Velocity, traveling distance and friction force on a sliding object

AI Thread Summary
The discussion centers on the sliding dynamics of two metal strips, A and B, which are initially pushed to the same velocity but differ in their orientation during sliding. Object A slides straight, while object B rotates to an angle of 45 degrees as it slides. The key point is that friction plays a crucial role in determining how quickly each object stops, with the frictional forces needing to be compared to answer which object travels a shorter distance. The conversation highlights that the angle of rotation affects the friction experienced by object B, potentially leading to a different stopping distance compared to object A. Ultimately, understanding the frictional forces is essential for solving the problem accurately.
Javad
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Homework Statement
Two equal metal strips (the same material, the same size and mass, mass for each one is 500 g, and size for each one is 50cm* 5cm) are pushed on a straight rigid surface to reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°) between the sliding direction and the longitudinal centerline of the object. Which object will stop sooner (which object will travel a shorter distance (d))?
Relevant Equations
F=ma
Kinetic energy = 1/2mv²
Power = Fv
d = vt + 1/2at²
d = 1/2 (v + v˳)t
Fᵪ=F.cosθ
friction question 4.jpg
 
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Well, work out your relevant equations for ##d## and there is your answer !

##\ ##
 
Javad said:
Homework Statement:: Two equal metal strips (the same material, the same size and mass, mass for each one is 500 g, and size for each one is 50cm* 5cm) are pushed on a straight rigid surface to reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°) between the sliding direction and the longitudinal centerline of the object. Which object will stop sooner (which object will travel a shorter distance (d))?
Relevant Equations:: F=ma
Kinetic energy = 1/2mv²
Power = Fv
d = vt + 1/2at²
d = 1/2 (v + v˳)t
Fᵪ=F.cosθ

View attachment 296671
Assuming object B is initially not rotating and is accelerated by F1 acting through its centre, there is nothing to make object B rotate.

So what you are describing is physically impossible unless there is/are other force(s) you haven't mentioned.
 
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BvU said:
Well, work out your relevant equations for ##d## and there is your answer !

##\ ##
so " d " for both would be equal, what is the effect of angle (ϴ = 45°) on d ?
 
Steve4Physics said:
Assuming object B is initially not rotating and is accelerated by F1 acting through its centre, there is nothing to make object B rotate.

So what you are describing is physically impossible unless there is/are other force(s) you haven't mentioned.
how about if the object rotates accidentally during sliding?
 
Javad said:
how about if the object rotates accidentally during sliding?
Then there must have been some 'accidental' additional forces -- or more precisely, two accidental net torques - one torque to start the rotation and another to stop it.
 
Steve4Physics said:
Then there must have been some 'accidental' additional forces -- or more precisely, two accidental net torques - one torque to start the rotation and another to stop it.
however the velocity of two objects at t1 is the same, what will happen next, is d equal for both objects?
 
Note that "object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°)."
To me, that angle is gradually increasing until reaching 45 degress just before stopping.
Perhaps one side is "feeling" more friction than the opposite one?
 
Javad said:
is d equal for both objects?

There is no ##\theta## in your equations for ##d##, so: yes !

I would like to read your thoughts on this, so could you say something about your views ? (telepathy not being one of my strengths :frown: )

##\ ##
 
  • #11
BvU said:
There is no ##\theta## in your equations for ##d##, so: yes !

I would like to read your thoughts on this, so could you say something about your views ? (telepathy not being one of my strengths :frown: )

##\ ##
Lnewqban said:
Note that "object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°)."
To me, that angle is gradually increasing until reaching 45 degress just before stopping.
Perhaps one side is "feeling" more friction than the opposite one?
They are two separated objects, A and B, not two sides of one object. Object B reaches 45 degrees at t1 and then freely slides to stop, what is the effect of 45 degrees angle on duration and length of sliding?
 

