Virtually all the 20 or so formulae studied in the double award
GCSE **science** syllabus are listed below - together with appropriate
units. Many of these formulae may turn up in your maths papers too - though
usually without referring to units. Answering the questions below (given with
each formula) will give you practice in rearranging and solving formulae for
the maths GCSE as well as the physics. (See the further
formulae page for additional formulae needed for the single-award GCSE Physics
syllabus).

*(NOTE: these formulae may not be on your particular syllabus,
and the list below of formulae required may be a bit out of date by the time
you come to view this page!)*

Isaac Newton (1643-1727) |

[1] **Newton's second law of motion: **
**F = ma** or **force = mass x acceleration**

where F is the force in Newtons (N), m is the mass in kilograms (kg) and
a is the acceleration (m/s^{2} ... this can also be written as ms^{-2}
).

[Newton discoved this law through experiment. It is the second of his three
laws of motion.]

[2] **Weight: W = mg**, where W
= weight of an object, m is its mass and g is the gravitational field strength.

*Question*s: (a) what is the combined mass of a cyclist and his bike
if an unbalanced force of 88 N is needed to produce an acceleration of 1.1
m/s^{2} ? (Answer is 80 kg). (b) What is the mass of a chicken that
weighs 15 N? Assume g = 10 N/kg. (Answer is 1.5 kg)

[3] **Turning forces: ** **M
= Fd **or **moment = force × perpendicular distance**
. F is the force in newtons (N), d is the perpendicular distance of the force's
line of action from the pivot and M is the moment of the force in newton-metres
(N m).

*Question *: what is the moment, about the pivotal point, produced
by a diver of mass 75 kg standing at the very end of a 3m diving board? (*Answer*
is 225 Nm).

James Joule (1818-1889) |

[4] **Work** : **W = E =
Fd** i.e. **work done = force × distance** . W is
the work done and E is the energy transferred - both in joules - when a force
F moves an object a distance d in the direction of the force.

*Question *: what distance does a force of 25 N, pushing a wooden block
at constant speed over a rough surface, have to act in order to produce 100
J of heat energy as a result of friction? (*Answer* is 4 m).

[5] The change in **gravitational potential
energy** when a mass m moves through a vertical height h: **GPE
= mgh** where g is the gravitational field strength (N/kg).

*Question *: how high must a 500 g ball be thrown in order to change
the ball's potential energy by 100 J (assume g = 10 N/kg)? (*Answer*
is 20 m).

[6] The **kinetic energy** of a
mass m moving at a velocity v is given by : **KE = ½mv ^{2}**.

James Watt (1736-1819) |

[7] **Power and energy: P = E/t **i.e.
**power = energy transfer per second**. P is the power in watts,
E is the energy transferred in joules during a time t seconds.

*Question* : how much energy is transferred while heating the water
in a 2kW electic kettle which takes 2 minutes to come to the boil (ignore
heat losses to suroundings) ? (*Answer* is 240 kJ)

[8] **Density = mass/volume**.

*Question:* calculate the volume of iron in a 1 kg mass. The density
of iron is 7.8 g/cm^{3}. (Answer is 128 cm^{3})

---oooOooo---

Charles Augustin de Coulomb (1736-1806) |

[9] **Current and charge:** **I
= Q/t** i.e. **current = charge / time**. I is current
in amps (A), Q is charge in coulombs (C) and t is time in seconds (s).

[ Imagine a mountain stream. In the same way that the *water* current
could be measured as the amount of water flowing past a point per second,
the *electrical* current I is the amount of *charge* Q that
flows per second (i.e. Q/t). ]

*Question* : how much charge flows in 10 seconds when the current is
3 A ? *(Answer:* 300C.)

[10] **Electrical resistance**:
**R = V/I **(** **or **V = IR**) where
V is the voltage in volts (V), I is the current in amps (A), R the resistance
in ohms (Ω).

André Marie Ampère (1775-1836) |

[The electrical current I corresponds to the amount of water per second
flowing past a place in the mountain stream analogy mentioned above; the voltage
V can be thought of as the amount of 'pull' on the electrons and corresponds
to the gravitational pull on the water molecules (the steeper the river bed
, the greater the current); and the resistance R corresponds to the drag caused
by the river bed, slowing down the current.]

