Question

4. 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° below the horizontal. Find mk between the box and the floor.

Answer 1

The coefficient of friction between the box and the floor is determined as 0.75.

How to calculate the coefficient of friction?

The coefficient of friction between the box and the floor is calculated by applying the following formula as shown below.

F (net) = ma

F(applied) - F(friction) = ma

F cosθ - μ mg = ma

Where;

• m is the mass of the box
• a is the acceleration of the box

Since the box moves at a constant velocity, the acceleration, a = 0

F cosθ - μmg = 0

F cosθ - μW = 0

μW = F cosθ

μ = (F cos θ ) / W

μ = ( 425 N x cos (90 - 35.2) ) / 325 N

μ = 0.75

Answer 2

0.61°

Step-by-step explanation:

Since the box move at constant velocity, it means there is no acceleration then we can say it has a balanced force system.

Pulling force= resistance force

From the formula for pulling force,

F(x)= Fcos(θ)

= 425×cos(35.2)

=347N

The force exerted downward at an angle of 35.2° below the horizontal= Fsin(θ)= 425sin(35.2)

=425×0.567=245N

Resistance force= (325N+ 245N) (α)= 570N(α)

We can now equates the pulling force to resistance force

570 (α)= 347N

(α)= 347/570

= 0.61