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Resultant force

The resultant force is a single force that has the same overall effect as two or more forces acting together. You can easily calculate the resultant force of two forces that act in a straight line.

Two forces in the same direction

Two forces that act in the same direction produce a resultant force that is greater than either individual force. Simply add the magnitudes of the two forces together.

Example

Two forces, 3 newtons (N) and 2 N, act to the right. Calculate the resultant force.

3 N + 2 N = 5 N to the right

Two forces in opposite directions

When two forces that act in opposite directions it is often easiest to subtract the magnitude of the smaller force from the magnitude of the larger force.

Example

A force of 5 N acts to the right, and a force of 3 N act to the left. Calculate the resultant force.

5 N – 3 N = 2 N to the right

Free body diagrams

A free body diagram models the forces acting on an object. The object or 'body' is usually shown as a box or a dot. The forces are shown as thin arrows pointing away from the centre of the box or dot.

Free body diagrams do not need to be drawn to scale but it can sometimes be useful if they are. It is important to label each arrow to show the magnitude of the force it represents. The type of force involved may also be shown.

Examples of free body diagrams

Weight and reaction force for a resting object

A box resting on a table experiences two forces. There is a downward pull from the Earth on the box, which we call its weight. There is also a push up on the box from the surface of the table. Because these forces are equal and opposite, there is no resultant force and so the body remains at rest.

Weight, reaction force and friction for an object placed on a hill

Three forces do not have to act in a line in order for there to be no resultant force. For the body on a slope, whichever direction is chosen the forces cancel out. For example vertically, the pull of the Earth down on the body is cancelled out by the combined upward push of the reaction force and the friction force.

Considering the forces acting along the slope, the pull of the Earth on the box would make it slide down the slope, but the friction force is exactly equal to cancel this out. The reaction force pushes neither up nor down the slope so does not have an effect along the slope.

Weight, upthrust, thrust and air resistance for an accelerating speedboat

In this example the boat experiences two vertical forces - a weight force downwards and an upthrust from the water on the boat. These two forces are equal and opposite so the boat does not accelerate up or down.

However, horizontally the air resistance opposing the motion of the boat is not as big as the thrust, so there is a resultant force horizontally forward on the boat and as a result it accelerates forwards.