How to Solve Dynamics Exercise Involving Force Representation?

[srnixo]

Homework Statement

Actually, I solved half of the exercise, but i couldn't solve question 4 and 5. help me please, even with numerical application.

For example: in question 4 when calculating the ∆x = T/K , i dunno if T we take it as 4N or ( T=F⁰ =5N ) or even (T=F'=8N)

And about question 5, i dunno even how to start.

Relevant Equations

Newton's second law.

This is the exercise:

Please help me ( question 4 and 5).​

Here is my effort:
First, I represented the forces on both objects.

Then, i found F⁰ = 5N (question 1)

After that, (question 2) + (question 3)

I hope it's even correct.

 

[erobz]

Would it be possible for you to concisely give the answers you get for each question you are in doubt about?

 

[srnixo]

Would it be possible for you to concisely give the answers you get for each question you are in doubt about?

I said: I tried all the questions, but I was not able to solve the fourth and fifth questions even though I had the numerical values from the above.

If anyone could help me , it would be great.

 

[erobz]

I said: I tried all the questions, but I was not able to solve the fourth and fifth questions even though I had the numerical values from the above.

If anyone could help me , it would be great.

for question 4. lets take the coordinate $x_1$ to be the displacement of block 1. Just before block 2 starts to move what are the forces acting on block 2 in the $x$ direction. Draw a simple diagram.

 

[srnixo]

for question 4. lets take the coordinate $x_1$ to be the displacement of block 1. Just before block 2 starts to move what are the forces acting on block 2 in the $x$ direction. Draw a simple diagram.

For block B: in the xx' we have:
Xx': T - Cbx' = 0 which means T=Cbx
In question 4: Block B is not in motion at all, so we were asked in the question to calculate ∆x.

+ ( I know that we calculate ∆x by the formula ∆x= T/K where K=200N/m, but i dunno the exact value of T.)
+ { Here my ability to complete the rest of the exercise ended )

 

[erobz]

Before block 2 moves the spring compresses by amount $x_1$

 

[srnixo]

Before block 2 moves the spring compresses by amount $x_1$

Yep which is Force T = Tension, i know this.

 

[erobz]

Yep which is Force T = Tension, i know this.

Ok, then write Newtons 2nd for block 1.

 

[srnixo]

Ok, then write Newtons 2nd for block 1.

And then!!!

 

[erobz]

Scratch that, we know the displacement $x_1$ ( max displacement of block 1 before block 2 moves). We know the value of $T$ as you call it. Write the force balance on 2 in terms of the known parameters...

 

[srnixo]

Scratch that, we know the displacement $x_1$. We know the value of $T$ as you call it. Write the force balance on 2 in terms of the known parameters...

I can directly calculate it by using ∆x=T/K , no need for equations, it's already the same , but i dunno the value of T , there are 3 possibilities which are T=4N or T=F⁰=5N or T=F'=8N, you need to well understand the situation.

 

[erobz]

I can directly calculate it by using ∆x=T/K , no need for equations, it's already the same , but i dunno the value of T , there are 3 possibilities which are T=4N or T=F⁰=5N or T=F'=8N, you need to well understand the situation.

The only forces acting on block 2 are the spring force and static friction...

 

[srnixo]

The only forces acting on block 2 are the spring force and static friction...

I'm truly confused , could you please provide me the solution directly if u're able :(

 

[erobz]

I'm truly confused , could you please provide me the solution directly if u're able :(

We aren't allowed to provide a solution until you have successfully solved the problem, by taking the advice given to you.

There are only 2 forces acting on block 2. The spring force pushing block 2 to the right ( the spring is in equilibrium as its being compressed - it has no mass - do a force balance on the spring if you have doubts ), and static friction is resisting motion of block 2...pushing to the left.

 

[srnixo]

There are only 2 forces acting on block 2. The spring force pushing block 2 to the right ( the spring is in equilibrium as its being compressed - it has no mass ), and static friction is resisting motion of block 2...pushing to the left.

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

 

[erobz]

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

Then what is $x_1$? The displacement of block 1, just before block 2 begins to move? Use the force balance on block 2.

 

[srnixo]

Then what is $x_1$? The displacement of block 1, just before block 2 begins to move? Use the force balance on block 2.

It is written that in ∆x=2cm block A starts moving with constant speed but B doesn't
Then in question 4: was all about ∆x of block B to start moving

 

[erobz]

It is written that in ∆x=2cm block A starts moving with constant speed but B doesn't
Then in question 4: was all about ∆x of block B to start moving

I think it's written that over range $\Delta x = 2 \rm{cm}$, the block A moves with constant velocity. Thats just letting you know what the force balance on block 1 over that range is.

Put that aside for a moment and figure out how far the spring would need to be compressed before block 2 begins to move. Write the force balance on block two in terms of $x_1$, and other parameters $\mu_s, k, M, g$

 

[srnixo]

I think it's written that over range $\Delta x = 2 \rm{cm}$, the block A moves with constant velocity. Thats just letting you know what the force balance on block 1 over that range is.

Put that aside for a moment and figure out how far the spring would need to be compressed before block 2 begins to move. Write the force balance on block two in terms of $x_1$, and other parameters $\mu_s, k, M, g$

Isn't 4N huh?

