A turntable has an angular velocity of 1.4 rad/s.The coefficient of static friction between the turntable and a block placed on it is 0.20.The maximum distance from the center of the turntable that the block can be placed without sliding is approximately
A)0.50 m
B)1.0 m
C)1.4 m
D)2.0 m
E)4.4 m

Question

Quizplus · Accepted Answer

The maximum distance from the center of the turntable that the block can be placed is given by the equation:

rmax = μs * R

Where μs is the coefficient of static friction and R is the radius of the turntable.

The angular velocity of the turntable is given by:

ω = v / r

Where v is the linear velocity of the block placed on the turntable.

We can rearrange this equation to solve for v:

v = ω * r

At the maximum distance from the center of the turntable, the block will experience the maximum centrifugal force, given by:

F = mv² / r

Where m is the mass of the block.

The maximum centrifugal force must be less than or equal to the maximum static friction force, given by:

F = μs * m * g

Where g is the gravitational acceleration.

Setting these equations equal to each other and solving for r, we get:

rmax = μs * g / ω²

Plugging in the values given in the problem, we get:

rmax = (0.20 * 9.81 m/s²) / (1.4 rad/s)²

rmax ≈ 1.0 m

Therefore, the maximum distance from the center of the turntable that the block can be placed without sliding is approximately 1.0 m.

A Turntable Has an Angular Velocity of 1