A turntable A is built into a stage for use in a theatrical production. It is observed during a rehearsal that a trunk B starts to slide on the turntable 10 s after the turntable begins to rotate. Knowing that the trunk undergoes a constant tangential acceleration of 0.32 m/s2, determine the coefficient of static friction between the trunk and the turntable.

Static friction coefficient, μ = 0.41796

Explanation:

radius, r = 2.5 m

constant acceleration, a = 0.32 m/s²

time, t = 10 s

∴ Tangential Velocity, V = at

⇒ 0.32 * 10 ⇒ 3.2 m/s

now,

radial acceleration = V² / r

⇒ (3.2) ² / 2.5 ⇒ 4.096 ms⁻²

Force required = m * radial acceleration

μmg = m * [ (3.2) ² / 2.5]

'm' cancels each other on both sides

μg = (3.2) ² / 2.5

multiply through by 'g' to make coefficient of static friction the subject

where g = 9.8

μ = (3.2) ² / 9.8 * 2.5

μ = 10.24 / 24.5

μ = 0.41796