Question

A box of mass 80kg is to be pulled along a horizontal floor by means of a light rope. The rope is pulled with a force of 100N and the rope is inclined 20 degrees to the horizontal

A. Draw a diagram showing forces acting on the box
B. Calculate the frictional force between the box and the floor and also the normal reaction

If the frictional force is 120N and the box is now pulled along the floor with the rope always inclined at 20 degrees to the horizontal
C. Calculate the force with which the rope must be pulled for the box to move at a constant speed.
D. Calculate the acceleration if the force Is 140N

Answer 1

A.

B. Calculate the normal reaction:

$$f=\mu N,\\\space\\ N=\frac{f}{\mu}.$$

On the other hand, assuming zero acceleration under 100N force and normal coordinate system (y up and x to the right), according to Newton's second law, we have

$$y: N-mg+F\text{ sin}20°=0, \\ N=mg-F\text{ sin}20°=750\text{ N}.\\ x: f-F\text{cos}20°=0,\\ f=F\text{cos}20°=94\text{ N}.$$

C. Write the same condition for equilibrium along x-axis:

$$x: f-F\text{cos}20°=0,\\ F=f/\text{cos}20°=130\text{ N}.$$

D. The acceleration is

$$f-F\text{ cos}20°=-ma,\\\space\\ a=\frac{F\text{ cos}20°-f}{m}=0.14\text{ m/s}^2.$$