Forces change how an object moves, or its size and shape
Definition
Force
A push or a pull on an object that comes from its interaction with something else, a vector with both size and direction, measured in newtons (N\text{N}N).
- A force can change an object's motion, its size and shape, or both at once.
- Forces that act on the shape can stretch, compress (squash), bend or twist an object.
- A load hung on a spring stretches it, a hand squeezing a tennis ball compresses it, and a diver standing on a springboard bends it.
- An object can be deformed without moving at all: press on a ball resting on a bench and its shape changes while its motion does not.
Forces on a straight line combine into one resultant
Definition
Resultant force
The single force that has the same effect on an object as all the separate forces acting on it combined.
- Real objects usually have several forces on them at once, so you replace them with one force that does the same job.
- When the forces act along the same straight line, finding the resultant is arithmetic, because a force one way cancels part of a force the other way.
- In words, the resultant force is the sum of the forces one way minus the sum of the forces the other way.
- Choose one direction as positive, usually the direction of motion or of the larger force.
- Add all the forces acting that way, then add all the forces acting the opposite way, and subtract the two totals.
- Always state the direction as well as the size in newtons, because force is a vector and a bare number is only half the answer.
Example
- A van drives along a level road while the engine provides a forward driving force of 2400 N2400\ \text{N}2400 N, and air resistance (900 N900\ \text{N}900 N) and wheel friction (300 N300\ \text{N}300 N) both act backwards.
- Backwards total: 900 N+300 N=1200 N900\ \text{N} + 300\ \text{N} = 1200\ \text{N}900 N+300 N=1200 N.
- Resultant: 2400 N−1200 N=1200 N2400\ \text{N} - 1200\ \text{N} = 1200\ \text{N}2400 N−1200 N=1200 N.
- The resultant is in the direction of motion, so the van speeds up.
With no resultant force, motion does not change
Key Idea
An object either stays at rest, or keeps moving in a straight line at constant speed, unless a resultant force acts on it.
- What keeps an object moving steadily is not a forward force but the absence of a resultant force.
- A book lying on a table has its weight balanced by an equal upward contact force, so the resultant is zero.
- A car cruising in a straight line at a steady 25 m/s25\ \text{m/s}25 m/s has its driving force exactly balanced by the total resistive force, so again the resultant is zero.
- Forces still act in both cases; there are simply no unbalanced ones.
- Read in reverse, this is a detective rule: if an object's motion is changing, a resultant force must be acting on it.
A resultant force changes speed, direction, or both
- Velocity is speed in a stated direction, so a resultant force can change velocity by changing the speed, the direction of motion, or both.
- A resultant force in the direction of motion makes the object speed up, like the van above.
- A resultant force opposite to the motion makes it slow down, like a cyclist braking.
- A resultant force at an angle to the motion changes the direction of travel, like a footballer heading a moving ball sideways.
- The change in velocity is always in the direction of the resultant force.
Common Mistake
- Do not assume constant speed needs a constant forward force: at constant speed in a straight line the resultant force is zero, because the driving force is balanced by the resistive forces.
- Do not say a zero resultant means no forces act, because balanced is not the same as absent.
- Never quote a resultant force without a direction, and never give it the wrong unit: 20 J20\ \text{J}20 J is energy, not force, and scores nothing.
- Do not add forces that point in opposite directions, because opposing forces subtract.
Exam technique
- Show the subtraction in your working, because a visible method can still earn the method mark even if the final number is wrong.
- Give every resultant as a size in newtons and a direction, since a bare number is only half the answer.
- To explain constant speed, make two separate points: the driving force is equal to the resistive forces, so the resultant force is zero.
- Saying only that the forces are balanced often loses the second mark, so add that the resultant force is zero.
Self review
- What is a resultant force?
- A box is pulled along one line by 30 N30\ \text{N}30 N to the right and 18 N18\ \text{N}18 N to the left. What is the resultant force?
- A car moves at a steady speed in a straight line. What is the resultant force on it?
- Name the three ways a resultant force can change an object's velocity.
- Give one example of a force changing an object's shape but not its motion.
