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How can we describe motion in terms of energy changes?

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# Conservation of energy

Energy is always conserved – the total amount of energy present stays the same before and after any changes.

## The pendulum

The pendulum shows the principal of conservation of energy in action. Gravitational potential energy is converted to kinetic energy and back, over and over again, as the pendulum swings.

The diagram shows a pendulum in three positions - the two the ends of it's swing and as it passes through the middle point.

When the pendulum bob is at the start of its swing it has no kinetic energy because it is not moving, but its gravitational potential energy (GPE)gravitational potential energy: The energy stored by an object lifted up against the force of gravity. is at a maximum, because it is at the highest point.

As the bob swings downwards it loses height. So its gravitational potential energy (GPE) decreases. The work done on the bob by the gravitational force (weight) pulling it downwards increases its kinetic energy. The loss of GPE = the gain in KE.

At the bottom of its swing, the bob’s kinetic energy is at a maximum and its gravitational potential energy is at a minimum - because it is at its lowest point.

As the bob swings upwards it slows down. Its kinetic energy decreases as work is done against its weight. As it gains height the gravitational potential energy increases again.

At the very top of its swing it stops for a moment. It once again has no kinetic energy, but its gravitational potential energy is at a maximum.

At all points during the swing, the total (GPE + KE) is constant.

Note that in a real pendulum the bob’s swing will become slightly lower with each swing, because some energy is lost (dissipated, ‘wasted’) through heating, due to air resistance.

## Falling objects

You should be able to calculate the kinetic energy gained when an object falls from a given height.

Question
A diver who has a mass of 50 kg dives off a diving board 3.0 metres above the water level. What is her kinetic energy when she reaches the water?

• Kinetic energy gained = gravitational potential energy lost
• Kinetic energy gained = weight × height

You must calculate her weight to use in this equation

• Weight = mass × gravitational field strength
• Weight = 50 kg × 10 N / kg
• Weight = 500 N
• Kinetic energy gained = weight × height
• Kinetic energy gained = 500 N × 3 m
• Kinetic energy gained = 1500 J

## Conservation of energy (higher tier)

You should be able to extend the previous calculation to work out the speed of the object.

Question
How fast is the diver moving when she reaches the water?

Put her kinetic energy (the 1500J you have calculated) into the kinetic energy equation together with her mass

• kinetic energy = 1/2 × mass × speed2
• 1500 J = ½ × 50 × speed2 = 25 × speed2
• so speed2 = 1500/25 = 60 (This is not the answer yet! It is speed2!)
• So her speed = square root of 60 = 7.7 m/s

Here is a version of the "Work and energy" podcasts, with drawings to help you out.

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