How to Solve Dynamics Exercise Involving Force Representation?

[erobz]

He asked me about the diagram, i dunno how to draw it cuz i didn't even understand the situation of the question, for that reason i asked him about the forces of block B. But, What do you think I should do in this case? give up? Or should I tear up the exercise paper because I couldn't understand it?

I don't really know what your problem is with me, but not all students are treated the same way, each person has his own way of understanding. + I'm trying my best to do everything by myself. And let you know, I also don't have the time. I still have to study mathematics, chemistry, and Computer science as well. So, if somebody can help me to understand just the last question without making it look harder than it is ,would be nice and humane too.

Thank you.

They want Free Body Diagrams of both blocks the instant before the second block begins to move. Leave forces resolved vertically and horizontally.

 

[PeroK]

What do you think I should do in this case? give up? Or should I tear up the exercise paper because I couldn't understand it?

I don't understand the question.

I don't understand why the block moves at constant speed, when it should accelerate under the force $F_0$?

If some complex dynamics involving the spring are intended, then I don't understand those either.

If $F_0$ is the minimum force to move the first block, it won't be enough to move both blocks. Not with those coefficients of friction.

 

[erobz]

I don't understand the question.

I don't understand why the block moves at constant speed, when it should accelerate under the force $F_0$?

If some complex dynamics involving the spring are intended, then I don't understand those either.

If $F_0$ is the minimum force to move the first block, it won't be enough to move both blocks. Not with those coefficients of friction.

I interpret it as "if this, then this", they say $F_o$ budges the first block. They then say the block then moves at constant velocity (implying $F$ instantaneously decreases-ignoring the spring dynamics). Then as the spring is compressing, the force $F$ must be increasing to maintain constant velocity of block 1 - but again "who cares". They also say it moves with constant velocity only over a certain range $\Delta x$, that we find to be less than the range of full compression, indicating another change in $F$, past displacement $\Delta x$ such that block 1 is accelerating just before block 2 budges.

It's certainly leaves much to be desired IMO, but that's my take up to this point?

 

[PeroK]

I interpret it as "if this, then this", they say $F_o$ budges the first block. They then say the block then moves at constant velocity (implying $F$ instantaneously decreases-ignoring the spring dynamics). Then as the spring is compressing, the force $F$ must be increasing to maintain constant velocity of block 1 - but again "who cares". They also say it moves with constant velocity only over a certain range $\Delta x$, that we find to be less than the range of full compression, indicating another change in $F$, past displacement $\Delta x$ such that block 1 is accelerating just before block 2 budges.

It's certainly leaves much to be desired IMO, but that's my take up to this point?

Hmm?

 

[erobz]

Hmm?

That bad?

 

[PeroK]

That bad?

If I were the OP, I would move on at this point.

 

[srnixo]

They want Free Body Diagrams of both blocks the instant before the second block begins to move. Leave forces resolved vertically and horizontally.

Is it like that?i'm not pretty sure about it btw.
( I think that even if B has not moved yet, but the effect of the spring remains because the other one moved before)
+ About Cb which is the contact force of object B Is it likely that it is inclined due to the presence of friction, and not directly vertically upward? Right?

[If I made anything wrong, please correct me and explain why]​

 

[srnixo]

They want Free Body Diagrams of both blocks the instant before the second block begins to move. Leave forces resolved vertically and horizontally.

Here is my attempt at the fifth question regarding numerical calculation.

i hope it's correct.

 

[Lnewqban]

I know this information,The problem is that I couldn't solve it. I understood all the exercise but i couldn't solve. I have writing problems and calculation issues

Block B does not "know" about the existence of block A or of force F.

F forces A to move, which compresses the left end of the spring, which accumulates elastic energy (increasing force as length decreases at rate K), which manifests itself as increasing pushing force at the right end of the spring, which is what block B "feels" on its left side.

Think of how both extreme situations change what block B "feels":
1) Replace the spring with a rope.
2) Replace the spring with a steel bar.

The situation described in our problem is something in between.

In order to better understand it, you can break the situation in several steps:

1) Between block A and the horizontal surface that supports it, a resistive force (static friction) develops to resist the movement of A induced by F.
If the magnitude of F is big enough, it could "break the grip of the surface", making block A slide.
That grip of the surface is nothing but the maximum possible value that the static friction force can reach, which is Nμs.

2) After the above happens, several things simultaneously develop. Kinematic friction opposes F and the sliding of A. Increasing force is transferred onto both, block A and B (not full magnitude of F, but Kx of the spring).

3) If the magnitude of the elastic force from the spring (Kx) grows big enough, it could "break the grip of the surface", making block B slide.

 

[PeroK]

Isn't the question in the book nonsense? Does no one agree with me on this?

@srnixo which textbook is this from?

 

[srnixo]

Block B does not "know" about the existence of block A or of force F.

F forces A to move, which compresses the left end of the spring, which accumulates elastic energy (increasing force as length decreases at rate K), which manifests itself as increasing pushing force at the right end of the spring, which is what block B "feels" on its left side.

Think of how both extreme situations change what block B "feels":
1) Replace the spring with a rope.
2) Replace the spring with a steel bar.

The situation described in our problem is something in between.

In order to better understand it, you can break the situation in several steps:

1) Between block A and the horizontal surface that supports it, a resistive force (static friction) develops to resist the movement of A induced by F.
If the magnitude of F is big enough, it could "break the grip of the surface", making block A slide.
That grip of the surface is nothing but the maximum possible value that the static friction force can reach, which is Nμs.

2) After the above happens, several things simultaneously develop. Kinematic friction opposes F and the sliding of A. Increasing force is transferred onto both, block A and B (not full magnitude of F, but Kx of the spring).

