Question

A janitor exerts a force on a 1.1-kg push broom as he walks across the floor air constant speed. The coefficient of friction between the floor and the broom is 0.45 and the broom handle makes an angle of 41° with the horizontal. Determine the amount of force with which the janitor pushes downward (along the handle of the broom) in order to achieve this constant speed motion.

Answer 1

To achieve constant speed motion, the janitor must push downward with a force of 10.78 N along the handle of the broom.

Step-by-step explanation:

To determine the force with which the janitor pushes downward to achieve constant speed motion, we need to analyze the forces acting on the broom.

First, let's draw a free-body diagram for the broom. The vertical component of the janitor's force is equal to the gravitational force acting on the broom, which is given by:

Fvertical = m * g = 1.1 kg * 9.8 m/s² = 10.78 N

The horizontal component of the janitor's force is what overcomes the friction force. The friction force is given by:

Ffriction = μN = 0.45 * (m * g) = 0.45 * (1.1 kg * 9.8 m/s²) = 4.882 N

Since the broom is moving at a constant speed, the horizontal component of the janitor's force must be equal to the friction force:

Fhorizontal = Ffriction = 4.882 N

Therefore, the force with which the janitor pushes downward (along the handle of the broom) to achieve constant speed motion is 10.78 N.