Force diagrams and resultant forces

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Key Points

  • Multiple forces act on an object at the same time.

  • The size and direction of these forces determines the movement of the object.

Free body diagrams

Show the forces acting on an object in a free body diagram. The arrows represent the size and direction of the forces acting.

When drawing a force diagram:

  • represent the object with a small box or dot
  • draw the arrows with a pencil and ruler
  • draw the arrows from the centre of the box or dot
  • label the arrow with the name of the force and the size of the force

Examples of force diagrams include:

A book resting on a table

There is a book resting on a table with two arrows, one pointing upwards labelled normal reaction force (1 N) and one pointing downwards labelled weight (1 N)

Skiing down a hill

Person skiing downhill. First arrow points upwards, labelled normal reaction force 400 N. Second arrow points backwards, labelled friction 300 N.  Third arrow points downwards, labelled weight 500 N.

A boat floating

A boat floating on water with two arrows pointing in different directions.  First arrow points upwards and labelled Upthrust (1000 N). Second arrow points downwards labelled weight (1000 N).

Which direction will the force arrow representing the normal reaction force be pointing in a free body diagram?

The force arrow representing the normal reaction force will be pointing at right angles to the surface.

Resultant forces

Multiple forces act on an object at once and the that is acting on the object can be calculated. A resultant force is the overall force that acts on the object.

Remember that forces are vectors.

When you calculate the resultant force you need to also say the direction it is acting in. You can calculate this in two ways.

1. Forces acting in the same direction

In this diagram there are two forces, which, when added together give a resultant force of 30 newtons (N).

Resultant force = 20 N + 10 N

Resultant force = 30 N to the right

One person pushes, the other pulls a block on wheels. Three arrows point forwards. Longest arrow labelled Resultant force 30 N. Medium length arrow labelled 20 N. Shortest arrow labelled 10 N.

2. Forces acting in opposite directions

In this diagram there are two forces, acting in opposite directions:

Resultant force = 20 N – 10 N

Resultant force = 10 N to the left

A rope pulled in opposite directions. One arrow points left labelled 20 N. Shorter arrow points rights labelled 10 N. Third arrow points left and shows resultant force is 10 N.

Shortly after a ball is dropped, the air resistance is 5 N and the weight of the ball is 8 N.

Calculate the resultant force and say which direction it is acting.

The forces are acting in opposite directions, so resultant force is calculated by subtracting the smaller one from the larger one:

8 – 5 = 3 N, acting downwards.

The effect of forces

The movement of the object and the resultant force acting on it are linked.

Balanced forces

If the forces acting on the object are balanced there is no resultant force. This means the object could be travelling at a constant velocity. It could also be stationary or not moving at all.

Have a look at these examples.

  1. A car is travelling down a motorway. The thrust from the engine is 500 N and the acting against the car is also 500 N.

Describe the motion of the car.

A moving car. 2 arrows point in opposite directions, from the front and back of the car. Resultant force diagram has 2 identical arrows pointing in opposite directions, labelled 500 N.

Resultant force = 500 N - 500 N

Resultant force = 0 N

There is no resultant force and the car is travelling on a motorway, this means that the car is travelling at a constant velocity.

  1. A box is placed on a table. The weight of the force on the box acting downwards is 100 N. The table applies a 110 N on the box upwards.

Describe the movement of the box.

A box on a table. 2 arrows point in opposite directions from the point at which they meet on the table. Resultant force diagram has 2 identical arrows pointing in opposite directions, labelled 110 N.

Resultant force = 100 N – 100 N

Resultant force = 0 N

There is no resultant force acting on the box and the box is on the table, meaning that the box is stationary.

Unbalanced Forces

If the forces acting on the object are not balanced then there is a resultant force acting on the object this means that the object is either accelerating or decelerating.

Have a look at these examples.

  1. A rocket has just launched. The thrust from the engine is 50 000 N and the of the rocket is 10 000 N.

Describe the motion of the rocket.

A rocket. An arrow points up from the rocket. Shorter arrow points down. Resultant force diagram shows up arrow labelled 50,000 N and shorter down arrow labelled 10, 000 N. Resultant force 40,000 N.

Resultant force = 50 000 N – 10 000 N Resultant force = 40 000 N upwards

The rocket has just launched. The resultant force is acting upwards, which in the same direction as the rocket is moving, which means the rocket is accelerating upwards.

  1. A sky diver has just opened her parachute. The weight of the sky diver is 500 N and the air resistance acting on her is 700 N
A parachute.  An arrow points up from the parachute, shorter arrow points down. Resultant force diagram shows up arrow of 700 N and a shorter down arrow of 500 N. The resultant force is 200 N.

Resultant force = 700 N – 500 N Resultant force = 200 N upwards

The parachutist is travelling downwards, the resultant force is acting against the movement. This means that the parachutist is decelerating.

As a racing car approaches the finish line of a race, the thrust from the engine is 1500 N and the air resistance is 1000 N.

Calculate the resultant force (including its direction) and describe the motion of the car.

The resultant force is 1500 – 1000 = 500 N and it is acting in the same direction as the car is moving (forwards).

The car is, therefore, accelerating towards the finish line.

Test your knowledge

Quiz - Multiple choice