Box being pulled across horizontal floor with friction

1. Apr 3, 2012

rocapp

1. The problem statement, all variables and given/known data
Sam is pulling a box of mass 30kg on a horizontal floor with a force FT= <50N, 30N>. The frictional force acting on the box by the floor is 20N.
A) By using Newton's second law find the acceleration of the block.
B) What is the normal force acting on the block by the floor?
C) What is the coefficient of kinetic friction between the floor and the box?

2. Relevant equations
Fnet=Fx+Fy
F=ma
Fnormal=m(g+ay) (g is approximated gravity coefficient, 9.8m/s2)
μkFnormal=Fk(force of kinetic friction)
|F|=√Fy2+Fx2
3. The attempt at a solution

A)
FTX=50N - 20N = 30N
FTY=30N +294N = 324N
|F|=√(324N)2 + (30N)2 = 326.77N
F=ma
326.77N = (30kg)a
a = 10.89 m/s2

B)
Fnormal=m(g+ay)
Fnormal=(30kg)(9.8m/s2+10.89 m/s2)
= 620.7N

C)
μkFnormal=Fk
μk(620.7N) = 20N
μk = .0322

2. Apr 3, 2012

PhanthomJay

You are given the x and y components of the applied pulling force. Leave it that way; do not try to combine the components into their resultant vector. Instead, since you know that the net force in the x direction is 30 N, you can now find the acceleration in the x direction using Newton 2. In the y direction, is there any acceleration in that direction if the box stays on the floor?