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

In summary, to find the angle of inclination theta at which a refrigerator starts to slide, use Newton's laws and express the answer in terms of possible g, Us, Uk, and m. The equation for finding theta is theta = a/g + mu_s*cos theta, where a is the acceleration (which is 0 in this case) and mu_s is the coefficient of static friction. The cosine is included to account for the magnitude of the normal force.
  • #1
taotao
5
0

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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  • #2
You lost a cosine (or just never included it). See if you can figure out where. That's the only thing I see.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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!
 
  • #6
Congrats, good job.
 
  • #7
For my final answer I get: theta = a/g + mu_s*cos theta
Is there any way to simplify that further?
 
  • #8
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?
 
  • #9
So a=0 and it would only be mu_S*costheta
 

1. How do Newton's laws help in finding an expression for the angle of inclination?

Newton's laws help in finding an expression for the angle of inclination by providing a framework for understanding the forces acting on an object. By applying Newton's laws to the forces acting on an object on an inclined plane, we can determine the relationship between the angle of inclination and the forces involved.

2. What is the first law of motion and how does it relate to finding the angle of inclination?

The first law of motion states that an object at rest will remain at rest and an object in motion will continue in motion at a constant velocity unless acted upon by an external force. This law is relevant in finding the angle of inclination as it helps us understand the forces acting on the object on an inclined plane and how they affect its motion.

3. How does the second law of motion contribute to finding the angle of inclination?

The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. By applying this law to the forces acting on an object on an inclined plane, we can determine the acceleration and use it to find the angle of inclination.

4. What is the role of the third law of motion in finding the angle of inclination?

The third law of motion states that for every action, there is an equal and opposite reaction. This law helps us understand the relationship between the forces acting on the object on an inclined plane and how they affect its motion. By considering the reactions to the forces, we can find the angle of inclination.

5. Are there any practical applications of using Newton's laws to find the angle of inclination?

Yes, there are many practical applications of using Newton's laws to find the angle of inclination. For example, engineers use this concept to design ramps and inclined planes for different purposes, such as wheelchair ramps, ski slopes, and car ramps. It is also useful in understanding the motion of objects on hills or inclines in everyday life.

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