Coaching Centre
Balanced and unbalanced forces
Adding forces to find the net force, balanced forces and staying still or moving at a steady speed, unbalanced forces and changes in motion, tug of war, and drawing force diagrams with arrows.
In a tug of war, both teams can be pulling with all their strength and the rope doesn't move at all. Then one person on the left slips, and suddenly the whole lot slides to the right. Nothing about the right team changed. What changed was the balance between the two forces.
Adding up forces
Most of the time, more than one force acts on an object. To work out what the object will do, you add the forces together to find the net force (also called the resultant force).
- Forces in the same direction add. If Sally pushes a trolley with 150 N and Marilla pushes the same way with 200 N, the net force is 350 N.
- Forces in opposite directions subtract. If they push against each other, the net force is 200 − 150 = 50 N in Marilla's direction.
That's why a few people working together can lift a piano that none of them could lift alone: their upward forces add until together they beat the piano's weight.
Balanced forces
When the forces on an object cancel out, the net force is zero and the forces are balanced. Balanced forces do not change an object's motion. So an object with balanced forces either:
- stays still, like a weightlifter holding a barbell steady above their head (they push up exactly as hard as gravity pulls down), or
- keeps moving at a steady speed in a straight line, like a car cruising at 60 km/h, where the engine's driving force exactly balances friction and air resistance.
The second one surprises people. You don't need a net force to keep something moving. You need a net force to change how it's moving. A spacecraft coasting between planets keeps going for years with its engines off because there's nothing out there to slow it down.
Unbalanced forces
When the forces don't cancel, there is a net force and the forces are unbalanced. An unbalanced force always changes the motion of an object, in the direction of the net force:
- net force in the direction it's moving → it speeds up
- net force against the direction it's moving → it slows down
- net force at an angle → it changes direction
The bigger the net force, the faster the change. And the more mass an object has, the harder it is to change its motion: the same push speeds up a shopping trolley much more than a car.
- Push gently from the left (try 80 N). Why doesn't the box move?
- Push harder until it moves, then reduce your push until the box travels at a steady speed. What is the net force now?
- Switch to ice, get the box moving and press "Let go". What happens, and why is it different on the floor?
- Push from both sides with equal forces. Then make one slightly bigger.
Drawing force diagrams
A force diagram shows every force acting on one object as an arrow:
- the arrow points in the direction of the force
- the length of the arrow shows how strong the force is (twice the force, twice the length)
- each arrow starts on the object and is labelled with what is causing it (the agent)
To read a force diagram, compare opposite arrows. If the up arrow and down arrow are the same length, there's no change up or down. If the forward arrow is longer than the backward arrow, the object speeds up forwards. Always use a ruler, and draw arrows from the object outwards.
Test yourself
Two people push a box in opposite directions with 120 N and 90 N. The net force is
120 − 90 = 30 N, in the direction of the bigger push.
A car travels along a straight motorway at a steady 100 km/h. The forces on it are
Steady speed in a straight line means zero net force.
A cyclist stops pedalling on a flat road and slowly comes to a stop. This is because
The net force is against the motion, so the bike slows.
In a force diagram, a longer arrow means
Arrow length shows the size of the force.
Which needs an unbalanced force?
Changing direction is a change in motion.
Label the forces on the car.
Balanced or unbalanced?
When all the forces on an object add up to zero, they are . The total of all the forces is called the force. An unbalanced force makes an object speed up, slow down or change . In a force diagram, the of each arrow shows how big the force is.
A weightlifter lifts a 1000 N barbell from the floor, holds it still above their head, then drops it. Using the terms balanced and unbalanced forces, explain what happens to the barbell in each of these three stages.
To lift the barbell, the weightlifter must push up with more than 1000 N. The forces are unbalanced, with a net force upwards, so the barbell starts to move up. When it is held still above their head, they push up with exactly 1000 N, the same as its weight, so the forces are balanced and the barbell doesn't move. When they let go, their upward push disappears and only gravity is left, so the forces are unbalanced downwards and the barbell speeds up as it falls to the floor.