3) If the magnitude of the elastic force from the spring (Kx) grows big enough, it could "break the grip of the surface", making block B slide.

Thank you so much. I appreciate your effort.

 

[srnixo]

Isn't the question in the book nonsense? Does no one agree with me on this?

@srnixo which textbook is this from?

@PeroK , i actually don't know, Our professor gave us many exercises regarding dynamics without a solution. Whoever wants to solve them should prepare for the exam, and whoever does not want to do so, that is his choice.

 

[PeroK]

@PeroK , i actually don't know, Our professor gave us many exercises regarding dynamics without a solution. Whoever wants to solve them should prepare for the exam, and whoever does not want to do so, that is his choice.

In my analysis, block A moves 1 cm then stops. Block B does not move.

 

[PeroK]

PS a good question would be to find the minimum force such that both blocks move!

 

[jbriggs444]

Isn't the question in the book nonsense? Does no one agree with me on this?

The question is not well written. It has several obvious shortcomings that I can identify. Let me reformat it so that we may dissect it properly.

Begin question:
Two blocks m₁ = 1 \kg, m₂ = 1 kg are connected to a spring of force K.
Assume the spring is light enough so that its own mass can be neglected.
The assembly is at rest and the spring is neither extended nor compressed.
The assembly can move horizontally on the horizontal surface. The friction between the plane and the masses is
characterized by $\mu_s$ and $\mu_k$. We give M = 1 \text{kg}; $m_A = 1 \text{kg}$; $m_B = 1 \text{kg}$; $\mu_s = 0.5$; $\mu_k=0.4$; $K=200\text{N/M}$ and $g=10 m/s^2$.

The spring is neither extended nor compressed; we apply a force $\vec{F}$ to the body A.

1. What minimum force $\vec{F_0}$ must be applied to block A to make it move?

2. Calculate and represent for $F=F_0$ the forces acting on A and B to scale; $1\text{cm} \to 2 \text{N}$

3. A having started moving, it then moves at constant speed on $\Delta x = 2 \text{cm}$. Calculate the represent the forces acting on the two blocks A and B.

4. For what minimum displacement of mass M block A, does mass block B start moving?

5. Calculate and represent the forces acting on the two blocks A and B just before B begins to move.
End question.

Error 1: The blocks are referred to as $m_1$ and $m_2$, then $A$ and $B$. This is an error in copy editting

Error 2: It is stated twice that the assembly is at rest with the spring neither extended nor compressed. It should have only been stated once. This is an error in copy editting.

Error 3. We are first given the masses of each block. Then later on we are told that $M=1 \text{kg}$ with no mention of what $M$ is. This is an error in copy editting.

Error 4. In part 4, block A is referred to as mass M. But mass M is not part of the problem. This is an error in copy editting. The two blocks are referred to as "masses". Another copy editting problem.

As I read the problem, force $\vec{F}$ is gradually increased until the block A (the left hand block) begins moving. After block A begins moving, force $\vec{F}$ is then modulated so that block A proceeds at constant speed.

There must be a small interval after block A begins moving while it accelerates to its constant speed. The problem does not point this out. However, it is unavoidable. If block A is to move at a constant speed, it must first accelerate to that constant speed. We are expected to understand that the duration of and the distance covered within this period of acceleration is as short as possible so that it may be safely neglected.

 

[haruspex]

If B hasn't moved yet, does this mean he has only two forces? ( The weight and contact force?)

No, it just means the forces are still all in balance, so B is not yet accelerating.
Vertically, the gravitational force balances the normal force from the ground, while horizontally the compression in the spring balances the static friction force.

In q5, we are told it is about to move. This means the static friction force has reached its limit.

 

[haruspex]

In my analysis, block A moves 1 cm then stops. Block B does not move.

Are you assuming the applied force is constant? Since we are told A moves at a constant speed, it must be increasing.

 

[PeroK]

Are you assuming the applied force is constant? Since we are told A moves at a constant speed, it must be increasing.

Which is physically impossible, without yet more unstated assumptions.

If the force on A is changing in some unspecified way, how can you calculate it in part 5? The applied force on block A could be anything by the time block B moves.

I don't understand trying to make sense of an ill-conceived, ill-posed problem.

 

[jbriggs444]

Which is physically impossible, without yet more unstated assumptions.

If the force on A is changing in some unspecified way, how can you calculate it in part 5? The applied force on block A could be anything by the time block B moves.

I don't understand trying to make sense of an ill-conceived, ill-posed problem.

We know that block A is moving at constant speed at [just prior to anyway] the time in question. So we know its acceleration. So we can write down a force balance. All of the other forces on block A are knowable. So we can solve for $\vec{F}$ at that time. [Technically a one sided derivative, but we can let that slide]

 

[PeroK]

We know that block A is moving at constant speed at the time in question. So we know its acceleration. So we can write down a force balance. All of the other forces on block A are knowable. So we can solve for $\vec{F}$ at that time.

No we don't. It only moves at constant speed for 2 cm. Block B doesn't move at that point.

 

[jbriggs444]

No we don't. It only moves at constant speed for 2 cm. Block B doesn't move at that point.

OK, I'll concede that.

 

[berkeman]

Thread is closed temporarily for Moderation, bruh.

 

[Mark44]

[+ I am one of those people who, if they see the solution directly, take a certain amount of time to find the steps of this solution. It is not a requirement that finding the solution directly is a bad thing and makes the student lazy.]

Being unable to find the solution directly is not a good thing. There's really not much learning going in when someone has to see the solution and then reverse-engineers the steps to it.

And let you know, I also don't have the time. I still have to study mathematics, chemistry, and Computer science as well.

Maybe you have bitten off more than you can chew.

 

[berkeman]

After a Mentor discussion, the thread will remain closed. Thank you to all who tried to help this poster.