Work and stored energy

Definition

Energy store

A way in which energy is held by an object or system, such as a kinetic, gravitational, elastic, thermal or chemical store.

The work done by a force is equal to the energy transferred by that force.
This means you can use $W = F s$ to calculate how much energy goes into or out of an energy store.
When a force does work on an object, the energy in one of the object's stores increases by the amount of work done.
1. A crane that does $kJ40\ \text{kJ}$ of work lifting a steel beam at a steady speed increases the gravitational store of the beam by $kJ40\ \text{kJ}$ .
2. A bow that is drawn back with $J60\ \text{J}$ of work stores $J60\ \text{J}$ in its elastic store, ready to transfer to the arrow.
When an object does work against a force, the energy in one of its stores decreases by the amount of work done.
1. A bicycle that freewheels to a stop on a level road loses all of the energy in its kinetic store as it does work against friction and air resistance.
Energy is never created or destroyed in these transfers, so the energy lost from one store always equals the total energy gained by the other stores.
Some of the energy transferred usually ends up in the thermal stores of the surroundings, where it spreads out and is no longer useful.

Calculating energy transfers

Energy transfer calculations follow the same steps whichever stores are involved.
1. Identify the force doing the work and the distance moved along its line of action.
2. Calculate the work done with $W = F s$ .
3. Use the work done as the energy transferred, then add it to or take it away from the store involved.
A transfer can happen in several stages, and the energy can be followed from one store to the next.
1. When a ball is lifted and then dropped, the work done lifting it fills its gravitational store, and as it falls this energy moves to its kinetic store.
2. When the ball hits the ground, the energy moves to the thermal stores of the ball and ground, with some carried away by sound.
If a store is given a value, such as the energy in the kinetic store of a moving car, you can use $W = F s$ in reverse to find a force or a distance.

Example

Energy in the gravitational store of a lifted crate

A forklift truck lifts a crate with a steady upward force of $N2400\ \text{N}$ through a height of $m3.5\ \text{m}$ .

W=Fs=2400\ \text{N}\times3.5\ \text{m}=8400\ \text{J}

The energy in the gravitational store of the crate increases by $J8400\ \text{J}$ , which is $kJ8.4\ \text{kJ}$ .

Example

Braking force from the kinetic store

A car has $kJ300\ \text{kJ}$ in its kinetic store and the driver brakes to a stop in a distance of $m50\ \text{m}$ .
All of the energy in the kinetic store is transferred by the work done against the braking force.

F=\dfrac{W}{s}=\dfrac{300\,000\ \text{J}}{50\ \text{m}}=6000\ \text{N}

The average braking force is $N6000\ \text{N}$ , and the energy ends up mainly in the thermal stores of the brakes.

Example

Energy remaining after work against friction

A sledge has $J900\ \text{J}$ in its kinetic store at the bottom of a hill and slides $m20\ \text{m}$ across flat snow against a friction force of $N25\ \text{N}$ .

W=Fs=25\ \text{N}\times20\ \text{m}=500\ \text{J}

\text{energy left in the kinetic store}=900\ \text{J}-500\ \text{J}=400\ \text{J}

The sledge is still moving after $m20\ \text{m}$ , with $J400\ \text{J}$ in its kinetic store, while $J500\ \text{J}$ has been dissipated to the thermal stores of the sledge and snow.

Newton-metres and joules

Definition

Newton-metre

The unit obtained by multiplying a force in newtons by a distance in metres, which is equal in size to one joule.

Multiplying a force in newtons by a distance in metres gives an answer in newton-metres, $m\text{N m}$ .
Work done is an energy, so its answer can also be given in joules, $J\text{J}$ .
The two units are identical in size, so $J1\ \text{N m}=1\ \text{J}$ .
Converting between them changes only the unit, not the number, so $J750\ \text{N m}=750\ \text{J}$ .
Large amounts of energy are given with prefixes, which do change the number.
1. $J1\ \text{kJ}=1000\ \text{J}$ , so $m4.2\ \text{kJ}=4200\ \text{J}=4200\ \text{N m}$ .
2. $J1\ \text{MJ}=1\,000\,000\ \text{J}$ , so $J0.35\ \text{MJ}=350\,000\ \text{J}$ .
Convert prefixed values into joules before substituting them into $W = F s$ , so that the force comes out in newtons and the distance in metres.

Example

Converting units in a work calculation

A winch does $kJ1.8\ \text{kJ}$ of work raising a load through $m12\ \text{m}$ .
Convert the energy into joules, so $JW=1800\ \text{J}$ , which is also $m1800\ \text{N m}$ .