*Question *: a current of 2.5 A flows through a wire when the voltage
across it is 12.5 V. Calculate the resistance of the wire. *(Answer*:
6Ω)

Georg Ohm (1789-1854) |

[11] **Resistors in series:**
**R = R _{1} + R_{2} + R_{3 }**. R is
the total resistance of resistors R

[ The current is the same through all the resistor, and the voltage of the
supply is split between them. In the analogy of the mountain stream, the water
has a succession of obstacles to get through: therefore it slows down.

*Question* : calculate the total resistance of three resistors conncted
in series, if their resitances are 6Ω, 8Ω and 24Ω. (*Answer*
is 38Ω).

[12] **Resistors in parallel:**
**I = I _{1} + I_{2} + I_{3 }**. The net
current I is the sum of the currents through the individual of resistors R

[13] **Voltage and Energy transfer**:
**V = E/Q** i.e. **one volt = one joule per coulomb**.
V is voltage (V), E is energy transferred in joules (J), and Q is the charge
in coulombs (C) flowing.

[In a resistor, the energy transfer is from electrical to heat.]

*Question* : what is the energy transfer when 5 C flows across a voltage
of 6 V ? (*Answer* is 30C.)

[14] **Electrical Power**: **P
= V×I** i.e. **watts = volts × amps** . P
is the power in watts (W).

[As with all forms of power, electrical power is enery transfer per second
i.e. energy-transfer / time]

*Question* : the current in a kettle element is 9.5 A when the voltage
across it is 240 V. Calculate the power of the kettle element. (*Answer*
is 2.28 kW.)

*Question* : what current flows through a 100W bulb connected to a
240 mains supply? (*Answer* is 0.42 A)

[15]** Power and energy: P = E/t **i.e.
**power = energy transfer per second** . E is the energy transferred
during a time t.

*See above: formula for electical power and energy same as for mechanical.*

[16] **Energy cost = number of kW ×
time in h × cost of 1 kW h**

*Question* : an 8 kW shower is used for a total of 90 minutes. Calculate
the cost of the energy transferred to the shower, if the cost 1 kW h is 8p.
(*Answer* is 96p).

---oooOooo---

[17] **Wave speed: ** **v
= fλ** i.e. **velocity = frequency × wavelength**,
f = frequency and λ = wavelength.

*Question *: the speed of sound in air is 330 m/s. Calculate the frequency
of a sound that has a wavelength of 0.50 m. (Answer is 660 Hz).

[18]**Frequency: ** **f
= 1/T** i.e. **frequency = 1 / Time Period**.

*Question *: What is the period of one vibration of an ear drum picking
up a sound of equency 1 kHz? (Answer is 1 ms.)

---oooOooo---

[19] The **half-life** of a radioactive
isotope is the average time it takes for the number of undecayed nuclei to
halve.

Henri Becquerel (1852-1908) |

The **rate of decay** (or **activity**) is the
number of nuclei that decay each second in a radioactive sample. It is measured
in Becquerel (Bq), where 1 BQ = 1 decay per second. Since the rate of decay
is proportional to the number of undecayed nuclei, the half-life is also the
time taken for the rate of decay to halve.

[Some elements exist in a number of forms called *isotopes*, depending
on how many *neutrons* they have. Some of these isotopes are radioactive.
The three types of radioactive emission are: alpha (α)
particles, which - consisting of 2 protons and 2 neutrons i.e. a helium
nucleus - are relatively heavy; beta (β) particles,
which, being electrons, are much lighter than the α particles; and gamma
(γ) rays, which are at short-wavelength end of the elecromagnetic
spectrum.]

*Question *: The activity of a sample of wood from a freshly cut tree
is measured to be 80 Bq. Estimate the activity of the sample after two half-lives
have elapsed. (Answer = 20 Bq).

Marie Curie (1867-1934) |

You cannot hope to build a better world without improving the individuals.

To that end, each of us must work for our own improvement and, at the same time, share a general responsibility for all humanity, our particular duty being to aid those to whom we think we can be most useful.

— *Marie Curie, who won a Nobel prize for her research into radioactivity.*