A 50-N applied force...

Question

A 50-N applied force (pulling 30 degrees up from the horizontal) accelerates a 5 kg box across a horizontal floor.
a. What is the normal force on the box?
b. If the coefficient of friction between the floor and box is 0.15, what is the acceleration of the box?

Answer 1

The 50 N force must be broken into vertical and horizontal components.

F_v = 50cos30 = 43.3 N

F_h = 50sin30 = 25 N

 

The normal force on the box is the net of its weight and F_v.

 

N = 5(9.81) - 43.3 = 5.75 N

 

We will find acceleration from F = ma, where F = F_h - F_f = 25 - .15(5.75) = 24 N

 

a = 24/5 = 4.8 m/s²