3. Learning objectives consider what happens when a spring is stretched
describe what is meant by gravitational potential energy
calculate the energy stored by an object raised above ground level.
What energy does the arrow have when moving? Where does this energy come from? What type of energy does the bow have when the bowstring is pulled back? How can the energy be increased? Why would different bows contain different amounts of energy?

4. What energy does the arrow have when moving?
Where does this energy come from?
What type of energy does the bow have when the bowstring is pulled back?
How can the energy be increased?
Why would different bows contain different amounts of energy?

5. Stored energy
When a spring is stretched it stores energy. We call this potential energy. The stretched spring stores energy transferred in stretching. It stretches more if a greater force is applied, and returns to its original length when the force is removed.
Compressed springs are also used to store energy, for example, to keep batteries in position.

6. Questions
Imagine slowly stretching a rubber band. Describe what you would feel as you stretch it more.
2. Suggest what happens to the amount of energy stored in the spring inside a the toy in Figure as the key is turned.

7. GPE
Water stored behind a dam also stores energy. It is called gravitational potential energy (GPE). The GPE stored by an object can be increased by moving it upwards. For example, you gain GPE by going up stairs.
An aircraft is flying horizontally at a height of m. Explain whether its gravitational potential energy is increasing, decreasing or remaining constant.

8. Calculating changes in GPE
Tom lifts a box. The amount of gravitational potential energy gained by the box depends on:
the mass of the box, m, in kilograms, kg
the height Tom raises the box, h, in metres, m.
We can calculate the amount of gravitational potential energy gained (Ep) using the equation:
Ep = mgh
where m is measured in kg, g is the gravitational field strength in N/kg and h is measured in m. Changes in Ep are measured in joules (J).

9. The pull of gravity on the box (its weight) is calculated using
gravity force (weight) = mass × gravitational field strength
W = m × g
The gravitational field strength is the pull of gravity on each kilogram. The value of g is 10 N/kg at the Earth’s surface.

10. An example
Zack gains gravitational potential energy when he walks up some stairs (Figure 2.55). The Ep Zack gains can be calculated using Ep = mgh where h is the vertical height he raises his body.
Zack then walks on a level floor. He does not gain or lose any gravitational potential energy now because his height above the floor does not change.

11. Questions
Lars is a weight lifter. He lifts a mass of 300 kg through a height of 2 m. Calculate the gravitational potential energy gained by the weight.
2. Sian picks up a ball from the floor and holds it 2 m above the ground. The ball has a mass of 60 g. Calculate the gravitational potential energy gained by the ball.

12. Practical

13. Data - sketch a graph of this data
r (m)
r^2 (m^2)
g (N/kg)
6.40 x 106
4.10 x 1013
9.72
8.00 x 106
6.40 x 1013
6.22
9.60 x 106
9.22 x 1013
4.32
1.12 x 107
1.25 x 1014
3.18
1.28 x 107
1.64 x 1014
2.43
1.44 x 107
2.07 x 1014
1.92
1.60 x 107
2.56 x 1014
1.56

14. Questions How much does an 85kg person weigh:
on Earth?
on the Moon?
The person in the question above climbs a flight of stairs of height 5m on Earth. How much GPE do they gain?
From the top of the stairs they drop a stone of mass 85kg. What velocity does it reach just before it impacts the floor?