A cable attached to a block of mass 14 kg pulls the block along a horizontal floor at a constant velocity. If the tension in the cable is 5.4 N, what is the coefficient of kinetic friction between the block and the floor?

0.3857142857

To find the coefficient of kinetic friction between the block and the floor, we can use the formula:

μ = Fk / N

where:
- μ is the coefficient of kinetic friction,
- Fk is the force of kinetic friction, and
- N is the normal force.

In this case, since the block is moving at a constant velocity, the force of kinetic friction is equal in magnitude and opposite in direction to the tension in the cable, which is 5.4 N. The normal force is the force exerted by the floor on the block, which is equal to the weight of the block since it is on a horizontal floor.

The weight of the block is given by the formula:

W = m * g

where:
- W is the weight of the block,
- m is the mass of the block, and
- g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the given values, we have:

W = 14 kg * 9.8 m/s^2
W = 137.2 N

Now, we can calculate the coefficient of kinetic friction:

μ = Fk / N
μ = 5.4 N / 137.2 N
μ ≈ 0.039

Therefore, the coefficient of kinetic friction between the block and the floor is approximately 0.039.