Curriculum
Course: Applied Mathematics — Second Secondary
Login

Curriculum

Applied Mathematics — Second Secondary

Unit 1: Statics

0/10

Unit 2: Solid and Analytic Geometry

0/10
Text lesson

Equilibrium on a Rough Horizontal Plane

Applied Mathematics — Second Secondary

Equilibrium on a Rough Horizontal Plane

Equilibrium of a body on a rough horizontal plane

Equilibrium of a body on a rough horizontal plane

  • If a body of weight W rests on a rough horizontal plane and no other vertical force acts on it, the normal reaction equals the weight: R = W.
  • If a force P makes an angle θ above the horizontal, its vertical component P sin θ reduces the pressure on the surface. Then:
Comparison aspectMain ideaKeywords
Horizontal component
  • P cos θ
  • acting in the direction of the motion
actingdirectionmotion
Vertical component
  • P sin θ
  • acting upwards
actingupwards
Normal reactionR = W − P sin θ
•
  • If the force is inclined downwards
  • the normal reaction becomes R = W + P sin θ
forceinclineddownwardsnormal
Comparison aspectMain ideaKeywords
ΣX = 0
  • P cos θ − F = 0
  • so the friction F equals the horizontal component of the force
frictionequalshorizontalcomponent
ΣY = 0
  • R + P sin θ − W = 0
  • so R = W − P sin θ
•
  • When the body is on the point of moving
  • F = μ R
bodypointmoving
Equilibrium on a Rough Horizontal Plane · 3 / 6