Review and Summary

REVIEW AND SUMMARY

• Force of friction always acts in the direction opposite to the direction of motion. 

• The friction that exists between two unlubricated surfaces is known as dry or solid friction.

• The maximum value of friction force acting on a body, when the body is on the point of motion is called limiting force of friction (F).

• The ratio of the limiting force of friction (F) to the normal reaction (Rμ) between the two bodies is known as coefficient of friction (μ) i.e., μ = F/RN.

• The limiting angle of friction (ϕ) is defined as the angle at which the resultant. reaction (R) makes with the normal reaction (RN).

• The relation between angle of friction (ϕ) and coefficient of friction (μ) is given by tan ϕ = μ.

• The angle of repose is defined as the maximum inclination of a plane at which a body remains in equilibrium over the inclined plane by the assistance of friction only.

• The minimum force required to drag a body of weight W placed on a rough horizontal plane, when the force is applied at an angle with the horizontal is equal to W sin θ and θ = ϕ for the least force. 

• Equilibrium of a body on an inclined plane:

ϕ = Limiting angle of friction for the contact surfaces, 

P0 = Effort required to move the body neglecting friction,

P = Effort required to move the body considering friction,

θ = Angle which the line of action of P makes with the weight of the body W, and

M.A = Mechanical advantage.

• The motion of the nut on a screw is analogous to the motion on an inclined plane.

• Friction of screw and nut:

where P, W, μ, α, ϕ and θ have usual meaning,

p = Pitch of the thread, and

d = Diameter of the screw.

• Condition for maximum efficiency of nut and screw:

• If the efficiency is less than 50%, then screw is said to be self-locking. Otherwise (i.e., η > 50%) the screw is known as overhauling screws.

• Screw jack:

• The bearing surfaces provided at the end of a shaft are known as pivots. The bearing surfaces provided at any place along the length of the shaft are known as collars. 

• When a bearing is new (and for the design of bearings), the uniform pressure theory may be used. When the bearing becomes old (and for the design of clutches), the uniform wear theory may be used.

• Pivot and collar friction: