Velocity, traveling distance and friction force on a sliding object

[Javad]

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

 

[BvU]

Well, work out your relevant equations for $d$ and there is your answer !

$\$

 

[Steve4Physics]

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.

 

[Javad]

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 ?

 

[Javad]

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?

 

[Steve4Physics]

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.

 

[Javad]

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?

 

[Lnewqban]

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?

 

[BvU]

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 )

$\$

 

[Steve4Physics]

however the velocity of two objects at t1 is the same, what will happen next, is d equal for both objects?

As far as I can see, this is essentially the same question as your other thread:
https://www.physicsforums.com/threa...ing-at-different-angles.1011952/#post-6596500

Carefully read Post# 23 in that thread. I can't add anything else.

 

[Javad]

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 )

$\$

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?

 

[Lnewqban]

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.

 

[BvU]

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 ?

$\$

 

[Javad]

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.

 

[BvU]

So no friction ?

 

[Javad]

So no friction ?

For sure there is friction.

 

[BvU]

Interesting. Good it's explicitly mentioned now. Does it appear in your relevant equations ?

$\$

 

[Javad]

Interesting. Good it's explicitly mentioned now. Does it appear in your relevant equations ?

$\$

No

 

[Steve4Physics]

@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!

 

[Javad]

@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.

 

[Steve4Physics]

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?

 

[Javad]

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).

 

[haruspex]

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.

 

[haruspex]

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.

 

[Steve4Physics]

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).

 

[haruspex]

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.

 

[Steve4Physics]

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.

 

[Javad]

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.

 

[Steve4Physics]

@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.

 

[Lnewqban]

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.

 

[Steve4Physics]

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'

 

[haruspex]

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.

 

[Steve4Physics]

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!

 

[haruspex]

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

 

[Steve4Physics]

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.