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

Category: A-level课程, 教材笔记, 福利干货 Date: 2022年7月18日下午4:00

Coefficient of Friction - Equilibrium

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

Worked Example

3.3.5_WE_CF-Harder_1

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 .

0n1-c-XM_3-3-5-coeff-of-frict-harder-problems-part-1-worked-solution

Exam Tip

Always draw a force diagram and label it clearly.
Look out for key vocabulary such as rough, smooth, equilibrium, on the point of moving and limiting equilibrium and know how to use each.

Coefficient of Friction – Connected Particles

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

Worked Example

3.2.4_WE_Pulleys_1

1KabZVXn_cie-3-2-4-fig5-we-solution-correction-part-1

c7L_52R__cie-3-2-4-fig5-we-solution-correction-part-2

Exam Tip

Be careful not to assume that the system will move in the direction of the heavier particle, remember to consider the angle too. Make sure your diagram is clear enough to work with, sometimes there can be a lot of information on the diagram.

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