Answer:
The kinetic coefficient of friction between box and floor is 0.443.
Explanation:
Let suppose that the box is accelerated uniformly, the acceleration (), measured in meters per square second, is determined by the following kinematic formula:
(1)
Where:
, - Initial and final speeds of the box, measured in meters per second.
- Time, measured in seconds.
If we know that , and , then the acceleration experimented by the box is:
Based on the body diagram, we proceed to form the equations of equilibrium:
(1)
(2)
Where:
- Magnitude of the force exerted on the box, measured in newtons.
- Direction of the force exerted on the box, measured in sexagesimal degrees.
- Kinetic coefficient of friction between box and floor, dimensionless.
- Normal force from the floor to the box, measured in newtons.
- Mass of the block, measured in kilograms.
- Gravitational acceleration, measured in meters per square second.
Now we proceed to solve the system of equation for the kinetic coefficient of friction between box and floor:
By (1)
By (2)
And then, we get the resulting expression:
(3)
If we know that , , , and , then the kinetic coefficient of friction between box and floor is:
The kinetic coefficient of friction between box and floor is 0.443.