ x 50 x 625
- Initial kinetic energy is 15625 Joules

- Assume all kinetic energy is transferred to gravitational potential energy
**Kinetic Energy = g.p.e. = mass × gravitational field strength × change in height**- 15625 = 50 x 9.8 x change in height
- change in height = 15625 / (50 x 9.8)
- change in height= 31.9 m

- The rocket will climb
**31.9 m**

**Question:** A 70kg person jumps from a 10m diving board. How fast are they moving just before they hit the water? (g = 9.8N/kg)

- Calculate initial gravitational potential energy
**g.p.e. = mass × gravitational field strength × change in height**- g.p.e = 70 x 9.8 x 10
- Initial gravitational potential energy = 6860 Joules

- Assume all initial G.P.E is transferred to kinetic energy on the way down
- g.p.e. =
**kinetic energy = ½ × mass × speed ²** - 6860 = ½ x 70 x speed
^{2} - speed
^{2}= 6860 / ( ½ x 70) - speed
^{2}= 196 - speed =
**√**196 - speed= 14 m/s

- g.p.e. =
- The person will be moving at
**14m/s**just before they hit the water