Forces & Their Interactions Notes

Q: What is the difference between scalars and vectors?

A scalar has only a size; a vector also has a direction. A scalar quantity is fully described by a number and a unit. A vector quantity also needs a direction.

Q: How do we calculate weight?

Weight is the force of gravity on a mass: W = m \times g. Here W is the weight (N), m is mass (kg) and g is gravitational field strength (N/kg). Weight acts towards the centre of the gravitational body, downwards on Earth. Mass is fixed, but weight changes with the field strength.

Oxford AQA IGCSE Physics: Revision notes

Key facts

Non-contact forces: gravity, electrostatic and magnetic. Contact forces: friction, air resistance, tension, normal contact force.
A force is a vector: it has size and direction.
Weight $W = m \times g$ , in newtons.
Hooke's Law: $F = k \times e$ , within the limit of proportionality.
Elastic objects return to their shape; inelastic ones do not.

Contact and non-contact forces

Contact forces need the objects to touch; non-contact forces act across a gap.

The friction force resists relative motion between surfaces and may heat them. The air resistance force is friction acting on an object moving through air.

Block pushed along a table: normal force, friction and the push are contact forces; weight (gravity) acts across a gap.

Non-contact forces

Gravity
Electrostatic force
Magnetic force

Contact forces

Friction
Air resistance
Tension and normal contact force

Which of these is a non-contact force?

Forces in pairs

Forces arise from an interaction between two objects, and are shown as vector arrows.

Each object exerts a force on the other. Forces are vectors: they have magnitude and direction, and are drawn as arrows.

A book on a table: weight down, normal contact force up (equal size)

How are forces usually drawn?

Scalars and vectors

A scalar has only a size; a vector also has a direction.

A scalar quantity is fully described by a number and a unit. A vector quantity also needs a direction.

Walk 4 m east then 3 m north. Distance (scalar) is 7 m; displacement (vector) is 5 m in the direction A to B.

Scalar (magnitude only)

Distance
Speed
Time

Vector (magnitude and direction)

Displacement
Velocity
Acceleration, force, momentum

Which of these is a vector?

Weight

Weight is the force of gravity on a mass: $W = m \times g$ .

Here $W$ is the weight (N), $m$ is mass (kg) and $g$ is gravitational field strength (N/kg). Weight acts towards the centre of the gravitational body, downwards on Earth. Mass is fixed, but weight changes with the field strength.

g = 10field strength g (N/kg)

Weight W = mg is directly proportional to mass. Drag g: at 10 N/kg a 50 kg student weighs 500 N.

Weight $W = m \times g$

Worked example

A student has a mass of 50 kg. Find their weight on Earth, where $g = 10$ N/kg.

1
Write the equation: $W = m \times g$ .
2
Substitute: $W = 50 \times 10$ .

An astronaut's mass is 70 kg on Earth. What is it on the Moon?

Elastic distortion

An elastic object returns to its original shape when the force is removed.

A force may change the shape of an object. A force applied to an elastic object stores elastic potential energy in it.

Force against extension: an elastic object unloads along the loading line; an inelastic one keeps a permanent extension. Illustrative values.

Elastic distortion Inelastic distortion After the force is removed Returns to original shape Does not return to original shape Condition Force removed Force removed

	Elastic distortion	Inelastic distortion
After the force is removed	Returns to original shape	Does not return to original shape
Condition	Force removed	Force removed

Elastic distortion

After the force is removed:: Returns to original shape
Condition:: Force removed

Inelastic distortion

After the force is removed:: Does not return to original shape
Condition:: Force removed

A paper clip is bent and stays bent. What type of distortion is this?

Hooke's Law

Within the limit of proportionality, force is directly proportional to extension: $F = k \times e$ .

Here $F$ is force (N), $k$ is the spring constant (N/m) and $e$ is extension (m). While Hooke's Law is obeyed, the graph is a straight line through the origin.

Hooke's Law for a spring with k = 20 N/m: force is directly proportional to extension

Worked example

A spring has a spring constant of 20 N/m. What force produces an extension of 0.15 m?

1
$F = k \times e$
2
$F = 20 \times 0.15$

1
Measure
the natural length of the spring with a ruler
2
Add a mass
hang one known weight from the spring
3
Measure again
find the new length and work out the extension
4
Repeat
add more weights one at a time
5
Plot
force against extension

Required practical: force and extension of a spring

A spring has $k = 100$ N/m. What is the extension for a force of 5 N?

Try an exam question

A 2.5 kg object hangs from a spring with spring constant 100 N/m. Calculate its weight (g = 10 N/kg) and the extension of the spring.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.