Box being pulled across horizontal floor with friction

[rocapp]

Homework Statement

Sam is pulling a box of mass 30kg on a horizontal floor with a force F_T= <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?

Homework Equations

F_net=F_x+F_y
F=ma
F_normal=m(g+a_y) (g is approximated gravity coefficient, 9.8m/s²)
μ_kF_normal=F_k(force of kinetic friction)
|F|=√F_y²+F_x²

The Attempt at a Solution

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

B)
F_normal=m(g+a_y)
F_normal=(30kg)(9.8m/s²+10.89 m/s²)
= 620.7N

C)
μ_kF_normal=F_k
μ_k(620.7N) = 20N
μ_k = .0322

 

[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?