A bureau rests on a rough horizontal surface ($\mu$_s = 0.50, $\mu$_k = 0.40). A constant horizontal force, just sufficient to start the bureau in motion, is then applied. The acceleration of the bureau is: A) 0 B) 0.98 m/s ² C) 3.3 m/s ² D) 4.5 m/s ² E) 8.9 m/s ²

Question

Quizplus · Accepted Answer

The coefficient of static friction is 0.5, which means that the minimum force required to start the bureau in motion is equal to the normal force on the bureau multiplied by 0.5. The normal force on the bureau is equal to the weight of the bureau, which is mg. Therefore, the minimum force required to start the bureau in motion is 0.5mg.

Once the force is applied, the bureau will experience a net force in the horizontal direction, given by F - friction, where F is the applied force and friction is the force of static friction. The maximum force of static friction is equal to the coefficient of static friction multiplied by the normal force, which is 0.5mg. Therefore, the force of static friction is 0.5mg as long as F is less than or equal to 0.5mg.

When F is equal to 0.5mg, the net force on the bureau is zero, so it does not accelerate. When F is greater than 0.5mg, the net force on the bureau is F - 0.5mg, which is greater than zero and causes the bureau to accelerate. The acceleration is given by (F - 0.5mg)/m.

Substituting F = 0.5mg into the acceleration equation gives (0.5mg - 0.5mg)/m = 0, which means the bureau does not accelerate. Therefore, the correct answer is B.

A Bureau Rests on a Rough Horizontal Surface μ\muμ s = 0

A Bureau Rests on a Rough Horizontal Surface $\mu$ _s = 0