Velocity, traveling distance and friction force on a sliding object

[haruspex]

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.

 

[Steve4Physics]

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.

 

[kuruman]

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 v_0A = 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 v_0B = 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°.

 

[Javad]

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?

 

[Javad]

@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))?

 

[Javad]

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 v_0A = 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 v_0B = 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

 

[Steve4Physics]

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?

 

[Javad]

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.

 

[Steve4Physics]

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.

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:

 

[Javad]

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.

 

[Javad]

does not affect

So that's your final answer, Thanks.

 

[Steve4Physics]

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?

 

[kuruman]

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.

 

[Javad]

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).

 

[Javad]

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 .

 

[Steve4Physics]

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).

You have a misconception.

At t1, B has stopped rotating; it has no ‘memory’ of how it was rotating previously (between t0 and t1).

Suppose, there is another identical object, C which (at t0) starts with its angle θ=45º. C then moves, with no rotation, and at time t1, C is also traveling left at 20m/s.

At t1, the motions of B and C are identical. After t1, C moves in exactly the same way as B.

The ‘histories’ of B and C are different, but they are in exactly the same state at t1. So they continue to move in the exactly same way. Their ‘histories’ don’t have any effect.

The fact that B had been rotating earlier is irrelevant.

 

[Javad]

is irrelevant

There is no more object, just A and B, I think the image shows all details. you say the rotation is irrelevant, but I think a huge value of velocity is wasted under an unknown process (unknown for me yet) and I try to find its answer through this thread or talking with the experts on physics and mechanical engineering. For me car drifting is a keyword and I will focus on it to help me find an answer to my question.

 

[Steve4Physics]

There is no more object, just A and B,

I know. I added a 3rd object (C) for comparison with B, to explan a particular point.

For me car drifting is a keyword and I will focus on it to help me find an answer to my question.

Is A meant to be a car sliding (locked brakes) and B is a car drifting at 45º (brakes locked or unlocked?)? If so, you need to tell us.

Sorry I haven't been able to help. Good luck.

 

[Javad]

Thank you for your time, I learned a lot. I follow your youtube channel that is very helpful for me.