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  • #12
If overall friction would be greater for case B than A, the metal piece simply would change its direction of travel to the path of less friction.
That is what makes the front wheels of a car roll in the steering direction rather than continuing moving forward (which only happens in very low friction conditions, like when asphalt is covered with ice).

https://i.makeagif.com/media/5-11-2015/mJxAPt.gif

Refering to your other thread:
https://www.physicsforums.com/threa...ing-at-different-angles.1011952/#post-6596517
That is also the reason for both skies to point against each other in a symmetrical way for reducing speed.
If both pointed in the same angled direction, a turn rather than a braking efect would follow.

In real life, there is less resistance to movement from the snow to parallel skies than to the V-shape arrangement used for slowing down because the energy is not wasted in fighting each other about what direction to turn to.
 
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  • #13
Javad said:
They are two separated objects, A and B, not two sides of one object. Object B reaches 45 degrees at t1 and then freely slides to stop, what is the effect of 45 degrees angle on duration and length of sliding?
That's not your thoughts, that's a snapshot of some book.
Is it all supposed to be frictionless ? I suppose not ('which will stop sooner') ...
Is there some context of static and dynamic friction here ? With one being greater than the other ?

##\ ##
 
  • #14
BvU said:
That's not your thoughts, that's a snapshot of some book.
Is it all supposed to be frictionless ? I suppose not ('which will stop sooner') ...
Is there some context of static and dynamic friction here ? With one being greater than the other ?

##\ ##
It's not a snapshot of a book, it is my original question.
 
  • #15
So no friction ?
 
  • #16
BvU said:
So no friction ?
For sure there is friction.
 
  • #17
Interesting. Good it's explicitly mentioned now. Does it appear in your relevant equations ?

##\ ##
 
  • #18
BvU said:
Interesting. Good it's explicitly mentioned now. Does it appear in your relevant equations ?

##\ ##
No
 
  • #19
@Javad, as an aside to the main discussion, note that the Post #11 attachment appears to say:

- object B rotates while it slides to a stop, which means angle θ is continuously changing (till rotation stops);

- angle θ = 45º, which is a fixed value.

Both can’t be true!
 
  • #20
Steve4Physics said:
@Javad, as an aside to the main discussion, note that the Post #11 attachment appears to say:

- object B rotates while it slides to a stop, which means angle θ is continuously changing (till rotation stops);

- angle θ = 45º, which is a fixed value.

Both can’t be true!
No, actually object B rotates to reach angle θ = 45º at t1 and then continues sliding to stop (between t1 to full stop time angle θ = 45º is a fixed value.
 
  • #21
Javad said:
For sure there is friction.
That is the whole point. It is friction (and only friction) which brings each object to a stop. The time to stop (and the distance covered) depend on friction.

Unless you compare the frictional forces on A and B, you can't answer the question.

Can you tell us how you can calculate the frictional force on A and the frictional force on B?
 
  • #22
Steve4Physics said:
That is the whole point. It is friction (and only friction) which brings each object to a stop. The time to stop (and the distance covered) depend on friction.

Unless you compare the frictional forces on A and B, you can't answer the question.

Can you tell us how you can calculate the frictional force on A and the frictional force on B?
Actually, I think the calculation of friction is not a matter (we can calculate it by measuring all parameters t, v, d, …), I think I need to focus on the kinetic energy, I think due to the initial applied force along the longitudinal centerline of the object (during t0-t1), and due to mass of the object, it tends to continue sliding along the longitudinal centerline (based on the kinetic energy), but it slides with an angle between the sliding direction and the longitudinal centerline (slip angle ϴ = 45°). Now I need to know how the slip angle ϴ = 45° leads to wasting of kinetic energy (Attached image).
 

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  • #23
Lnewqban said:
If overall friction would be greater for case B than A, the metal piece simply would change its direction of travel to the path of less friction.
That is what makes the front wheels of a car roll in the steering direction rather than continuing moving forward (which only happens in very low friction conditions, like when asphalt is covered with ice).

https://i.makeagif.com/media/5-11-2015/mJxAPt.gif

Refering to your other thread:
https://www.physicsforums.com/threa...ing-at-different-angles.1011952/#post-6596517
That is also the reason for both skies to point against each other in a symmetrical way for reducing speed.
If both pointed in the same angled direction, a turn rather than a braking efect would follow.

