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3.4Energy transfers

In previous sections we saw that in a system without external forces doing work the total mechanical energy of the system stays the same; it is conserved. During a motion, the individual stores of the total energy (kinetic energy, gravitational potential energy and elastic potential energy) change, but the total energy stays the same.

Energy can be transferred from one form to another. For example, a ball rolling down an inclined plane starts with gravitational potential energy (gpe) which transfers to kinetic energy. Eventually, the ball will stop rolling because its kinetic energy is ‘lost’ to the surroundings as it transfers to thermal energy (and some sound).

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A ball rising up an inclined plane does the reverse—its kinetic energy is transferred to gpe.

When a mass at the end of a compressed spring is released, the elastic potential energy transfers into kinetic, and so on.

As we move on in this course, we will encounter other forms of energy (thermal, electrical, magnetic, nuclear and so on). We will find that if we include these other forms of energy into the total energy of the system then this new total energy will always be conserved. This generalised energy conservation law has been tested in every system at every scale (from the microscopic subatomic level to the very large cosmological scale) and has never been found to be violated.

The law of conservation of energy energy cannot be created or destroyed—it can only be transferred from one form to another states that energy cannot be created or destroyed—it can only be transferred from one form to another.

So a block slowing down and stopping because of friction can be described equivalently in these two ways:

Description 1: the total energy consists of just kinetic, and this is not conserved because an external force is doing work on the system.

Description 2: the frictional force did work reducing the kinetic energy of the block, but this resulted in generation of thermal energy. Including thermal energy as part of the total energy of the system means the total energy is conserved.

CHECK YOURSELF 5

A block slides down an inclined plane at constant speed. What energy transfers are taking place?

agravitational potential energy to kinetic energy

bkinetic energy to gravitational potential energy

ckinetic energy to thermal energy

dgravitational potential energy to thermal energy

Sankey diagrams

A convenient way to represent energy transfers is by using a Sankey diagram. Each energy transfer is represented by an arrow. The arrow’s width is proportional to the amount (or percentage) of energy transferred. Figure 3.33 shows a Sankey diagram for a wind turbine that produces electricity from the kinetic energy of the wind.

Figure 3.33: Sankey diagram for a wind turbine.

100 units of energy are coming in from the kinetic energy of the wind. The down arrows represent losses of energy, leaving a useful output for electricity production of 30 units. The efficiency of the system is then 30%.

CHECK YOURSELF 6

What is the efficiency of the transfers shown in the Sankey diagram in Figure 3.34?

Figure 3.34: For check yourself question 6.

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TEST YOUR UNDERSTANDING

32Describe the energy transfers in an oscillating pendulum as frictional forces bring it slowly to rest.

33Describe the energy transfers in an oscillating horizontal mass–spring system as frictional forces bring the system slowly to rest.

34Describe the energy transfers in an oscillating vertical mass–spring system. Ignore frictional effects.

35An elevator starts on the ground floor and stops on the tenth floor of a high-rise building. The elevator reaches a constant speed by the time it reaches the first floor and decelerates to rest between the ninth and tenth floors. Describe the energy transfers taking place between the first and ninth floors.

36A ball falls vertically moving at terminal velocity. Describe the energy transfers taking place.

37A car with its engine turned off coasts down an inclined plane at constant speed. Describe the energy transfers taking place.

Links

●We will meet the law of conservation of energy in many other parts of the course. Conservation of energy is useful also in solving many kinematics questions. In Unit B, for example, we will see how conservation of energy and a few simple assumptions allow us to calculate the average temperature of the earth and how the law is applied to thermodynamics. Also how the motion of electrons inside a conductor involves collisions between the electrons and the ions which are inelastic so the electrons transfer energy to the ions. This makes the ions vibrate faster about their equilibrium positions and so the conductor gets warmer, its temperature increases.

●In Unit C we will see that conservation energy implies that the ripples in a lake created when a stone is dropped in the lake get smaller as the ripples move away. In Unit D we will see what conservation of energy has to say about planetary orbits. And in Unit E we will see that conservation of energy and Einstein’s equivalence of mass and energy imply that vast amounts of energy may be released in nuclear reactions.