Question

A box of books weighing 325 N moves at a constant velocity across the floor when the box is pushed with a force of 425 N exerted downward at an angle of 35.2 degrees below the horizontal. Fink Mu,k between the box and the floor

Answer 1

Answer:

Mu,k between the floor and the box is 0.609

Explanation:

given information:

weight of the book, W = 325 N

applied force, F = 425 N

angle, θ = 35.2°

to find the coefficient kinetic between the floor and the box, wee need to calculate the horizontal and vertical force.

first we calculate the vertical force, there are weight, normal force(N) and applied vertical force.

according to Newton's first law

ΣF = 0

Σ$F_{y}$ = 0

W - N + F sin θ = 0

N = W + F sin θ

Next, we calculate the force in horizontal direction. applied force and friction force($F_{friction}$)

Σ$F_{x}$ = 0

F cos θ - $F_{friction}$ = 0

F cos θ - μk (W - F sin θ) = 0

μk =  (F cos θ) / (W + F sin θ)

    = (425 cos 35.2°)/(325+425 sin 35.2°)

    = 0.609