AQA A Level Maths: Mechanics复习笔记3.3.5 Coefficient of Friction - Harder Problems

How is friction used when a body is in equilibrium?

• When a body is in static equilibrium under the action of a number of forces, including friction, the value of friction will be less than or equal to the value of μR
• When the value of friction is equal to μR, the body is in limiting equilibrium and is on the point of moving
• When a body is stationary on an inclined plane then it is either in equilibrium or in limiting equilibrium, we cannot assume that F = μR

How is friction used when a body is moving?

• When a body is moving under the action of a number of forces, including friction, the value of friction will be equal to the value of μR

A wooden block of mass m is stationary on a plane inclined at 25° above the horizontal. The coefficient of friction between the block and the plane is µ.  Find the least possible value of µ .

How is friction used for connected particles?

• When two particles are connected by means of a light, inextensible string, friction will act only on any particle that is resting on a rough surface
• On an inclined slope, friction will act in the direction opposite to the direction the particle is moving in or on the point of moving in
• The direction they will move in depends on both the weight of the particles and the angles of the slopes they are resting on
  • Compare the components of the weight in the direction of the motion the particles will move in
  • The particle with the heavier component will move down the slope