In real life, there is less resistance to movement from the snow to parallel skies than to the V-shape arrangement used for slowing down because the energy is not wasted in fighting each other about what direction to turn to.
I don't think you can trust skis as a model for these problems. Those have effects due to the action of snow on the edges and the tendency of the skis to dip in the middle.
 
  • #24
Javad said:
Actually, I think the calculation of friction is not a matter (we can calculate it by measuring all parameters t, v, d, …), I think I need to focus on the kinetic energy, I think due to the initial applied force along the longitudinal centerline of the object (during t0-t1), and due to mass of the object, it tends to continue sliding along the longitudinal centerline (based on the kinetic energy), but it slides with an angle between the sliding direction and the longitudinal centerline (slip angle ϴ = 45°). Now I need to know how the slip angle ϴ = 45° leads to wasting of kinetic energy (Attached image).
The energy isn't going to tell you anything about the distance covered unless you can say something about the frictional forces.

My reading of the question is that B is given some initial rotation as well as its forward velocity, so starts with more energy in total.
Try simplifying it it by reducing each plate to a pair of small discs (say) connected by a light rod (frictionless, or not touching the ground). Think about the directions the forces act on each disc for B at various orientations.
 
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  • #25
haruspex said:
My reading of the question is that B is given some initial rotation as well as its forward velocity, so starts with more energy in total.
For information, in Post #20 @Javad specifically says that object B slides without rotating during the period of interest. θ is constant (45º).
 
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  • #26
Steve4Physics said:
For information, in Post #20 @Javad specifically says that object B slides without rotating during the period of interest. θ is constant (45º).
But it does not say they still have the same speed at that time.
 
  • #27
haruspex said:
But it does not say they still have the same speed at that time.
Post #1 tells us that A and B have the same speed (v=20m/s) at the sane time (t1=5s). The question is about slowing down afer t1.

Well, that's how I read it.
 
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  • #28
Steve4Physics said:
Post #1 tells us that A and B have the same speed (v=20m/s) at the sane time (t1=5s). The question is about slowing down afer t1.

Well, that's how I read it.
Absolutely correct.
 
  • #29
@Javad, the question is *entirely* about friction.

Can you tell us what course/level this is from?

Assuming it is an introductory level physics course, then you should remember:
- frictional force is needed to find acceleration (or deceleration if you want to call it that here);
- the acceleration is needed to calculate the time and distance needed to stop.

To answer the question you must compare the sizes of the frictional forces on A and B, There is no other way.
___________________________

Additional note

If you don't already know, you might also want to note that what happened before t1 is irrelevant.

At time t1:
- A is moving left at 20m/s oriented 0º to its velocity;
- B is moving left at 20m/s oriented 45º to its velocity;
- A and B are not rotating.

How the objects reached this state does not change how they behave after t1.
 
  • #30
haruspex said:
I don't think you can trust skis as a model for these problems. Those have effects due to the action of snow on the edges and the tendency of the skis to dip in the middle.
As usual, you are correct.
My reasons come from posts #7 and #15 of the referenced other thread.
OP: “I want to learn how making angles on skis helps to reduce the velocity of a skier to stop.”
Probably incorrect, my perception is that this thread as a continuation of the previous one, where the plowing effect of skies and pure friction where mixed up in a confusing manner.
 
  • #31
Lnewqban said:
My reasons come from posts #7 and #15 of the referenced other thread.
OP: “I want to learn how making angles on skis helps to reduce the velocity of a skier to stop.”
Probably incorrect, my perception is that this thread as a continuation of the previous one, where the plowing effect of skies and pure friction where mixed up in a confusing manner.
It is worth noting that the Homework Statement in this current thread specifically says "rigid surface" which seems to eliminate consideration of any snow-ploughing effects.

The question seems to be asking what (if any) is the effect of the orientation of a sliding surface on the frictional force.

Using the elementary (ideal, empirical) laws of friction, the answer is clear. But in a real-world situation there might be some dependence on, for example, the width of the leading edge.

