Question

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 0.25 m/s2, determine the coefficient of static friction between the trunk and the turntable.

Answer 1

Answer:

0.26

Explanation:

The radius of the table is 2.5 m.

Tangential velocity,

$v=u+at\\u=0\\t=10s\\a=0.25m/s^2\\v=0+0.25\times 10 = 2.5 m/s$

Net force on the trunk in the plane of the table:

$F=m\sqrt{a^2+(\frac{v^2}{r})^2}\\F= m\sqrt{0.25^2+(\frac{2.5^2}{2.5})^2}=2.5m$

The trunk slides because the frictional force equals the net force acting on the table:

$\mu m g = 2.5 m\\\mu =\frac{2.5}{g} = 0.26$