The court jester forgot to remove the King's treasure chest from the drawbridge. The jester is now closing the drawbridge, and if the chest falls and breaks, it will cost him his head!

What is known:

The mass of the chest is 20 kg.

Initially, the chest is located 4 m from the foot of the drawbridge.

The drawbridge starts from rest in a horizontal position and rotates with a constant angular acceleration of 0.1 rad/s^{2}.

Question

Problem Parameters

If the drawbridge reaches an angle of 30° before the jester can stop it, what is the coefficient of static friction that must exist between the chest and the drawbridge so that the chest will not slide down the drawbridge.

Approach

Using the expressions for acceleration in polar coordinates (derived in
Curvilinear Motion: Polar Coordinates section),
express Newton's Second Law in terms of polar coordinates.

Determine the normal force exerted on the chest by the bridge at 30°.

Use the normal force at 30° to find the minimum static coefficient
of friction that must exist.

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