F=\dfrac{W}{s}=\dfrac{1800\ \text{N m}}{12\ \text{m}}=150\ \text{N}

The winch pulls with a force of $N150\ \text{N}$ .

Common Mistake

Do not multiply or divide by $1000$ when converting between newton-metres and joules, because $m1\ \text{N m}$ is exactly $J1\ \text{J}$ .
Do not forget the $1000$ when converting kilojoules into joules, because the prefix "kilo" means a thousand.
Do not write "heat energy" or "movement energy", because the correct names are the thermal store and the kinetic store.

Exam technique

Energy transfer calculations

State which store gains energy and which store loses energy before you calculate, as this often earns the first mark.
Show the conversion from $kJ\text{kJ}$ or $MJ\text{MJ}$ into $J\text{J}$ as a separate line of working.
If a question asks for an answer in $m\text{N m}$ , give the same number you found in joules with the new unit.
In a multi-stage transfer, describe each stage in order and name the store at each point.

Self review

How is the work done by a force related to the energy transferred?
What happens to the energy in the kinetic store of a bicycle that freewheels to a stop?
Convert $kJ2.5\ \text{kJ}$ into newton-metres.
A $N40\ \text{N}$ force does work over $m6.0\ \text{m}$ , so how much energy is transferred?
A car with $kJ200\ \text{kJ}$ in its kinetic store brakes to a stop in $m40\ \text{m}$ , so what is the average braking force?

Work and stored energy

Definition

Energy store

A way in which energy is held by an object or system, such as a kinetic, gravitational, elastic, thermal or chemical store.

The work done by a force is equal to the energy transferred by that force.
This means you can use $W = F s$ to calculate how much energy goes into or out of an energy store.
When a force does work on an object, the energy in one of the object's stores increases by the amount of work done.
1. A crane that does $kJ40\ \text{kJ}$ of work lifting a steel beam at a steady speed increases the gravitational store of the beam by $kJ40\ \text{kJ}$ .
2. A bow that is drawn back with $J60\ \text{J}$ of work stores $J60\ \text{J}$ in its elastic store, ready to transfer to the arrow.
When an object does work against a force, the energy in one of its stores decreases by the amount of work done.
1. A bicycle that freewheels to a stop on a level road loses all of the energy in its kinetic store as it does work against friction and air resistance.
Energy is never created or destroyed in these transfers, so the energy lost from one store always equals the total energy gained by the other stores.
Some of the energy transferred usually ends up in the thermal stores of the surroundings, where it spreads out and is no longer useful.

Calculating energy transfers

Energy transfer calculations follow the same steps whichever stores are involved.
1. Identify the force doing the work and the distance moved along its line of action.
2. Calculate the work done with $W = F s$ .
3. Use the work done as the energy transferred, then add it to or take it away from the store involved.
A transfer can happen in several stages, and the energy can be followed from one store to the next.
1. When a ball is lifted and then dropped, the work done lifting it fills its gravitational store, and as it falls this energy moves to its kinetic store.
2. When the ball hits the ground, the energy moves to the thermal stores of the ball and ground, with some carried away by sound.
If a store is given a value, such as the energy in the kinetic store of a moving car, you can use $W = F s$ in reverse to find a force or a distance.

Example

Energy in the gravitational store of a lifted crate

A forklift truck lifts a crate with a steady upward force of $N2400\ \text{N}$ through a height of $m3.5\ \text{m}$ .

W=Fs=2400\ \text{N}\times3.5\ \text{m}=8400\ \text{J}

The energy in the gravitational store of the crate increases by $J8400\ \text{J}$ , which is $kJ8.4\ \text{kJ}$ .

Example

Braking force from the kinetic store

A car has $kJ300\ \text{kJ}$ in its kinetic store and the driver brakes to a stop in a distance of $m50\ \text{m}$ .
All of the energy in the kinetic store is transferred by the work done against the braking force.

F=\dfrac{W}{s}=\dfrac{300\,000\ \text{J}}{50\ \text{m}}=6000\ \text{N}

The average braking force is $N6000\ \text{N}$ , and the energy ends up mainly in the thermal stores of the brakes.

Example

Energy remaining after work against friction

A sledge has $J900\ \text{J}$ in its kinetic store at the bottom of a hill and slides $m20\ \text{m}$ across flat snow against a friction force of $N25\ \text{N}$ .