.It is not 100% clear if the OP is asking about the ideal or real-world cases. Maybe @Javad could clarify this?

Edit - typo'
 
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  • #32
Steve4Physics said:
Post #1 tells us that A and B have the same speed (v=20m/s) at the sane time (t1=5s). The question is about slowing down afer t1.

Well, that's how I read it.
I cannot read it that way:
"reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates"

The sequence stated is
- they reach the same velocity, then
- continue sliding, while
- B rotates.

With your reading, there is no point in mentioning any active rotation. They might as well have been released at different orientations, but with no continuing rotation, in the first place.
 
  • #33
haruspex said:
I cannot read it that way:
"reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates"

The sequence stated is
- they reach the same velocity, then
- continue sliding, while
- B rotates.

With your reading, there is no point in mentioning any active rotation. They might as well have been released at different orientations, but with no continuing rotation, in the first place.
But that is exactly the point I made in Post #19!
 
  • #34
Steve4Physics said:
But that is exactly the point I made in Post #19!
I don't think so. The sequence I spelt out in post #32 is not contradicted by post #20. Let me extend it:

The sequence stated is
- they reach the same velocity, then
- continue sliding, while
- B rotates until it reaches angle 45°, then
- continues at that angle
 
  • #35
haruspex said:
I cannot read it that way:
"reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates"
That is exactly the issue I raised in Post #19! That part of the question conflicts with the information about angle θ.

Check the OP's reply in Post #20.

The question is badly written. I'm basing my responses on the OP's interpretation – but, yes, that could be wrong.
 
  • #36
Steve4Physics said:
That is exactly the issue I raised in Post #19! That part of the question conflicts with the information about angle θ.

Check the OP's reply in Post #20.

The question is badly written. I'm basing my responses on the OP's interpretation – but, yes, that could be wrong.
Sorry, just not seeing it. I read my interpretation in post #34 as consistent with post #1 (which is unclear) and post #20.
 
  • #37
haruspex said:
With your reading, there is no point in mentioning any active rotation. They might as well have been released at different orientations, but with no continuing rotation, in the first place.
Yes. The very same point struck me. That’s why I queried the issue.

But when asked, the OP explicitly said (in Post #20) that there is no rotation after time t1 (which is the period of interest).

I decided to run with the OP's interpretation. I agree it could be wrong.

It's worth noting that the question and diagram may be the OP's own work (rather than from teaching resources). The diagram looks professional but is a modified version of the diagram in the OP’s preceding thread. I get the impression that he is expressing the question in his own words – but has not been entirely accurate/clear. That’s why I’m running with his interpretation.
 
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  • #38
haruspex said:
I don't think so. The sequence I spelt out in post #32 is not contradicted by post #20. Let me extend it:

The sequence stated is
- they reach the same velocity, then
- continue sliding, while
- B rotates until it reaches angle 45°, then
- continues at that angle
I am a latecomer to this so forgive if I show unmitigated naiveté. I looked at the photo in #11 and read all the posts trying to orient myself. This is what think is the physical picture
Strip A is the control strip. At t1 = 5 s its CM has a speed of v0A = 20 m/s and it travels with its length along the x-axis until it stops.
Strip B is the subject strip. At t1 = 5 s its CM has a speed of v0B = 20 m/s along the x-axis while its longitudinal axis forms angle θ = 45° with respect to the x-axis. Its CM continues traveling along the x-axis while the rest of the strip rotates about its CM until it stops at some angle relative to the x-axis.

I base this interpretation because (a) the photo clearly has a time stamp of the two strips with the same velocities and different orientations; (b) angle θ is clearly labeled in the diagram and the text clearly mentions that θ = 45°; (c) the text mentions that the strips got to their respective orientations under the influence of the forces driving them ". . . then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°) between the sliding direction and the longitudinal centerline of the object.

