Limiting friction on slopes, connected particles and forces in equilibrium
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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
- The slope that almost slips
- Weight on a slope
Read the transcript of the teaching part
Last time
Before we start: last time, in Particles on strings, the resultant of forces and a smooth ring, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The slope that almost slips
Put a book on a tilted board and raise the board slowly. For a while it stays put. Then, at one angle, it is about to slide. That moment, the point of sliding, is called limiting equilibrium. Friction is at its maximum, so one equation, F equals mu R, joins everything together.
Weight on a slope
On a plane inclined at theta, resolve the weight m g. Down the slope it is m g sine theta. Into the plane, perpendicular to the slope, it is m g cosine theta. That is balanced by the normal reaction. With an extra force, add its components too. The normal reaction changes if the force pushes into or pulls off the plane.
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 · Limiting friction on an inclined plane.
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.