FORCES 3. Calculating resultant forces

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

What is a resultant force? Why is it a vector?

How do we draw scale diagrams to deduce a resultant force?

What do we mean by balanced and unbalanced forces?

When dealing with acting forces, what is an equilibrium?

Introduction

Forces were introduced in "What is a force?" including contact and non-contact forces AND, importantly for this page, free body diagrams showing multiple forces on an object.

Force data is useless without its direction of action. You not only need to know the value of a force in newtons (N) but the precise direction or angle of the line of action of one force with respect to at least one other force.

That is why force is always a vector - it has magnitude and direction!

When a body is subjected to multiple known forces (usually >= vectors in newtons) how can we deduce and calculate the net resultant force and its direction?

It is possible to replace multiple forces acting at a single point with a single force known as the resultant force.

Some resultant forces are easily deduced with a simple addition or subtraction.

For example image an object of weight 12 N falling vertically in air. If the air resistance opposing the fall was 5 N, what would be the resultant force? Quite simply it would be 12 - 5 = 7 N. So the object would continue to fall and accelerate due to the 7 N resultant fall.

Others require a scale drawing showing all the forces involved and the direction (e.g. angle) in which each individual force acts.

From such graph work you can measure and calculate the resultant force and its direction of action.

Examples of problem solving to calculate a resultant force

APPENDIX 1: right angle triangle rules

Important formulae in the trigonometry of a right angled triangle:

for angle θ shown on the right diagram

tangent rule: tan θ = opposite / adjacent

sine rule: sin θ = opposite / hypotenuse

cosine rule: cos θ = adjacent / hypotenuse

APPENDIX 2 Calculating work done from a resultant force

If a source of energy is available, you can calculate the work done from the acting force and the distance the force acts through.

work done (joules) = force (newtons) x distance along the line of action of the force (metres)

W (J) = F (N) x d (m),   F = W/d,   d = W/F

Q1 If you drag a heavy box with a force of 200 N across a floor for 3 m, what work is done?

work done = 200 x 3 = 600 J

Q2 If a machine part does 500 J of work moving linearly 2.5 m, what force was applied by the machine?

work done = force x distance, rearranging,  force (N) = work done (J) ÷ distance (m)

force = 500 ÷ 2.6 = 200 N

Q3 Part of a machine requires a continuous resultant force of 500 N from a motor to move it in a linear direction.

(a) How much work is done in moving it a distance of 50 m?

work done = force x distance = 500 x 50 = 25000 J (25 kJ)

Q4 A toy model car has a clockwork motor, whose spring can store 8.75 J of elastic potential energy.

On release the clockwork motor can deliver a continuous force of 2.5 N.

How far will the car travel in one go?

energy store = total work done = force x distance

distance = energy store / force = 8.75 / 2.5 = 3.5 m

These examples were 'borrowed' from  Types of energy stores, mechanical work done and power calculations

Forces revision notes index

FORCES 1. What are contact forces & non-contact forces?, scalar & vector quantities, free body force diagrams

FORCES 4. Elasticity and energy stored in a spring

FORCES 5. Turning forces and moments - from spanners to wheelbarrows and equilibrium situations

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