# JAMB QUESTION AND ANSWER ON FRICTION

## WHAT IS FRICTION

#### Friction is a force which opposes relative motion between two surfaces in contact with each other. Coefficient of static friction, µ is defined as the ratio of the limiting frictional force (F) to the normal reaction (R).

To obtain the coefficient of static friction, µ, the angle of inclination of the plane, , is slowly increased until the block just begins to slide down the plane. At this point, the parallel component of the weight, W sin acting downwards along the plane is equal to the limiting frictional force, F = µR acting upwards along the plane.
That is, F = Wsin ………………………………………….(1)
Or µR = Wsin
Also, on an inclined plane, the normal reaction R is not equal to the weight, W, but to the perpendicular component of the weight, Wcos
That is R = Wcos ……………………………………………(2)
Combining equation (1) and (2),

### Example 1

A wooden block of mass 1.6kg rests on a rough horizontal surface. If the limiting frictional force between the block and the surface is 8N, calculate the coefficient if friction (g = 10m/s2)
Solution
Mass = 1.6kg, f = 8N, µ = ?
R = Mg; 1.6 × 10 = 16N

### Example 2

Calculate the magnitude of the force required to just move a 20kg object along a horizontal surface if the coefficient of friction is 0.2.
400.0N B. 40.0N C. 4.0N D. 0.4N (g = 10ms–¹)
Solution
R = Mg; = 20×10 = 200N
F = µR; 0.2×200
40N

### Example 4

A motorcycle of mass 100kg moves around in a circle of radius 10cm with a velocity of 5m/s–¹. Find the coefficient of friction between the road and the tyres.
25.00 B. 2.50 C. 0.50 D. 0.25 (g = 10m/s²)
Solution
Mass m = 100kg, radius = 10cm., vel. = 5 m/s–¹, µ = ?
F = mv²/r
(100×5²)/10 = 250N
R = mg = 100×10

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