# Topic 5 - Forces

?

## Vector and Scalar Quantities

Vectors quantities have a magnitude and direction.
Lots of physical quantities are vector quantities.
The vector quantities are:

• Force
• Velocity
• Displacement
• Acceleration
• Momentum
Scalar quantities only have magnitude and no direction.
The scalar quantities are:
• Speed
• Distance
• Mass
• Temperature
• Time
Vectors are usually represented by an arrow with the length of the arrow showing the magnitude and the direction showing the direction of the quantity.
E.g. If two arrows are the same length but different directions, on a car for example, the speed (scalar) is the same but the velocity (vector is different).
1 of 9

## Contact and Non-Contact Forces

A force is a push or a pull on an object that is caused by it interacting with something.
When two objects have to be touching for a force to act, the force is a contact force.
Examples of contact forces:

• Friction
• Air resistance
• Tension (in ropes)
• Normal contact force
When two objects do not have to be touching for a force to act, the force is a non-contact force.
Example of non-contact forces:
• Magnetic force
• Gravitational force
• Electrostatic force
When two objects interact there is a force produced on both objects.
An interaction pair is a pair of forces that are equal and opposite and act on two interacting objects.
2 of 9

## Weight, Mass and Gravity

Gravity attracts all masses and anything near a planet or a star is attracted to it very strongly.
It has two important effects:

• On the surface of a planet, it make all things fall towards the ground
• It gives everything a weight.
Mass is the amount of ‘stuff’ in an object and has the same value anywhere in the universe.
Weight is the force acting on an object due to gravity (the pull of the gravitational force on the object). Close to Earth, the force is caused by the gravitational field around the Earth.
Gravitational field strength is stronger the closer you are to the mass causing the field, and stronger for larger masses.
A 1kg mass will weigh less on the Moon (about 1.6N) than it does on Earth (about 9.8N), because the gravitational field strength on the surface of the moon is less.
Weight is measured in newtons and the force acts from a single point on the object called its centre of mass (a point at which you assume the whole mass is concentrated).
Weight is measured using a calibrated spring balance (or newtonmeter).
Mass is not a force, it is measured in kilograms with a mass balance (or scales).
Weight is directly proportional to mass.
3 of 9

## Resultant Forces

When multiple forces act on an object at a single point, they can add together or subtract from each other until there’s the equivalent of just one force acting in a single direction called the resultant force.
You need to be able to describe all of the forces acting on an isolated object or a system (every force acting on the object or system but none of the forces the object or system exerts on the rest of the world).
For example, with a skydiver, their weight acts on them, pulling them towards the ground and drag (air resistance) pulls them in the opposite direction to their motion.
This can be shown by a free body diagram using arrows to represent the magnitude and direction of the forces.
If the forces all act along the same line (they are parallel), the overall effect is found by adding those going in the same direction and subtracting any going in the opposite direction.
For example, with a car with 1500N ⬆️, 1500N ⬇️, 1200N ⬅️ and 1000N ➡️ you would minus the 1500-1500= 0N and minus the 1200-100 = 200N and so therefore the resultant force is 200N to the left.

4 of 9

## Work Done and Resultant Forces

If a resultant force moves an object, work is done.
When a force moves an object through a distance, energy is transferred and work is done.
To make something move (or keep it moving if there is a frictional force), a force must be applied.
The thing applying the force needs a source of energy and the force does ‘work’ to move the object and energy is transferred from one store to another.
Whether energy is transferred usefully or wasted you can still say that work is done.
Work done and energy transferred are the same thing.
1 Joule = 1 Newton Metre
When you push something along a rough surface (like a carpet) you are doing work against frictional forces. Energy is being transferred to the kinetic energy store of the object because it starts moving, but some is also being transferred to the thermal energy stores due to friction. This causes the overall temperare of the object to increase.
To use a scale drawing to find out the resultant force you draw all of the forces acting on an object (to scale and ‘tip-to-tail’) and then draw a straight line from the start of the first force to the end of the last force (this is the resultant force). Measure the length of the resultant force on the diagram to find the magnitude, angle and therefore direction.