The text in red is where there might be room for interpretation. Clearly, the sentence that begins with "Object A ##~\dots~##" describes the situation after we have let the strips to slide freely. Clearly, the text mentions that object B slides and rotates after the strips are allowed to slide freely. Clearly, the angle labeled θ at time t1 in the photo is given the value of 45° in the text. Putting all this together I concluded that, at time t1, strip B is translating while rotating and forms an angle with an instantaneous initial value of 45° relative to the x-axis. An alternative interpretation could be that at time t1 the initial angle is some θ as shown in the photo and the final angle is 45°.
 
  • #39
Steve4Physics said:
B is moving left at 20m/s oriented 45º to its velocity
This “B is moving left at 20m/s oriented 45º to its velocity” is correct, does it can help to find an answer for the question?
 
  • #40
Steve4Physics said:
@Javad, the question is *entirely* about friction.

Can you tell us what course/level this is from?

Assuming it is an introductory level physics course, then you should remember:
- frictional force is needed to find acceleration (or deceleration if you want to call it that here);
- the acceleration is needed to calculate the time and distance needed to stop.

To answer the question you must compare the sizes of the frictional forces on A and B, There is no other way.
___________________________

Additional note

If you don't already know, you might also want to note that what happened before t1 is irrelevant.

At time t1:
- A is moving left at 20m/s oriented 0º to its velocity;
- B is moving left at 20m/s oriented 45º to its velocity;
- A and B are not rotating.

How the objects reached this state does not change how they behave after t1.
Sorry if the question was badly written, I made it better to be clear for everyone.

Two equal metal strips (the same material, the same size and mass, mass for each one is 500 g, and size for each one is 50cm* 5cm) are pushed on a straight rigid surface to reach the same velocity (v1 = 20m/s) at the same time (t1, 5s), then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it starts with the sliding direction along the longitudinal centerline, and during t0 to t1 it gradually rotates about its central-vertical axis to make an angle (ϴ = 45°) between the sliding direction and the longitudinal centerline of the object, and with the fixed angle (ϴ = 45°) it continues sliding. Which object will stop sooner (which object will travel a shorter distance (d))?
 

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  • #41
kuruman said:
I am a latecomer to this so forgive if I show unmitigated naiveté. I looked at the photo in #11 and read all the posts trying to orient myself. This is what think is the physical picture
Strip A is the control strip. At t1 = 5 s its CM has a speed of v0A = 20 m/s and it travels with its length along the x-axis until it stops.
Strip B is the subject strip. At t1 = 5 s its CM has a speed of v0B = 20 m/s along the x-axis while its longitudinal axis forms angle θ = 45° with respect to the x-axis. Its CM continues traveling along the x-axis while the rest of the strip rotates about its CM until it stops at some angle relative to the x-axis.

I base this interpretation because (a) the photo clearly has a time stamp of the two strips with the same velocities and different orientations; (b) angle θ is clearly labeled in the diagram and the text clearly mentions that θ = 45°; (c) the text mentions that the strips got to their respective orientations under the influence of the forces driving them ". . . then we let them freely continue sliding. Object A slides while the sliding direction is along the longitudinal centerline of the object, object B slides while it rotates about its central-vertical axis to make an angle (ϴ = 45°) between the sliding direction and the longitudinal centerline of the object.

The text in red is where there might be room for interpretation. Clearly, the sentence that begins with "Object A ##~\dots~##" describes the situation after we have let the strips to slide freely. Clearly, the text mentions that object B slides and rotates after the strips are allowed to slide freely. Clearly, the angle labeled θ at time t1 in the photo is given the value of 45° in the text. Putting all this together I concluded that, at time t1, strip B is translating while rotating and forms an angle with an instantaneous initial value of 45° relative to the x-axis. An alternative interpretation could be that at time t1 the initial angle is some θ as shown in the photo and the final angle is 45°.
Sorry if the question was badly written, I made it better to be clear for everyone. Please check post #40
 
  • #42
Javad said:
Sorry if the question was badly written, I made it better to be clear for everyone. Please check post #40
Hi@Javad. It would be clearest if the motion were described in time-order.

