Finding the applied force and normal force for a box against a frictionless wall

[blazeuofa]

Homework Statement

A box of mass (m) is held against a frictionless wall by a force of magnitude F at an angle $$\theta$$ (above right). Determine F in terms of whatever variables are necessary. Similarly, determine the magnitude of the normal force (n) in terms of whatever variables are necessary. (Hint: you can only have m, $$\theta$$, and g in your answers)

Homework Equations

The Attempt at a Solution

F=ma, a=g
F=mg


n=F?

 

[LowlyPion]

They want you to resolve the Force into the horizontal and vertical components of force necessary to hold the box with no net force.

If you don't have a sinθ or cosθ in your answer you can be certain it isn't correct.

 

[blazeuofa]

They want you to resolve the Force into the horizontal and vertical components of force necessary to hold the box with no net force.

If you don't have a sinθ or cosθ in your answer you can be certain it isn't correct.

so F_x=Sin$$\theta$$ and F_y=mg

I know the answer is F=mg/sin $$\theta$$, but I thought you divide F_x by F_y? So why is the answer F=mg/sin $$\theta$$?

 

[LowlyPion]

Not quite, because they defined the angle θ with respect to "rightward" axis. Hence the component that balances the m*g is going to be the vertical sinθ component.