Newton's Second Law of Motion -- Three masses, an inclined plane and a pulley

[mustafamistik]

Homework Statement

It's not Homework.

Relevant Equations

F=m*a

I did part a and part b but stuck in part c. Could you help me? (Part a and b attached.)

 

[haruspex]

Homework Statement:: It's not Homework.
Relevant Equations:: F=m*a

I did part a and part b but stuck in part c. Could you help me?

Please post your answers to parts a and b.

 

[mustafamistik]

Please post your answers to parts a and b.

I edited. You can help even if you tell me a solution way. Cause I don't even know what to do .

 

[haruspex]

I edited. You can help even if you tell me a solution way. Cause I don't even know what to do .

You are missing a force on m₁.

 

[mustafamistik]

You are missing a force on m₁.

Is it Friction force ?

 

[haruspex]

Is it Friction force ?

Yes.

 

[mustafamistik]

Yes.

Thanks. Could you give a hint for part c?

 

[PeroK]

Thanks. Could you give a hint for part c?

Think about the maximum acceleration that is possible with the given coefficient of friction.

 

[mustafamistik]

Think about the maximum acceleration that is possible with the given coefficient of friction.

friction-m*g*sin(16)=m*a
Is this equation true ?

 

[PeroK]

friction-m*g*sin(16)=m*a
Is this equation true ?

It's hard to make sense of that out of context. Please describe what you are trying to say with that equation.

 

[mustafamistik]

It's hard to make sense of that out of context. Please describe what you are trying to say with that equation.

This equation to find maximum acceleration. (m2*g*cos(16)* μ) -(m2*g*sin(16))=m2*a (F=ma)

 

[PeroK]

This equation to find maximum acceleration. (m2*g*cos(16)* μ) -(m2*g*sin(16))=m2*a (F=ma)

Okay, and the mass cancels out, of course.

What is the relationship between the large mass, $M$, and the acceleration of $m_2$?

 

[mustafamistik]

Okay, and the mass cancels out, of course.

What is the relationship between the large mass, $M$, and the acceleration of $m_2$?

I think,
$T=M*g$
$M*g - (m_1+m_2)*sin(16)=(m_1+m_2)*a$
The acceleration above is the acceleration of the $m_1 and m_2$ since, acceleration of $m_1 and m_2$ must be equal.
But maximum acceleration is,
(m_2*cos(16)* μ )-(m_2*sin(16) )=m_2 * a_max
a_max=cos(16)* μ -sin(16)
Am i right?

 

[haruspex]

$T=M*g$

How are you getting that from Newton's Laws? What are you wrongly assuming?

 

[mustafamistik]

How are you getting that from Newton's Laws? What are you wrongly assuming?

Is it wrong? I don't understand.

 

[haruspex]

Is it wrong? I don't understand.

Answer my question: which of Newton's Laws did you use to write the equation?

 

[mustafamistik]

Answer my question: which of Newton's Laws did you use to write the equation?

I used Newton's Second Law.

 

[haruspex]

I used Newton's Second Law.

Which says..?

 

[mustafamistik]

Which says..?

F=ma

 

[haruspex]

F=ma

And what is a for the mass M?

 

[mustafamistik]

And what is a for the mass M?

g? I get it its not. We should consider all the system. Am i right ?

 

[haruspex]

g? I get it its not

That would be free fall.
What is the relationship between M's acceleration and the acceleration of the masses on the slope?

 

[mustafamistik]

That would be free fall.
What is the relationship between M's acceleration and the acceleration of the masses on the slope?

They are same.

 

[haruspex]

They are same.

Right. And what is the net force on M?

 

[mustafamistik]

Right. And what is the net force on M?

(M*g)-((m_1+m_2)*g*sin(16)) ?

 

[haruspex]

(M*g)-((m_1+m_2)*g*sin(16)) ?

Only consider the forces that act directly on M. What are they?

 

[mustafamistik]

Only consider the forces that act directly on M. What are they?

Gravitational force and T

 

[haruspex]

Gravitational force and T

Right, so write out the ΣF=ma equation for the mass, putting the sum of those forces on the left and its mass times acceleration on the right. Careful with signs.

 

[mustafamistik]

Right, so write out the ΣF=ma equation for the mass, putting the sum of those forces on the left and its mass times acceleration on the right. Careful with signs.

$(M*g)+(m_1+m_2)*g*sin(16) =M*a$

 

[haruspex]

$(M*g)+(m_1+m_2)*g*sin(16) =M*a$

As you correctly stated in post #28, the forces that act on M are gravity and the tension. Those are the only forces that should appear in the equation. Yes, it may turn out that the tension is equal to $(m_1+m_2)*g*\sin(16)$, but take it one step at a time.
And think about the way each force acts on M.