Acceleration of gravity problem

[allora_97]

Homework Statement

A(n) 43 kg block is pushed along the ceiling
with a constant applied force of 560 N that
acts at an angle of 67◦ with the horizontal,
as in the figure. The block accelerates to the
right at 4.5 m/s2.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the normal force
the ceiling exerts on the block?
Answer in units of N.

Homework Equations

F=ma
Fn = mg

The Attempt at a Solution

I tried to find Fn = mg = 560sin67, it didn't work
any ideas?

 

[allora_97]

here's the image

 

[PhanthomJay]

Homework Statement

A(n) 43 kg block is pushed along the ceiling
with a constant applied force of 560 N that
acts at an angle of 67◦ with the horizontal,
as in the figure. The block accelerates to the
right at 4.5 m/s2.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the normal force
the ceiling exerts on the block?
Answer in units of N.

Homework Equations

F=ma
Fn = mg

The normal force, F_n, is the perpendicular contact force exerted by the ceiling on the block. It is not the weight of the block.

The Attempt at a Solution

I tried to find Fn = mg = 560sin67, it didn't work
any ideas?

Your equation makes no sense. 560sin67 is the upward vertical component of the applied 560 N force. Look at all the forces acting in the vertical direction, determine the net force acting in that direction, and then use one of Newton's laws to solve for F_n.