Question

You pull on a large box using a rope as in (Figure 1), except the rope is at an angle of 15.0∘ below the horizontal. The weight of the box is 265 N, and the coefficient of kinetic friction between the box and the floor is 0.270. What must be the tension in the rope to make the box move at a constant velocity?

What is the normal force that the floor exerts on the box?

Answer 1

Solution

To resolve this problem, we make a FBD. Also, we apply the Newtom Second Law.

Data

We can see the forces in the figure:

(1)

The rope pushes the box at constant speed, so the acceleration is zero

Then

(2)   

(3)

The Friction Force is defined, as follows:

(4)

Sustitute eq(4) and eq(3):

(5)

But

(6)

(7)

(8)

Now, we make the vertical Components:

(9)

(10)

(11)

Also:

(12)

(13)

Sustitute the eq(13) in eq(11) in , we have:

(14)

What must be the tension in the rope to make the box move at a constant velocity?

Sustitute the equation (14) in (8):

What is the normal force that the floor exerts on the box?

With the equation (14):