A 4.10 kg block is pushed along a floor by a constant applied force that is horizontal and has a magnitude of 39.0 N. Figure 6-26 gives the block's speed v versus time t as the block moves along an x axis on the floor. What is the coefficient of kinetic friction between the block and the floor?
To find the coefficient of kinetic friction between the block and the floor, we need to analyze the forces acting on the block. The only horizontal force acting on the block is the applied force, which is 39.0 N in this case. From the graph of speed vs. time, we can determine that the block moves with a constant velocity (as the speed remains constant over time).
Since the block moves at a constant velocity, we know that the net force acting on it is zero. This means the force of friction (which is in the opposite direction of the applied force) must be equal in magnitude to the applied force.
Therefore, the force of kinetic friction is 39.0 N.
The force of friction can be calculated using the formula:
force of friction = coefficient of friction x normal force,
where the normal force is the force exerted by the floor on the block, which is equal to the weight of the block (mg).
To find the coefficient of kinetic friction, we need the mass of the block. In this case, the mass of the block is given as 4.10 kg.
Now, we can calculate the coefficient of kinetic friction as follows:
force of friction = coefficient of friction x normal force
39.0 N = coefficient of friction x (4.10 kg x 9.8 m/s^2)
39.0 N = coefficient of friction x 40.18 N
Divide both sides of the equation by 40.18 N:
coefficient of friction = 39.0 N / 40.18 N
coefficient of friction ≈ 0.97
Therefore, the coefficient of kinetic friction between the block and the floor is approximately 0.97.