Can Conservative Forces Be Neglected During Collision Analysis?

[Tanya Sharma]

Homework Statement

While solving problems ,during collision ,we neglect impulse of external forces like gravitational force , spring force , acting on the system .

The cases are

1) An object falling from a height on a pan attached to a vertically hanging massless spring and colliding inelastically to it.

2)Two balls,one thrown vertically upwards ,other moving vertically downwards colliding mid way in air .

Does that mean we can always neglect impulse of all the conservative forces namely spring force,gravitational force,electrostatic force during collision?

Kindly clear my conceptual doubt .

Homework Equations

The Attempt at a Solution

 

[ehild]

Homework Statement

While solving problems ,during collision ,we neglect impulse of external forces like gravitational force , spring force , acting on the system .

The cases are

1) An object falling from a height on a pan attached to a vertically hanging massless spring and colliding inelastically to it.

2)Two balls,one thrown vertically upwards ,other moving vertically downwards colliding mid way in air .

Does that mean we can always neglect impulse of all the conservative forces namely spring force,gravitational force,electrostatic force during collision?
[/b]

No, we cannot neglect all forces -conservative or not- during a collision. What we do is to consider the collision instantaneous - happening in a very short time Δt. During the collision, the external forces accelerate the centre of mass, so the overall momentum changes by F(external)Δt. If Δt is very short the change of the overall momentum can be neglected with respect to the change of momentum of the parts and conservation of momentum applies. How fast the collision is it depends on the internal forces between the colliding parts. To decide if it is fast enough you should know the internal forces in detail. Usually you do not know these forces so experience will tell if the model has been appropriate or not.

When the external force is some kind of constraint that force can change during the collision process and can be very large. In that case you can not apply conservation of momentum.

ehild

 

[Tanya Sharma]

Hi ehild :) hope you are doing well...

No, we cannot neglect all forces -conservative or not- during a collision.
ehild

Yes,we cannot neglect the forces ,but the impulse of the conservative forces during collisions is almost always neglected , and hence momentum is conserved before and after the collision while solving problems The cases I have mentioned before

1) An object falling from a height on a pan attached to a vertically hanging massless spring and colliding inelastically to it.

2)Two balls,one thrown vertically upwards ,other moving vertically downwards colliding mid way in air .

Another case can be

3)Two blocks colliding on an inclined plane having friction .

Here we neglect impulse of friction .I can't remember the problem right now.

Can you explain why we neglect impulse of spring force in 1) , gravitational force in 2) , friction in 3) ?

How should I determine when to neglect impulse of forces while solving numericals ?

 

[ehild]

Have you read my previous post?

We can neglect the effect of an external force if the collision process is very fast, so the external force does not have enough time to change the momentum of the colliding bodies. You can know from experience when this approximation is valid.

Try to solve the problem with the two balls colliding in mid-air, if both balls have the same mass of 1 kg, speeds of 2 m/s, and consider the balls elastic so keeping one ball compressed by ΔD force F=kΔD is needed, with k=2500 N/m. Can conservation of momentum assumed during the interaction between the balls? What happens if k=250000 N/m?

ehild

 

[Tanya Sharma]

Have you read my previous post?
ehild

Yes I read your post...I understand what you have explained .I know that during collision the contact forces are large enough and the interaction time duration is very small , and hence impulse of external forces at times may be neglected .I had thought that some other concept related to conservative and nonconservative forces was involved , and hence put my doubt on the forum.

 

[ehild]

Both the impulse of a force, FΔt and the work of the force FvΔt can be neglected if Δt is very small, no matter if the force is conservative or not.

It is different if the external force changes during the interaction to a high extent. Such happens when a sand bag is suspended on a string of fix length and a bullet is shot into it. The string resists stretching and exerts reaction force that can be considered infinite. Conservation of momentum can not be applied, you need to use conservation of angular momentum instead.

ehild

 

[Tanya Sharma]

Is friction an impulsive force ? Does it depend on the context of the problem i.e it might be impulsive in some cases and non-impulsive in other cases ?

A sample case is -

A bullet moving horizontally hits a block placed on a surface with friction . Should we conserve linear momentum in this case ?

