If the coefficient of static friction between the block and the platform is μs = 0.4, determine the maximum speed which the block can attain before it begins to slip. Assume the angular motion of the disk is slowly increasing.

Question:

A disc of radius 6m is rotating about its fixed centre with a constant angular velocity 3rad/s ( in the horizontal plane). A block is also rotating with the disc without slipping. If coefficient of friction between the block and disc is 0.4, determine the maximum speed which the block can attain before it begins to slip. Assume the angular motion of the disk is slowly increasing.

Maximum Radius = 0.44m

Given

r = Radius = 6m

w = Angular Velocity = 3rad/s

μ = coefficient of friction between the objects = 0.4

There are four forces acting on the objects

1. Centripetal Forces

2. Friction

3. Blocks weight

4. Normal force on the block

The centripetal force acts inward toward the disk center.

The friction hinders the block's motion.

The block's weight acts on the disk

The normal force of the disk acting on the block.

The block's weight is equal to the normal force on the block because the block sits on the desk surface.

Centripetal force, Fc = mw²r

Friction,Fr = μN where N = Normal force = mg

Friction = μmg

The maximum distance rmax that we could place the block would be when Ff < Fc

We assume they are equal to solve for r

Ff = Fc

μmg = mw²r divide through by m

μg = w²r make r the subject of formula

r = μg/w² where g = 9.8m/s²

Plugging in the values

r = 0.4 * 9.8/3²

r = 0.435555555555555

r = 0.44m Approximated

Explanation:

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