Unbalanced Forces — Edexcel International GCSE Science Double Award 4SD0 - Physics Revision Notes & Topical Questions

An object stays at rest, or continues at constant velocity in a straight line, unless acted on by a resultant force. This tendency to resist changes in motion is called inertia. Mass is the measure of an object's inertia: the bigger the mass, the harder it is to change its motion.

When the resultant force on an object is not zero, the object accelerates. The acceleration is directly proportional to the resultant force and inversely proportional to the mass:

F = m a

where F is the resultant force in newtons (N), m is the mass in kilograms (kg) and a is the acceleration in metres per second squared (m/s²). One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

The law connects motion and force in both directions.

Rearranging gives a = F/m and m = F/a. Double the force on a trolley and its acceleration doubles; double the mass and its acceleration halves. The acceleration points in the same direction as the resultant force, and the direction of velocity can be different: a ball thrown up has a downward acceleration all the time.

Newton's first law explains why passengers lurch forwards when a bus brakes: the bus slows down but the passengers tend to keep going at their original velocity until seat belts or friction provide a force. It also explains why a coin on a card flicks into a glass when the card is flicked sideways: the coin has inertia and stays where it was.

A negative acceleration means slowing down when velocity is positive. A braking car has a resultant force opposite to its motion. The same equation applies: use the resultant force as a negative number or state it is backwards.

Combine with the equations of motion, such as v = u + at, to solve for speed or distance after a time.

A trolley can be pulled along a bench by a string passing over a pulley carrying a hanging mass.

Plotting acceleration against 1/m for a constant force gives a straight line through the origin, showing that a is inversely proportional to m. Typical errors in the experiment include friction in the track (reduced by tilting the track slightly so the trolley just keeps moving) and the fact that the hanging weight also accelerates, so the total mass being accelerated includes both trolley and hanger.

Rockets, cars, runners and falling objects all follow F = ma. In a car, the engine force minus drag and friction is the resultant force. As drag increases with speed, the resultant falls, so acceleration falls, which links to terminal velocity.

Always check your unitsmass in kilograms, force in newtons, acceleration in metres per second squared.