Particles on strings, the resultant of forces and a smooth ring
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 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
- Forces that cancel, forces that add
- Resolving a force
- Two strings
Read the transcript of the teaching part
Forces that cancel, forces that add
A lamp hangs from two strings. Each pulls at an angle, yet the lamp stays still, because the pulls and the weight cancel exactly. Break every force into two directions, and equilibrium becomes two simple equations. If the forces do not cancel, the same split gives you the single resultant force.
Resolving a force
A force F at an angle theta to the horizontal has a horizontal part F cos theta and a vertical part F sin theta. Check by example: twelve newtons at 30 degrees gives 10.39 across and 6 up. Notice 6 is half of 12. In equilibrium, the total across is zero and the total up is zero. Those are your two equations.
Two strings
Take eight kilograms hung from strings at 60 and 45 degrees above the horizontal. The weight is eighty newtons. Horizontally the pulls cancel: T one cos 60 equals T two cos 45. Vertically the upward parts balance the weight: T one sin 60 plus T two sin 45 equals 80. Solving, T one is 58.6 newtons and T two is 41.4 newtons. Check both equations.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Coplanar forces in equilibrium · Particle suspended by strings · Resultant of coplanar forces.
The whole chapter: Forces and Equilibrium.
Chapter 4.1: Forces and equilibrium
- Particles on strings, the resultant of forces and a smooth ring 5 min
- Limiting friction on slopes, connected particles and forces in equilibrium 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.