Resolving forces and equilibrium of a particleEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

Component of a force F at angle \theta to a direction, in that direction?
Component of a force F at angle \theta to a direction, perpendicular to it?
What is the condition for a particle to be in equilibrium?
Weight component down a plane at \alpha to the horizontal?
Weight component into a plane at \alpha to the horizontal?
Acceleration down a smooth slope at angle α?
Normal reaction on a particle on a smooth slope with no other perpendicular forces?
Horizontal force P holds a particle of weight W at rest on a smooth slope at α?
Which directions do you resolve in on a slope?
What is the acceleration perpendicular to a slope for a particle that stays on it?
What happens to a string when the hanging particle lands?
40 N weight, string at 30^\circ to the vertical and a horizontal string: tension in the sloping string?

Exam questions on Resolving forces and equilibrium of a particle

A particle of weight 40 N is in equilibrium, supported by two light inextensible strings. String 1 makes an angle of $30^\circ$ with the upward vertical, and string 2 is horizontal.
String 2 will break if its tension exceeds 30 N. The strings stay at the same angles. Find the greatest weight that this arrangement can support.2 marks
A particle of mass 6 kg is placed on a smooth plane inclined at $25^\circ$ to the horizontal. Take $g=9.8\ \text{m s}^{-2}$ .
A horizontal force of magnitude $P$ N, in the vertical plane containing a line of greatest slope and directed towards the plane, holds the particle at rest on the plane. Find $P$ .2 marks
A particle of mass 2 kg is pulled up a smooth plane inclined at $30^\circ$ to the horizontal by a light string parallel to a line of greatest slope. The tension in the string is 20 N. Take $g=9.8\ \text{m s}^{-2}$ .
Find the acceleration of the particle and the magnitude of the normal reaction between the particle and the plane.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).