Topic 3 of 8 · Form 5
Newton's laws and connected particles
Resultant force = ma, applied in the direction of motion.
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Newton's second law
Resultant force = ma, applied in the direction of motion.
Connected particles
Two particles joined by a light, inextensible string over a smooth pulley have the same acceleration and the same tension on each side. Write F = ma for each particle separately, then solve.
Worked example: Masses of 3 kg and 5 kg hang on either side of a smooth pulley. Find the acceleration and tension (g = 9.8).
5 kg: 5g − T = 5a; 3 kg: T − 3g = 3a
Adding: 2g = 8a → a = 2.45 m s⁻²; T = 3(9.8 + 2.45) = 36.75 N
Worked example: A 4 kg block on a smooth table is joined by a string over a pulley at the edge to a hanging 1 kg mass. Find the acceleration.
1 kg: g − T = a; 4 kg: T = 4a → g = 5a → a = 1.96 m s⁻²
Lifts and vehicles
- A person in a lift accelerating upwards: R − mg = ma (apparent weight increases).
- A car towing a trailer: consider the whole system for acceleration, then each part for the tension in the tow bar.
Motion on rough slopes
Include friction (opposing motion) and the component of weight along the slope.
Check yourself
- A 60 kg person stands in a lift accelerating upwards at 2 m s⁻². Find the reaction (g = 9.8).
- Why is the tension the same on both sides of a smooth pulley?
- A 1 200 kg car pulls a 400 kg trailer with a driving force of 3 200 N (no resistance). Find the acceleration.
Show answers
- R = 60(9.8 + 2) = 708 N
- The pulley is smooth (no friction) and the string is light, so tension does not change.
- a = 3 200 ÷ 1 600 = 2 m s⁻²
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