 

[erobz]

Isn't 4N huh?

No, $T$ is not $4 \rm{N}$.

$x_1$?

 

[srnixo]

No, $T$ is not $4 \rm{N}$.

$x_1$?

Then it's 5N , i considered the F⁰ case.

 

[erobz]

Then it's 5N , i considered the F⁰ case.

Yes, its static friction acting on block 2...it's not moving.

 

[srnixo]

Yep yep what about question 5 mr. Do u know anything about it! I actually didn't understand anything about it

 

[erobz]

Yep yep what about question 5 mr. Do u know anything about it! I actually didn't understand anything about it

What did you get for $x_1$? Something should stick out at you when comparing it to the range where block 1 moves at constant velocity $\Delta x$.

 

[srnixo]

What did you get for $x_1$?

Bruh i wanna cry for real, if u're talking about question 4, i just understood the situation and used ∆x=5N\200 N/m. So simple

 

[erobz]

Bruh i wanna cry for real, if u're talking about question 4, i just understood the situation and used ∆x=5N\200 N/m. So simple

Bruh...you want to cry... This is like pulling my own teeth. I'm out, Good luck.

 

[srnixo]

Bruh...you want to cry... This is like pulling my own teeth. I'm out, Good luck.

Haha, at least thank you for giving me a hint about the tension force. I hope i find who will help me with question 5.

 

[kuruman]

Haha, at least thank you for giving me a hint about the tension force. I hope i find who will help me with question 5.

I can pitch in. Start by drawing two free diagrams, one for each block, just before block B begins to move. Draw it to scale and point out which forces have equal magnitudes. Please post your diagram right side up.

 

[haruspex]

First, a nitpick: you keep writing "tension", but the spring is under compression.

about question 4, i just understood the situation and used ∆x=5N\200 N/m. So simple

So the situation is now the same as in q3 but with a different displacement.

 

[erobz]

Haha, at least thank you for giving me a hint about the tension force. I hope i find who will help me with question 5.

Pro tip: If you come here for help, try not to arrogantly resist every question/task that is asked of you. We aren't paid for our service. People are trying to help you learn how to solve the problem on their own time for their own reasons. Trust me, it's the more difficult route for both parties, but it's the most beneficial for you.

 

[srnixo]

Pro tip: If you come here for help, try not to arrogantly resist every question/task that is asked of you. We aren't paid for our service. People are trying to help you learn how to solve the problem on their own time for their own reasons. Trust me, it's the more difficult route for both parties, but it's the most beneficial for you.

I am nothing but a student of science, and a student of the most difficult sciences, physics, and I am studying for my first university degree, so it is natural that I need help, and I am here to ask if anyone can help me and simplify things for me, not to make them more difficult. In addition, it is not a requirement that I help someone in exchange for money. If I have information, I will be happy to save someone from drowning in problems related to science. On top of all this, we are human beings with different abilities. Perhaps you are a person who is quick to calculate and understand quickly, but I am not necessarily like you. Perhaps I am a person of weak understanding.

[+ 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.]

If you want to help, do it with conscience and good intentions. Do not incite people to deal with others in the same way you do. Every human being has a certain intention and certain principles.Thank you again.

 

[srnixo]

First, a nitpick: you keep writing "tension", but the spring is under compression.So the situation is now the same as in q3 but with a different displacement.

Alright alright thank you :)

 

[srnixo]

I can pitch in. Start by drawing two free diagrams, one for each block, just before block B begins to move. Draw it to scale and point out which forces have equal magnitudes. Please post your diagram right side up.

Alright, i'm sorry my english is not that good for that reason i didn't understand the question.

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

 

[erobz]

I am nothing but a student of science, and a student of the most difficult sciences, physics, and I am studying for my first university degree, so it is natural that I need help, and I am here to ask if anyone can help me and simplify things for me, not to make them more difficult. In addition, it is not a requirement that I help someone in exchange for money. If I have information, I will be happy to save someone from drowning in problems related to science. On top of all this, we are human beings with different abilities. Perhaps you are a person who is quick to calculate and understand quickly, but I am not necessarily like you. Perhaps I am a person of weak understanding.

[+ 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.]

If you want to help, do it with conscience and good intentions. Do not incite people to deal with others in the same way you do. Every human being has a certain intention and certain principles.Thank you again.

Before progress can be made, both the helper and helpee must get on the same page. This requires cooperation with the helper. For instance, if they ask for diagrams give them the diagram. If they ask you to calculate something - calculate it - no matter how trivial it may seem. You may be taking a few steps backward, before you can move forward so the helper can access what you actually know and where a potential issue may be. There are many talented educators here - not saying I'm one of them - but you must trust the process they created and cooperate if you expect to learn.

 

[srnixo]

Before progress can be made, both the helper and helpee must get on the same page. This requires cooperation with the helper. For instance, if they ask for diagrams give them the diagram. If they ask you to calculate something - calculate it - no matter how trivial it may seem. You may be taking a few steps backward, before you can move forward so the helper can access what you actually know and where a potential issue may be. There are many talented educators here - not saying I'm one of them - but you must trust the process they created and cooperate if you expect to learn.

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.

 

[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.