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2.2.7 Free body diagrams and resultant force

Reading a free body diagram

Definition

Free body diagram

A diagram of a single object showing every force that acts on it as a labelled arrow.

Definition

Unbalanced forces

Forces acting on an object that do not cancel each other out, so that there is a non-zero resultant force.

  1. A free body diagram shows one object with an arrow for each force acting on it, so it lets you see at a glance whether the forces are balanced or unbalanced.
  2. Forces are unbalanced when they do not cancel out, so there is a resultant force in one direction.
  3. A resultant force makes the object accelerate in the direction of the resultant force.
  4. To find the resultant force from a free body diagram, work in two perpendicular directions, usually horizontal and vertical.
    1. Add up the forces in one direction and subtract the forces in the opposite direction.
    2. Do the same for the other direction.
    3. If one direction gives zero, the resultant force lies along the other direction only.
  5. The direction of the resultant is the direction of the larger total force, so it is shown by the longer arrows on the diagram.
  6. The resultant force is not an extra force on the object, so it is not drawn as another arrow alongside the real forces.

Resultant force along one line

Definition

Resultant force

The single force that has the same effect on an object as all of the forces acting on it combined.

  1. When all of the forces act along one line, choose one direction as positive and treat forces in the other direction as negative.
  2. The resultant force is the sum of the forces with their signs.
  3. A positive answer means the resultant acts in the positive direction, and a negative answer means it acts in the opposite direction.
  4. More than two forces can act along the same line, such as a car with a driving force forwards and both air resistance and friction backwards.
Example

Resultant force on an accelerating car

  • A car pulling onto a dual carriageway has a driving force of 3200 N3200\ \text{N}3200 N forwards, air resistance of 700 N700\ \text{N}700 N backwards and friction of 500 N500\ \text{N}500 N backwards.
  • Take forwards as positive.
FR=3200 N−700 N−500 N=2000 N F_{\text{R}}=3200\ \text{N}-700\ \text{N}-500\ \text{N}=2000\ \text{N} FR​=3200 N−700 N−500 N=2000 N
  • The vertical forces, weight and normal contact force, are equal and opposite, so they make no contribution.
  • The resultant force is 2000 N2000\ \text{N}2000 N forwards, so the car speeds up.

Examples of unbalanced forces

  1. Free body diagrams can describe many everyday situations where two or more forces give a resultant force.
  2. A car speeding up on a level road has a forward driving force that is larger than the total backward resistive forces.
  3. A cyclist braking has a backward friction force from the brakes and road that is larger than any forward force, so the resultant force acts backwards and the cyclist slows down.
  4. A skydiver straight after jumping has a weight that is much larger than the upward air resistance, so the resultant force acts downwards and she speeds up.
  5. A lift starting to rise has an upward tension in its cable that is larger than its weight, so the resultant force acts upwards.
  6. A rocket at lift-off has an upward thrust from its engines that is larger than its weight, so it accelerates upwards.
  7. A ball thrown upwards has its weight and air resistance both acting downwards while it rises, so the resultant force is downwards and the ball slows down.
Example

Resultant force on a lift

  • A lift with a weight of 8000 N8000\ \text{N}8000 N is pulled upwards by a cable tension of 9200 N9200\ \text{N}9200 N.
  • The free body diagram shows a longer upward arrow for tension and a shorter downward arrow for weight.
FR=9200 N−8000 N=1200 N F_{\text{R}}=9200\ \text{N}-8000\ \text{N}=1200\ \text{N} FR​=9200 N−8000 N=1200 N
  • The resultant force is 1200 N1200\ \text{N}1200 N upwards, so the lift accelerates upwards.
Example

Resultant force on a ball thrown upwards

  • A tennis ball with a weight of 0.6 N0.6\ \text{N}0.6 N is moving upwards, and the air resistance on it is 0.1 N0.1\ \text{N}0.1 N.
  • The ball is moving upwards, so air resistance acts downwards in the same direction as the weight.
FR=0.6 N+0.1 N=0.7 N F_{\text{R}}=0.6\ \text{N}+0.1\ \text{N}=0.7\ \text{N} FR​=0.6 N+0.1 N=0.7 N
  • The resultant force is 0.7 N0.7\ \text{N}0.7 N downwards, so the ball slows down as it rises.
Common Mistake
  • Do not choose the largest single force as the resultant, because the resultant depends on every force and its direction.
  • Do not draw a forward force on an object only because it is moving forwards, because a ball rising upwards has no upward force on it after it leaves your hand.
  • Do not add an arrow labelled "resultant force" to a free body diagram unless the question asks for it, because it is not a separate force.
Exam technique

Describing a resultant from a diagram

  • Name each force and state which forces are larger, using evidence from the arrow lengths or the values given.
  • Show your working for the resultant as a single line, such as 3200−700−500=2000 N3200-700-500=2000\ \text{N}3200−700−500=2000 N, so a method mark can be given even if you slip.
  • Always give the resultant with a unit and a direction, such as "2000 N2000\ \text{N}2000 N forwards".
  • Finish by linking the resultant force to the effect on the motion: speeding up, slowing down or changing direction.
Self review
  • What are unbalanced forces?
  • How do you find the resultant of several forces acting along one line?
  • Find the resultant force on a car with a driving force of 1500 N1500\ \text{N}1500 N and resistive forces totalling 900 N900\ \text{N}900 N.
  • Why does a ball thrown upwards slow down as it rises?
  • Why should the resultant force not be drawn as an extra arrow on a free body diagram?
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Revision notes for OCR GCSE Physics 2.2.7 Free body diagrams and resultant force: explanations and worked examples.

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