Question

Two students move a 38kg piece of furniture across a flat, horizontal floor. Student A pushes the furniture piece with a force of 140N [W] and student B pulls with a force of 120N [W]. The two students move the furniture piece from rest to a maximum velocity of 3.0m/s [W] over a distance of 13.5m. Determine:

a. The coefficient of friction between the furniture piece and the floor.
b. How many meters will the furniture slide if the students stop pushing at 3.0m/s [W]?
c. What additional force would be required to keep the furniture moving at a constant velocity?

Answer 1

The student's question relates to determining the coefficient of friction for a piece of furniture moved across a floor, how far it will continue to slide if released at a certain speed, and the force needed to maintain a constant velocity.

Step-by-step explanation:

The question pertains to determining the coefficient of friction between a piece of furniture and the floor, calculating the distance it will slide if pushed to a certain velocity and then released, and identifying the additional force required to keep it moving at a constant velocity. To find the coefficient of friction, we use Newton's second law and the work-energy principle. The net force acting on the furniture is the sum of applied forces minus the friction force. As the furniture reaches a maximum velocity, the kinetic energy gained is equal to the work done by the net force over the distance of 13.5 m.

To determine how far the furniture will slide if the students stop pushing, we consider that the only force acting on it would be the force of friction, which will decelerate the furniture until it comes to a stop—this involves the concept of kinetic energy dissipation through friction. Lastly, the additional force required to maintain constant velocity is equivalent to the frictional force acting on the furniture. This can be calculated using the identified coefficient of friction and the normal force exerted on the furniture due to gravity.