Work and Power

Energy

Define work done.

The energy transferred when a force moves an object through a distance.

What is the unit of work done?

Joule (J).

What does 1 joule of work mean?

1 J of work is done when 1 J of energy is transferred.

What equation calculates work done when a force acts in the direction of motion?

ΔW = FΔs.

What does F represent in ΔW = FΔs?

Force in newtons (N).

What does Δs represent in ΔW = FΔs?

Distance moved in the direction of the force, in metres (m).

What is the relationship between work done and energy transferred?

Work done equals the amount of energy transferred.

What happens to the total amount of energy when work is done?

Energy is transferred between stores but the total energy is conserved.

What is the principle of conservation of energy?

Energy cannot be created or destroyed; it can only be transferred between stores.

How is work done calculated when lifting an object vertically at constant speed?

ΔW = mgΔh.

Why is the force needed to lift an object at constant speed equal to mg?

The lifting force balances the object's weight, so F = mg.

What energy store increases when an object is lifted?

Its gravitational potential energy store.

How are work done and gravitational potential energy related when lifting an object?

The work done on the object equals its gain in gravitational potential energy.

A 2.2 kg brick is lifted vertically by 1.24 m. Calculate the work done.

W = mgΔh = 2.2 × 9.81 × 1.24 = 26.8 J.

What equation calculates work done when the force acts at an angle to the displacement?

ΔW = FΔs cosθ.

What does θ represent in ΔW = FΔs cosθ?

The angle between the force and the displacement.

Why is cosθ used when calculating work done by a force at an angle?

Only the component of the force parallel to the displacement does work.

What is the component of a force F acting in the direction of motion when the angle between them is θ?

F cosθ.

What is the work done if a force is perpendicular to the displacement?

Zero, because cos90° = 0.

What is the work done if the force and displacement are in the same direction?

W = FΔs because cos0° = 1.

A 120 N force pulls a kite at 30° to the horizontal while it moves 40 m horizontally. What is the work done?

W = 120 × 40 × cos30° ≈ 4.16 × 10³ J.

Define power.

The rate of energy transfer or the rate of doing work.

What is the unit of power?

Watt (W).

What does one watt mean?

One joule of energy transferred per second: 1 W = 1 J s⁻¹.

What equation links power, energy transferred and time?

P = E/t.

What equation links power, work done and time?

P = ΔW/t.

What does P represent?

Power in watts (W).

What does E represent in P = E/t?

Energy transferred in joules (J).

What does t represent in power equations?

Time in seconds (s).

How can power be calculated from force, distance and time?

P = FΔs/t.

How can the power needed to lift an object vertically be calculated?

P = mgΔh/t.

What does a more powerful machine do compared with a less powerful machine?

It transfers energy or does work at a greater rate.

Does greater power necessarily mean more total energy is transferred?

No. Power describes how quickly energy is transferred.

A forklift lifts a 120 kg crate vertically by 5.00 m in 4.0 s. Calculate its useful power.

P = mgΔh/t = (120 × 9.81 × 5.00)/4.0 ≈ 1470 W.

Convert 1470 W to kW.

1.47 kW.

How many watts are in 1 kilowatt?

1000 W.

How many watts are in 1 megawatt?

1 × 10⁶ W.

How many watts are in 1 gigawatt?

1 × 10⁹ W.

How many watts are in 1 terawatt?

1 × 10¹² W.

Define efficiency.

The proportion of the total input energy or power that is transferred usefully.

What equation calculates efficiency using energy?

Efficiency = useful energy output ÷ total energy input.

What equation calculates efficiency using power?

Efficiency = useful power output ÷ total power input.

Why can efficiency be calculated using either energy or power?

Power is energy transferred per unit time, so for the same time interval the ratio is unchanged.

What range of values can efficiency have as a decimal?

Between 0 and 1.

How do you convert efficiency from a decimal to a percentage?

Multiply by 100.

How do you convert percentage efficiency to a decimal?

Divide by 100.

Can a machine have an efficiency greater than 100%?

No, because useful energy output cannot exceed the total energy input.

What happens to energy that is not transferred usefully?

It is transferred to other stores, often the thermal energy stores of the surroundings.

Why are real machines never perfectly efficient?

Some energy is always transferred to unwanted stores, for example through friction, heating or sound.

A machine has a useful power output of 1470 W and total power input of 3000 W. Calculate its efficiency.

Efficiency = 1470/3000 = 0.49 = 49%.

If a machine is 80% efficient, what fraction of its input energy is transferred usefully?

0.80.

If a machine receives 500 J of energy and is 80% efficient, how much useful energy does it transfer?

Useful energy = 0.80 × 500 = 400 J.

If a machine has a useful output of 400 J and an efficiency of 80%, what is its total energy input?

Total input = 400/0.80 = 500 J.

How can total power input be calculated from useful power output and efficiency?

Total power input = useful power output ÷ efficiency.

How can useful power output be calculated from total power input and efficiency?

Useful power output = efficiency × total power input.

What happens to work done against friction?

Energy is transferred mainly to thermal energy stores.

Why does energy lost to heating not violate conservation of energy?

The energy has not disappeared; it has been transferred to a different energy store.

What is meant by useful energy transfer?

Energy transferred to the store or form required for the intended purpose.

What is meant by wasted energy?

Energy transferred to stores that are not useful for the intended purpose.