Forces questions are worth lots of marks, and nearly all of them come back to two ideas: the resultant force and Newton’s laws of motion.
What is a resultant force?
The resultant force is the single force that has the same effect as all the forces acting on an object added together. Forces in the same direction add; forces in opposite directions subtract.
Example: a box is pushed right with 10 N while friction acts left with 4 N. The resultant force is 10 − 4 = 6 N to the right.
Newton’s three laws
- First law: if the resultant force is zero, a stationary object stays still and a moving object carries on at the same speed in the same direction.
- Second law: the acceleration of an object is proportional to the resultant force and inversely proportional to its mass. This gives F = m × a.
- Third law: when two objects interact, they exert equal and opposite forces on each other. The forces are the same type but act on different objects.
Worked example
A car of mass 1200 kg has a driving force of 4000 N and a total resistive force of 1000 N. Calculate its acceleration.
- Resultant force: 4000 − 1000 = 3000 N
- Rearrange F = ma: a = F ÷ m
- Substitute: a = 3000 ÷ 1200
- Answer: a = 2.5 m/s²
Common mistakes
- Using the driving force in F = ma instead of the resultant force.
- Thinking a moving object needs a resultant force to keep moving. It doesn’t; it only needs one to speed up, slow down or change direction.
- Saying weight and the normal contact force are a Newton’s third law pair. They act on the same object, so they’re not.
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