Answer:
Friction = μ * normal force
where μ is the coefficient of friction between the box and the floor, and the normal force is the force exerted on the box by the floor.
Since the box is moving at a constant velocity, the net force acting on the box is zero. This means that the sum of all the forces acting on the box must be zero. The applied force is pulling the box in the direction of the angle of 35.0°, and the force of friction is opposing the applied force and acting in the opposite direction.
To find the force of friction, we can set up the following equation:
Friction + 212N * cos(35.0°) = 0
The normal force is equal to the weight of the box, which is 55.7 kg * 9.8 m/s2 = 544.66 N.
Substituting this value for the normal force and the coefficient of friction into the equation above, we get:
Friction = μ * 544.66 N
Solving for μ, we get:
μ = Friction / 544.66 N
Substituting the known values into this equation, we get:
μ = -212N * cos(35.0°) / 544.66 N
Simplifying this expression and substituting in the value for the cosine of 35.0°, we get:
μ = -0.6386
Therefore, the force of friction acting on the box is -0.6386 * 544.66 N = -350.66 N.
Step-by-step explanation: