Work DoneWork is done (or energy is used up), when a force moves an object.

d

F The amount of work done depends on the distance the object is moved.

The work done (EW) is given by the formula:

d FEW

x

÷EW

F d

Quantity UnitWork Done ( EW )

Force ( F )

Distance ( d )

Joules ( J )

Newtons ( N )

Metres ( m )

Example 1Calculate the work done when a force of 12 N moves a suitcase a distance of 20 m.

N 12F

m 20d?EW

d FEW

2012

J 240EW

Example 2A gardener does 12 kJ of work by pushing a wheelbarrow a distance of 150 m.Calculate the force exerted on the wheelbarrow by the gardener.

kJ 12EW J 10 12 3

m 150d?F

dEF W

1501012 3

N 80F

Yellow BookWork Done – Page

Q

Potential EnergyWhen an object is situated above ground level, it is said to have potential energy (EP), sometimes known as gravitational potential energy.

m

hground level

x

÷

The potential energy stored in a mass m which is a height h metres above ground level is given by: h g mEP

EP

m g h

Quantity UnitPotential Energy

( EP )

Mass ( m )

Gravitational Field Strength ( g )

Height ( h )

Joules ( J )

Kilograms ( kg )

Newtons per Kilogram ( N kg-1 )

Metres ( m )

Example 1A 3 kg box is on a shelf 4 m above the ground.Calculate the potential energy stored in the box.

kg 3mm 4h

-1kg N 10g?EP

h g mEP 4 10 3

J 120EP

Example 2A 2 kg flowerpot sits on a windowsill. The flowerpot has 50 J of energy.Calculate the height of the windowsill above the ground.

kg 2m

J 50EP

?h

g mEh P

10 250

m 2.5h

-1kg N 10g

Yellow BookPotential Energy – Page 71

Q87 (a) (b) (c), 89, 92, 93, 95, 96

My Potential EnergyHere is how to calculate my potential energy as I run up a set of stairs.

hm

ResultsMy mass, kg m

1kg N 10g

m h

The amount of energy supplied by me is J.The energy used up by me as I run up the stairs is J.

Calculate your potential energy using:

h g mEP

My PowerMeasuring my power when I climb up stairs.

I can calculate the power I develop if I know the time it takes to get up the stairs.Calculation

J E

s t

?P

tEP

W P

The energy supplied by me as I climbed up the stairs was

J.(from previous work)

stopwatch

Yellow BookEnergy and Power – Page 73

Q109, 110, 111, 112

Kinetic EnergyAll moving objects have kinetic energy (EK).

The formula for kinetic energy is 2K v m2

1E

x

÷EK

m v221

Quantity UnitKinetic Energy

( EK )

Mass ( m )

Speed ( v )

Joules ( J )

Kilograms ( kg )

Metres per Second ( ms-1 )

Example 1A car has a mass of 500 kg and a speed of 15 ms-1.Calculate the kinetic energy of the car.

kg 500m-1ms 15v

?EK

2K v m 2

1E

215 500 21

J 56,250EK

Example 2An 8 kg object has 36 J of kinetic energy.Calculate the speed of the object.

kg 8m

J 36EK ?v

m Ev21

K2

8 36

21

436

9v2

9v-1ms 3v

Yellow BookKinetic Energy – Page 72

Q99, 102, 103, 104

Potential to KineticPotential energy is always turned into kinetic energy (e.g when a high object falls to the ground).

We can use the relationship to calculate the speed reached by a falling object.

KP EE

all kinetic

all potential

all kinetic

Example 1A 3 kg object is on a window ledge 45 m above the ground.It then falls off the ledge to the ground below.

45 m

m = 3 kg

(a) Calculate the potential energy at the start.

kg 3mm 45h

-1kg N 10g?EP

h g mEP

45 10 3 J 1350EP

(b) State how much kinetic energy the object has, just as it reaches the ground.

PK EE

J 1,350EK

(c) Calculate the speed of the object at the ground.

2K v m 2

1E

2v m 211,350

2v 3 211,350

2v 1.51,350

1,350v 1.5 2

1.51,350v2

900v2

900v-1ms 30v

Q1. A 7 kg flowerpot sits on a window ledge 25 m above the ground.

(a) Calculate the potential energy of the flowerpot on the window ledge.

(b) The flowerpot falls off the ledge. State the kinetic energy as the flowerpot hits

the ground.(c) Calculate the speed it hits the ground at.

1,750 J

1,750 J

22.4 ms-1

Q2. An object of mass 5 kg falls off a shelf.It hits the ground with a speed of 12 ms-1.

(a) Calculate the kinetic energy of the object just as it hits the ground.

(b) Calculate the height of the shelf.360 J

7.2 m

Combining Potential and Kinetic

PK EE

h g mv m 21 2

mh g mv 2

1 2

h gv 21 2

h g 2v2

h g 2v Don’t need mass to calculate speed.

Yellow BookPotential and Kinetic Energy – Page 74

Q115, 116, 119, 120