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

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Homework Help Overview

The discussion revolves around using Newton's laws to derive an expression for the angle of inclination (theta) at which a refrigerator begins to slide. The problem involves concepts of forces, friction, and motion in a physics context.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the inclusion of cosine factors in the equations, questioning the representation of the normal force and its relationship to the gravitational force. There is an exploration of the conditions under which the refrigerator starts to slide, including the role of static friction.

Discussion Status

The discussion is active, with participants providing feedback on attempts and clarifying the role of various forces. Some guidance has been offered regarding the inclusion of cosine in the equations, and questions about the acceleration when the refrigerator is on the verge of sliding have been raised.

Contextual Notes

Participants are working under the constraints of expressing their answers in terms of variables such as g, Us, Uk, and m, while also adhering to the requirements of the homework assignment.

taotao
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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 :)
 

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

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?
 
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?
 
taotao said:
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!
 
Congrats, good job.
 
For my final answer I get: theta = a/g + mu_s*cos theta
Is there any way to simplify that further?
 
taotao said:
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?
 
So a=0 and it would only be mu_S*costheta
 

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