A number of forces acting on an object may be replaced by a single force…

The idea

When several forces act on one object, they can be replaced by a single force that has exactly the same effect on that object as all of them acting together. Along a straight line, forces pointing the same way add and forces pointing opposite ways subtract. A brick lying on the bottom of a pool has three forces on it: its weight downwards, upthrust from the water upwards and the normal contact force from the floor upwards. It stays still because the weight equals the upthrust plus the normal contact force, so the single equivalent force is zero. A hailstone at terminal velocity is the same story with two forces: air resistance has grown until it equals the weight, so the single force replacing them is zero and the velocity stops changing.

What earns the marks

• The single force having exactly the same effect on the object as all the original forces together.
• Adding forces that act in the same direction and subtracting those that act in opposite directions.
• A worked case, such as the weight of a brick equalling the upthrust plus the normal contact force.
• The single force being zero when the original forces are balanced, as for a hailstone at terminal velocity.

Common mistakes and how to put them right

• Adding the magnitudes of forces that point in opposite directions.

• Leaving out one of the forces acting, most often upthrust on a submerged object.

• Assuming balanced forces must mean the object is stationary, when constant velocity also qualifies.

• Treating the single equivalent force as an extra force acting in addition to the originals.

• Claiming a resultant of zero only if all the individual forces are zero.

Exam tips

• List every force acting before you combine them; the missing force is where most marks go.
• State the direction you are calling positive, then let the signs do the work.
• For a floating or submerged object, always ask whether upthrust belongs in the list.