# Friction on Inclined Plane

Inclination angle Normal Reaction Limiting Frictional Force Component of weight along the surface Frictional Force acting on the block
The block shown is lying on a rough surface. The angle of inclination of the surface can be increased. As the inclination is increased the component of gravitational force (mg Sin θ) along the incline increases and limiting value of frictional force (μmg Cos θ) decreases. Friction being a self adjusting force, the friction acting will be equal to (mg Sin θ). For some inclination when the force down the incline is greater than the limiting frictional force, the block starts moving. Once in motion, the frictional force drops to a lower value ( Kinetic friction being less than the static friction) and the block moves down the surface with an acceleration.
Angle of repose θr is the maximum angle of the inclined surface for which the block will be at rest. Angle of repose and coefficient of static friction are related as μs = Tan θr
Set the frictional coefficient to some value, and increase the angle of inclination and observe the values in the table.
You will notice that the friction acting is always equal to the component of the weight along the incline till the block starts moving. Repeat this for a different value for coefficient of friction.
 Materials Coeff.ofStatic Frictionμs Coeff.ofKinetic Frictionμk Steel on Steel 0.74 0.57 Aluminum on Steel 0.61 0.47 Copper on Steel 0.53 0.36 Rubber on Concrete 1.0 0.8 Wood on Wood 0.25-0.5 0.2 Glass on Glass 0.94 0.4 Waxed wood on Wet snow 0.14 0.1 Waxed wood on Dry snow - 0.04 Metal on Metal(lubricated) 0.15 0.06 Ice on Ice 0.1 0.03 Teflon on Teflon 0.04 0.04 Synovial joints in humans 0.01 0.003

## Rolling Friction

When a wheel rolls on a surface it flattens out at the bottom and a small depression is formed in the supporting surface. The normal force is now distributed over the contact area. Also there is an increased deformation at the front of the wheel, while the rear of the wheel undergoes less deformation which causes the normal force (N) to shift forwards. There is some amount of static friction acting on the wheel. This results in a force acting against the motion of the wheel and is given by the equation: f = μrN ⁄ R , where μr is coefficient of rolling friction R is radius of wheel. This static frictional force (shown in red) acts backwards (opposing translation and aiding rotation) and the normal force creates a torque opposing the rotational motion and the net torque due to normal reaction and static friction opposes the rotation. Also energy is lost during rolling motion due to the deformations and relaxations that occur which generate heat in both the wheel and the surface.
 μr Description 0.001 to 0.0025 train wheel (steel on steel) 0.0015 to 0.0025 low resistance tubeless radial tire 0.006 to 0.01 low rolling resistance car/truck tires on a smooth road 0.010 to 0.015 ordinary car tires on concrete 0.020 car on stone plates 0.030 car/bus on tar/asphalt