W=Fs=25\ \text{N}\times20\ \text{m}=500\ \text{J}

\text{energy left in the kinetic store}=900\ \text{J}-500\ \text{J}=400\ \text{J}

The sledge is still moving after $m20\ \text{m}$ , with $J400\ \text{J}$ in its kinetic store, while $J500\ \text{J}$ has been dissipated to the thermal stores of the sledge and snow.

Newton-metres and joules

Definition

Newton-metre

The unit obtained by multiplying a force in newtons by a distance in metres, which is equal in size to one joule.

Multiplying a force in newtons by a distance in metres gives an answer in newton-metres, $m\text{N m}$ .
Work done is an energy, so its answer can also be given in joules, $J\text{J}$ .
The two units are identical in size, so $J1\ \text{N m}=1\ \text{J}$ .
Converting between them changes only the unit, not the number, so $J750\ \text{N m}=750\ \text{J}$ .
Large amounts of energy are given with prefixes, which do change the number.
1. $J1\ \text{kJ}=1000\ \text{J}$ , so $m4.2\ \text{kJ}=4200\ \text{J}=4200\ \text{N m}$ .
2. $J1\ \text{MJ}=1\,000\,000\ \text{J}$ , so $J0.35\ \text{MJ}=350\,000\ \text{J}$ .
Convert prefixed values into joules before substituting them into $W = F s$ , so that the force comes out in newtons and the distance in metres.

Example

Converting units in a work calculation

A winch does $kJ1.8\ \text{kJ}$ of work raising a load through $m12\ \text{m}$ .
Convert the energy into joules, so $JW=1800\ \text{J}$ , which is also $m1800\ \text{N m}$ .

F=\dfrac{W}{s}=\dfrac{1800\ \text{N m}}{12\ \text{m}}=150\ \text{N}

The winch pulls with a force of $N150\ \text{N}$ .

Common Mistake

Do not multiply or divide by $1000$ when converting between newton-metres and joules, because $m1\ \text{N m}$ is exactly $J1\ \text{J}$ .
Do not forget the $1000$ when converting kilojoules into joules, because the prefix "kilo" means a thousand.
Do not write "heat energy" or "movement energy", because the correct names are the thermal store and the kinetic store.

Exam technique

Energy transfer calculations

State which store gains energy and which store loses energy before you calculate, as this often earns the first mark.
Show the conversion from $kJ\text{kJ}$ or $MJ\text{MJ}$ into $J\text{J}$ as a separate line of working.
If a question asks for an answer in $m\text{N m}$ , give the same number you found in joules with the new unit.
In a multi-stage transfer, describe each stage in order and name the store at each point.

Self review

How is the work done by a force related to the energy transferred?
What happens to the energy in the kinetic store of a bicycle that freewheels to a stop?
Convert $kJ2.5\ \text{kJ}$ into newton-metres.
A $N40\ \text{N}$ force does work over $m6.0\ \text{m}$ , so how much energy is transferred?
A car with $kJ200\ \text{kJ}$ in its kinetic store brakes to a stop in $m40\ \text{m}$ , so what is the average braking force?

2.2.14 Work, stored energy and units of energy

Work and stored energy

Calculating energy transfers

Energy in the gravitational store of a lifted crate

Braking force from the kinetic store

Energy remaining after work against friction

Newton-metres and joules

Converting units in a work calculation

Energy transfer calculations

Review 2.2.14 Work, stored energy and units of energy by teaching Genie

2.2.14 Work, stored energy and units of energy

Work and stored energy

Calculating energy transfers

Energy in the gravitational store of a lifted crate

Braking force from the kinetic store

Energy remaining after work against friction

Newton-metres and joules

Converting units in a work calculation

Energy transfer calculations

Review 2.2.14 Work, stored energy and units of energy by teaching Genie

2.2.14 Work, stored energy and units of energy

Work and stored energy

Calculating energy transfers

Energy in the gravitational store of a lifted crate

Braking force from the kinetic store

Energy remaining after work against friction

Newton-metres and joules

Converting units in a work calculation

Energy transfer calculations

Review 2.2.14 Work, stored energy and units of energy by teaching Genie

2.2.14 Work, stored energy and units of energy Revision Guide

2.2.14 Work, stored energy and units of energy

Work and stored energy

Calculating energy transfers

Energy in the gravitational store of a lifted crate

Braking force from the kinetic store

Energy remaining after work against friction

Newton-metres and joules

Converting units in a work calculation

Energy transfer calculations

Review 2.2.14 Work, stored energy and units of energy by teaching Genie

2.2.14 Work, stored energy and units of energy Revision Guide