Physics homework question revised

A 4.5kg cat is sitting at rest on a level fence rail.

1. How large is the normal force on the cat?

2. Suppose the fence rail is tilted to 24 degree angle above horizontal, but the cat remains at rest because of friction. What is the normal force on the cat?

3. To what angle should the fence rail be tilted so that the normal force on the cat is exactly 6N?

Here is what I have.

1. n=mg (m=0.23kg and g=9.8) n=0.23kg(9.8m/s^2) n= 2.254N

2. I think the second one is solved using a ramp vectors and the equation would be: m x g x cos θ
If so it would be 0.23kg x 9.8m/s^2 x cos 24 = 2.05913N

3. If the last problem is set up right then the last problem should just be algebra right? But I'm not sure how to set it up/solve it.

I am not feeling very good about this problem at all. Can you please walk me through this, especially parts 2 and 3.

Thank you in advance!

Where did the frog come from ?? Parts one and two look OK. except the cat's mass seems to have changed ??
For 3 just put m g costheta = 6N and solve for theta 4.5 x 9.8 costheta = 6 so theta = arccos ( 6/44.1) or about 82 degrees (the cat would probably slide down by then!!)

You seem to be using .23 kg where the problem specifies 4.5 kg

1. Fn = m*g*cosΘ = 4.5*9.8*cos0° = 44.1 N

2 Fn = m*g*cosΘ = 4.5*9.8*cos24° = 40.287 N

3. 6 = m*g*cosΘ → cosΘ = 6/(m*g) = .136 → Θ = 82.18°