Using Newton's laws to find an expression for the angle of inclination

[taotao]

Homework Statement

Use Netwon's laws to find an expression for the angle of incilination theta at which the refrigerator starts to slide. Express your answer in terms of possible g, Us, Uk and m.

Homework Equations

Fnet=ma
Ff=UFn

The Attempt at a Solution

I attached my attempt at the solution, I would like to know if I did it properly or made a mistake somewhere.

Thanks :)

 

[BiGyElLoWhAt]

You lost a cosine (or just never included it). See if you can figure out where. That's the only thing I see.

 

[nrqed]

Homework Statement

Use Netwon's laws to find an expression for the angle of incilination theta at which the refrigerator starts to slide. Express your answer in terms of possible g, Us, Uk and m.

Homework Equations

Fnet=ma
Ff=UFn

The Attempt at a Solution

I attached my attempt at the solution, I would like to know if I did it properly or made a mistake somewhere.

Thanks :)

The friction force is $\mu_s N$ where N is the normal force. The normal force here is $not$ mg. Do you see why?

 

[taotao]

On the third line: Fg x sin theta - Us x mg x cos theta? =ma

The cosine should be there to account for the magnitude of the normal force right?

 

[nrqed]

On the third line: Fg x sin theta - Us x mg x cos theta? =ma

The cosine should be there to account for the magnitude of the normal force right?

That's correct!

 

[BiGyElLoWhAt]

Congrats, good job.

 

[taotao]

For my final answer I get: theta = a/g + mu_s*cos theta
Is there any way to simplify that further?

 

[nrqed]

For my final answer I get: theta = a/g + mu_s*cos theta
Is there any way to simplify that further?

I don't see how you get a $\theta$ alone, outside a trig function.

Also, you are considering the case when it is just about to start sliding. So what is the acceleration then?

 

[taotao]

So a=0 and it would only be mu_S*costheta