From t=0 to t1=5s: A is accelerated to 20m/s aligned as shown and B is accelerated to 20m/s while rotating.​
At t1=5s: B stops rotating with θ=45º as shown; the accelerating forces are removed.​
After t1=5s: A and B slide (with B’s angle θ=45º constant) and come to rest.​
Is that correct?

It would be helpful if you would you tell us:
1) Is this a question from a course (which course?) or one you have made up?
2) Have you learned about the coefficient of kinetic friction?
 
  • #43
Steve4Physics said:
Hi@Javad. It would be clearest if the motion were described in time-order.

From t=0 to t1=5s: A is accelerated to 20m/s aligned as shown and B is accelerated to 20m/s while rotating.​
At t1=5s: B stops rotating with θ=45º as shown; the accelerating forces are removed.​
After t1=5s: A and B slide (with B’s angle θ=45º constant) and come to rest.​
Is that correct?

It would be helpful if you would you tell us:
1) Is this a question from a course (which course?) or one you have made up?
2) Have you learned about the coefficient of kinetic friction?
That's correct.

That is my original question and is not from a book or a course.
I increased my knowledge about the coefficient of kinetic friction.
 
  • #44
Javad said:
That is my original question and is not from a book or a course.
Aha! It helps us to know that.

The way you have written the question suggests that you believe the rotation (between 0 and 5s) is important. It isn't!

Rotation stops at 5s. How object B got to 45º at 5s does not affect how it moves after 5s.

Javad said:
I increased my knowledge about the coefficient of kinetic friction.
You will need to understand it to answer the question.

If it helps, I made an introductory-level video lesson about friction a few years ago. But it's about 30 minues long:
 
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  • #45
Steve4Physics said:
Aha! It helps us to know that.

The way you have written the question suggests that you believe the rotation (between 0 and 5s) is important. It isn't!

Rotation stops at 5s. How object B got to 45º at 5s does not affect how it moves after 5s.You will need to understand it to answer the question.

If it helps, I made an introductory-level video lesson about friction a few years ago. But it's about 30 minues long:

Thank you, I'll see.
 
  • #46
Steve4Physics said:
does not affect
So that's your final answer, Thanks.
 
  • #47
Javad said:
So that's your final answer, Thanks.
No. "does not affect" is not my final answer.

You are quoting a phrase from my Post #44 out of context. In Post #44 I said [my underlining added]:

“Rotation stops at 5s. How object B got to 45º at 5s does not affect how it moves after 5s.”

You still need to decide if the stopping-distance with θ=0 is less than, equal to, or more than the stopping-distance with θ=45º.

What do you think happens?
 
  • #48
Javad said:
Sorry if the question was badly written, I made it better to be clear for everyone. Please check post #40
Your question makes more sense now, thank you. What @Steve4Physics says in post #47 is important. You could have phrased the question by saying "At t = 0, one strip is moving with its longitudinal axis parallel to the direction of motion while the other strip is moving with its longitudinal axis at a fixed angle of 45° relative to its direction of motion." That says it all. Note that there is mention of what happens before t = 0 because that information is irrelevant to which strip travels the farthest after t = 0.
 
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  • #49
Steve4Physics said:
is not my final answer
That’s good hearing it
I think due to mass and fast rotation (that happens for object B), object B experiences inertial pulls in the opposite direction of rotation at the center of mass thus the object would have the tendency to skid towards the opposite direction of rotation (probably it is the actual heading direction), while there is lateral friction for object on the opposite side, therefore if the skidding force be greater than the lateral friction the object can slide but there is a waste of energy (velocity or force, actually I don’t know what!) in comparison with object A. (Please find attached image).
 

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  • #50
kuruman said:
Your question makes more sense now, thank you. What @Steve4Physics says in post #47 is important. You could have phrased the question by saying "At t = 0, one strip is moving with its longitudinal axis parallel to the direction of motion while the other strip is moving with its longitudinal axis at a fixed angle of 45° relative to its direction of motion." That says it all. Note that there is mention of what happens before t = 0 because that information is irrelevant to which strip travels the farthest after t = 0.
I shared my thoughts in post #49 .
 
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