Forces and Newton’s laws · Year 13
In Year 13 you learn: connected particles.
Newton’s three laws connect force and motion. A resultant force causes an acceleration, F = ma, and forces come in equal and opposite pairs. In mechanics problems, you draw a force diagram, resolve forces in useful directions and apply F = ma to each object.
Key facts
- First law: no resultant force means constant velocity (or rest). Second law: F = ma, with F the resultant force in newtons. Third law: if A pushes B, B pushes A equally and oppositely.
- Weight W = mg with g = 9.8 m/s². On a horizontal surface with no other vertical forces, R = mg.
- Connected particles on an inextensible string move with the same acceleration. The tension is the same throughout a light string over a smooth pulley.
- A force P at angle θ to a direction has components P cos θ along it and P sin θ perpendicular to it.
Worked examples
Example 1
Particles of 3 kg and 5 kg hang over a smooth pulley on a light string. Find the acceleration and the tension. (g = 9.8 m/s²)
Answer: a = 2.45 m/s², T = 36.75 N