# Book push Forces problem

## Homework Statement

A 0.407 kg book rests at an angle against one side of a bookshelf. The magnitude and direction of the total force exerted on the book by the left side of the bookshelf are given by:

Force Left = 2.17 Newtons and θ=59 degrees

What must the magnitude and direction of the total force exerted on the book by the bottom of the bookshelf be in order for the book to remain in this position?

Force book = ___?___Newtons
θ = ___?___degrees

## The Attempt at a Solution

Sum of forces in x:

2.17sin(59) - Fcos(θ) = 0 => Fcos(θ) = 1.86

Sum of forces in y

2.17cos(59) + Fsin(θ) = 0 => Fsin(θ) = -1.1176

tan(θ) = (-1.1176)/(1.86) => θ = 211 degrees

F = 2.17 N

this is wrong though

Related Introductory Physics Homework Help News on Phys.org
rcgldr
Homework Helper
The sum of the forces in y must counter the force exerted by gravity, which is m g.

So I was in the right track?
I just need to change my formula to 2.17cos(59) + Fsin(θ) = mg

rcgldr
Homework Helper
Is the 59 θ the angle from vertical or the angle from horizontal?