A ninety kilogram sofa is being pushed by four meters to the other side of a hall. After an initial push the sofa is pushed with a 600 N force. In this case, 0.6 is the coefficient of kinetic friction. (The diagram shows the sofa being pushed from the right).

Question

1) What is the value and direction of the total force on the sofa?

I got 70.26 Newtons but don't know how to get the direction.

2) What is the value and direction of the acceleration of the sofa?

.78m/s^2, but don't know the direction again.

3. How long would it take to push the sofa 4 meters across?

Not sure what I am supposed to use to solve this.

Answer 1

total force on the sofa:
a. floor holding it up: 90*9.8N
b. person pushing on it: 600N
c. Fricion from floor: .6*90

ok, net horizontal force is 600-54
net vertical force= 882N
so net force=sqrt(882^2+546^2)
direction: arc tan (882/546)above the horizontal.

acceleration: 546/90 horizontal.