Particles connected by a string, over a pulley, and with a plane
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Joined together
- The three facts
- Two particles in a line
Read the transcript of the teaching part
Last time
Before we start: last time, in Collisions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Joined together
Two particles joined by a light string. Because the string is light and does not stretch, the tension is the same all along it, and both particles share one acceleration. Write Newton's law for each particle, or once for the whole system, and solve. Over a smooth pulley, the same two rules hold.
The three facts
A light string has no mass, so the tension is the same at both ends. An inextensible string does not stretch, so both particles move the same distance. They have the same speed and same acceleration. A smooth pulley changes the direction of the tension but not its size.
Two particles in a line
P has mass 0.5 and Q has mass 0.3, joined by a string, P above Q. A force of 10 newtons lifts P. For the whole system: 10 minus 0.8 g equals 0.8 a. With g equal to 10, 10 minus 8 is 2, so a is 2.5. For Q alone: T minus 0.3 g equals 0.3 times 2.5. So T is 3 plus 0.75, which is 3.75 newtons.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Particles connected over a pulley · Pulley with a particle on a plane.
The whole chapter: Newton's Laws of Motion.
Chapter 4.4: Newton's laws of motion
- Particles connected by a string, over a pulley, and with a plane 6 min
- A car against a resistance, and motion on rough and smooth inclined planes 6 min
- A vehicle towing a trailer, vertical motion against a resistance, and a lift 6 min
Also for A Level Maths 9709 Paper 4
Which topics come up most in A Level Maths 9709 Paper 4 past papers, counted from every paper since 2004.