Checking if velocity and position graphs are consistent

[Differentiate it]

Homework Statement

Acceleration of Blocks Due to a Time Varying Force: A block m, is placed on smooth ground over which another mass m, is placed. Friction coefficient between m, and m₂ is u. Now a time varying horizontal external force F = bt is applied on m2. Find acceleration of block with time and plot acceleration v/s time graph of both blocks.

Relevant Equations

F = ma

I have attempted this question - Are the graphs correct?

 

[erobz]

Is $m_2$ sitting on top of $m_1$? It isn't clear in the problem statement.

 

[Differentiate it]

Is $m_2$ sitting on top of $m_1$? It isn't clear in the problem statement.

Yes, it is. Sorry for not mentioning it earlier

 

[hutchphd]

What causes the discontinuity?

 

[erobz]

1) What is the reasoning that you expect a drop in acceleration for $m_2$ once the force $F$ exceeds the static friction between the masses (think about the change in force acting on each of the masses from static to kinetic friction)?

2) The slope of the acceleration vs time before and after the discontinuity appear parallel to me, is that drawn to scale (they won't be parallel)?

3) For the same reason in (1), how does that effect the graph for $m_1$ (there is a missing discontinuity there)?

 

[Differentiate it]

1) What is the reasoning that you expect a drop in acceleration for $m_2$ once the force $F$ exceeds the static friction between the masses?

2) The slope of the acceleration vs time before and after the discontinuity appear parallel to me, is that drawn to scale?

Yes, it is supposed to be parallel Here is my working if you want to take a look

 

[Differentiate it]

1) What is the reasoning that you expect a drop in acceleration for $m_2$ once the force $F$ exceeds the static friction between the masses?

2) The slope of the acceleration vs time before and after the discontinuity appear parallel to me, is that drawn to scale?

 

[erobz]

So, you think the slope of $a_2(t)$ before and after $t = \frac{\mu m_2g}{b}$ are equal. Hmmm.

Before the force of static friction is exceeded what is the acceleration $a_2(t)$ of $m_2$? What is the acceleration $a_1(t)$ of $m_1$?

 

[Differentiate it]

So, you think the slope of $a_2(t)$ before and after $t = \frac{\mu m_2g}{b}$ are equal. Hmmm.

Before the force of static friction is exceeded what is the acceleration $a_2(t)$ of $m_2$? What is the acceleration $a_1(t)$ of $m_1$?

Both are the same: bt/m1

 

[erobz]

Both are the same:

The first part is correct. They are both the same.

bt/m1

The second part is not.

 

[Differentiate it]

The first part is correct. They are both the same.

The second part is not.

Could you please explain why?

 

[erobz]

Could you please explain why?

How much mass is being accelerated by the applied force $F$ on $m_2$?

Spoiler: Hint

Remember, we are talking about a time before they ($m_1$ & $m_2$) "unstick" at this point.