Question

A block slides down an inclined surface of inclination 30° with the horizontal. Starting from rest it covers 8 m in first two seconds. Find the coefficient of kinetic friction between the two.

Answer 1

Initial velocity = 0

Distance covered in 2 seconds = 8 m.

Time = 2 seconds.

Applying the Formula,

v - u  =  at

∴ v = 2a

Applying third equation of motion,

v² - u² = 2aS

⇒ v² = 2 × a × 8

∴ 4a² = 16a

∴ a = 4 m/s².

Now, we know, In case a body is moving down along the Incline, then,

mgSin30° - f = ma

⇒ f = m (gsin30° - a)

μmgcos30° = m(gsin30° - a)

∴ μg√3/2 = g/2 - a

⇒ μg√3/2 = 5 - 4

⇒ μg = 2/√3

∴ μ = 0.11

Hence, the coefficient of the Kinetic Friction is 0.11

Hope it helps.