5 of 9

## Forces and Equilibrium

Scale diagrams can also be used to check if forces are balanced and to split a force into component parts.
If all the forces acting on an object combine to a resultant force of zero, the object is in equilibrium.
If an object is in equilibrium, on a scale diagram the top of the last force you draw you should end where the tale of the first force begins (e.g. for three forces, the scale diagram will form a triangle).
When drawing the last force, it’s in the opposite direction to how you’d draw a resultant force.
To find a missing force in an object of equilibrium, draw the scale diagram and the line connecting the first force to the last force is the missing force (measure size and direction).
Not all forces act horizontally and vertically, so when drawing a scale diagram these forces can be split into two components at right angles to each other and acting together these components have the same effect as a single force.
This is called resolving a force and can be drawn on a scale grid:
1 - Decide on a scale factor (e.g. 1cm = 1N)
2 - Draw the force to scale on the grid and at the right angle and form a right angled triangle
3- Measure the lengths of the horizontal and vertical components and covert to N

6 of 9

## Forces and Elasticity

Forces can make objects change shape as well as making them move.
They can change shape temporarily or permanently depending on the objects and the forces applied.
When you apply force to an object it may cause it to stretch, compress or ben .
To do this, you need more than one force acting on an object, otherwise the object would simply move in the direction of the applied force, instead of changing shape.
Work is down when a force stretches are compresses and object and causes energy to be transferred to the elastic potential energy store of the object.
If the object is ‘elastically deformed’ all this energy is transferred to the object’s elastic potential energy store.
An object is elastically deformed if it can go back to its original shape and length after the force has been removed.
Objects that can be elastically deformed are called elastic objects (e.g. a spring or an elastic band).
An object has be inelastically deformed if it doesn’t return to its original shape and length after the force has been removed.

7 of 9

## Force and Extension

Extension is directly proportional to force.
If a weight is attached to the bottom of a spring and it is supported at the top, it stretches.
The extension of a stretched spring (and other elastic objects) is directly proportional to the load or force applied.
Force (N) = spring constant (N/m) x extension (m).
The spring constant depends on the material that you are stretching (e.g. a stiffer spring has a great spring constant).
The equation also works for compression where the extension is simply the difference between the natural and compressed lengths (the compression).
There’s a limit to the amount of force you can apply to an object for the extension to keep on increasing proportionally.
On a graph of force against extension for an elastic object, there is a maximum force above which the graph curves, showing that extension is no longer proportional to force.
This is known as the limit of proportionally and is marked on the graph as ‘P’.
If you reverse the axes so it is extension against force, the graph still starts with a straight part but starts to curve upwards once you go past the limit of proportionally, instead of downwards.

8 of 9

## Investigating Springs - Required Practical

Set up a weighted stand with a spring attached to the top using a clamp.
Clamp a fixed ruler beside this and attach a hanging mass to the spring.
Use tape to mark the end of the spring and be sure to have plenty of extra masses on hand.
Measure the mass of each of your masses and calculate their weight (the force applied) before you start the experiment.
You could also do a pilot experiment and see if the six or more masses you’re using limit the proportionality of the spring. If they do, you should use smaller masses so that you still have enough measurements for your graph.
Throughout the experiment, to check if the deformation is elastic or inelastic, you can remove each mass temporarily to see if the spring goes back to the previous destination.
Practical method:
1 - Measure the natural length of the spring (when no load is applied) with a millimetre ruler clamped to the stand. Make sure you the the reading at eye level and add a marker (e.g. a thin ***** of tape) to the bottom of the spring to make the reading more accurate
2 - Add a mass to the spring and allow the spring to come to rest. Record the mass and measure the new length of the spring. The extension is the change in length.
3 - Repeat this process until you have 6 or more measurements to work with.

9 of 9