Answer :
The coefficient of kinetic friction between the floor and the box is approximately 0.21.
The coefficient of kinetic friction can be determined using the equation:
friction force = coefficient of kinetic friction * normal force
First, let's find the normal force acting on the box. The normal force is equal to the weight of the box, which can be calculated using the formula:
weight = mass * gravitational acceleration
The mass of the box is given as 5.00 kg, and the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight of the box is:
weight = 5.00 kg * 9.8 m/s^2 = 49.0 N
Next, we need to calculate the work done by friction. The work done by friction is equal to the initial kinetic energy of the box since it comes to rest. The initial kinetic energy can be calculated using the formula:
kinetic energy = 0.5 * mass * velocity^2
Substituting the given values, we get:
kinetic energy = 0.5 * 5.00 kg * (5.00 m/s)^2 = 62.5 J
Since the work done by friction is equal to the initial kinetic energy, we can write:
work done by friction = friction force * distance
Substituting the given values for distance (6 m) and the work done by friction (62.5 J), we can solve for the friction force:
62.5 J = friction force * 6 m
friction force = 62.5 J / 6 m = 10.42 N
Finally, substituting the friction force (10.42 N) and the normal force (49.0 N) into the equation for the coefficient of kinetic friction, we can solve for the coefficient:
10.42 N = coefficient of kinetic friction * 49.0 N
coefficient of kinetic friction = 10.42 N / 49.0 N ≈ 0.21
Therefore, the coefficient of kinetic friction between the floor and the box is approximately 0.21.
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