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Force, Scalars and Vectors

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Force, Scalars and Vectors

There are essentially only three types of forces in the universe:

gravitational

electric and nuclear (two types which are covered in the Particle Physics section).

Force, Scalars and Vectors

All forces are vectors.

They have an associated direction attributable to them as well as magnitude (size)

e.g. weight is a force which acts towards the centre of the Earth

(scalars only have magnitude e.g. mass).

The magnitude of a vector is measured in newton (N).

Force, Scalars and Vectors

Adding and subtracting vectors is easy! consider the following forces:

10 N

7 N

17 N

=

OR

10 N

-7 N

3 N

=

Note that these forces act through one point.

That is convenient for the moment and practical as it is often true - the point is often the centre of gravity (mass).

Force, Scalars and Vectors

Centre of gravity.

The point through which the weight of a rigid body acts.

You might wish to research neutral, stable and unstable equilibrium if you are not familliar with the terms.

Centre of mass

of a rigid body is the point through which any resultant force must act if it is to accelerate the body without causing the body to rotate.

CofG and CofM coincide for terrestrial sized objects.

Normal reaction

Weight

Force, Scalars and Vectors

We can use these principles to help to draw force diagrams without the complication of drawing the body. These are called Free Body Diagrams.

e.g. 1

- If a body is in equilibrium
- all forces acting on it will sum to zero
- and
- act through the same point.

A person standing on the floor.

Force, Scalars and Vectors

e.g. 2

A parachutist before reaching terminal velocity.

How do you add vectors if they are not in the same line of action?

Drag

- What is drag?
- Which way does it act?
- Why is one vector longer than the other?
- What does it indicate?
- What happens as the parachutist gets faster?

Weight

A

RESULTANT

B

Force, Scalars and Vectors

Use the parallelogram of forces:

R = A + B

R

This is best achieved at A level by drawing a scale diagram - measure the angle between the vectors accurately.

RESULTANT

A

B

Force, Scalars and Vectors

It is also easy to convert this to just a triangle of forces.

R

tan =3/4 = 37

R2 = 32+42 = 25

R = 5N

3N

4N

Force, Scalars and Vectors

e.g. 1 A body of mass 0.3kg falls vertically. A wind blows horizontally with a force of 4N. What is the magnitude and direction of the resultant force on the mass? (g=10 Nkg-1)

Forces on the wheel

Weight

Normal Reaction

Friction

Force, Scalars and Vectors

Mark the forces acting on a wheel as it drives a car from left to right on your paper. Draw another diagram to show the forces acting on the road.

Question

Force of wheel on the road

Friction

Normal Reaction of tyre on road

Force, Scalars and Vectors

- We have conveniently ignored internal friction in the tyre, air resistance - drag etc.
- DID YOU NOTICE THAT:
- the vectors for weight and reactions were all the same length?
- both friction vectors were the same length?

The

End

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