 

[ehild]

A sample case is -

A bullet moving horizontally hits a block placed on a surface with friction . Should we conserve linear momentum in this case ?

If there is friction you have three interacting bodies instead of two. The bullet interacts with the block, the block interacts with the ground. There are limiting cases when the problem is easy to solve.

1. The friction is strong, the block is large, so the force of the bullet on the block can not overcome static friction. The block does not move while the block penetrates into it. The bullet moves for some Δt times till it loses all momentum, the impulse from the block is mΔv=FΔt.

2. The force between bullet and block is greater than static friction. And it is so great that the bullet decelerates inside the block very fast so that the force of kinetic friction does not change the overall momentum appreciably during the time Δt when the bullet is in motion relatively to the block.

In all other cases you need to know the forces in detail and solve the problem of three interacting bodies.

ehild

 

[Tanya Sharma]

Hi ehild

Thanks for the response :)

Please have a look at the attachment . The question was asked in a prestigious national examination .The question along with the solution is given.The answer is given to be option c) .

At other places answer is given to be a) and c) . Different opinions on this question exist .

I know how to solve the problem .

Solution 1)If friction is considered to be impulsive ,then we will get option c) .We can't conserve linear momentum .By applying angular impulse angular momentum relation we find , angular velocity to be anticlockwise ,hence friction towards left .

Solution 2) If friction is considered non-impulsive, then we get both a) and c) . In this case we conserve linear momentum and get the linear speed of the center of the ring to be zero. By applying angular impulse angular momentum relation we find, angular velocity to be anticlockwise, hence friction towards left.

Now I feel there is a third case which nowhere has been discussed which is as follows –

There might not be friction present at all i.e the surface might be frictionless. The ring would have been rolling without slipping happily on a frictionless surface .The stationary ring could have been set into motion with an impulse such that it could have started rolling straightaway without slipping.

In that case the answer would be option a) and d).

Kindly give your thoughts on this problem especially the third case.

 

[consciousness]

Hi ehild

Thanks for the response :)

Please have a look at the attachment . The question was asked in a prestigious national examination .The question along with the solution is given.The answer is given to be option c) .

At other places answer is given to be a) and c) . Different opinions on this question exist .

I know how to solve the problem .

Solution 1)If friction is considered to be impulsive ,then we will get option c) .We can't conserve linear momentum .By applying angular impulse angular momentum relation we find , angular velocity to be anticlockwise ,hence friction towards left .

Solution 2) If friction is considered non-impulsive, then we get both a) and c) . In this case we conserve linear momentum and get the linear speed of the center of the ring to be zero. By applying angular impulse angular momentum relation we find, angular velocity to be anticlockwise, hence friction towards left.

Now I feel there is a third case which nowhere has been discussed which is as follows –

There might not be friction present at all i.e the surface might be frictionless. The ring would have been rolling without slipping happily on a frictionless surface .The stationary ring could have been set into motion with an impulse such that it could have started rolling straightaway without slipping.

In that case the answer would be option a) and d).

Kindly give your thoughts on this problem especially the third case.

About Case 2- Friction (if present) will be impulsive. This is because friction is always directly proportional to normal reaction and normal reaction is impulsive here (otherwise the ring would go inside the ground!).

About Case 3- I am not sure but I think that the paper setters didnt think of the possibility you mention.

 

[ehild]

Hi Tania,

consciousness is right. If we consider the normal force between the ball and ring impulsive so should be the normal force between the ground and the ring. So the force of static friction is as big as needed: it is impulsive. The ball will roll after the collision.

If the static friction was not great enough, that would have caused slipping during the collision, but the force of friction would be finite and the change of linear momentum would be so small in the very short time of the collision that you could consider the linear momentum to be conserved.

Your version, (zero friction) can happen in principle. The ground can not exert horizontal force on the ball. Then both the linear momentum and angular momentum are conserved. In the real world, there is friction between the ground and the rolling object, but it can happen that the coefficient of static friction is very small: that again, means the friction is not impulsive.


ehild

 

[utkarshakash]

Hi ehild

Thanks for the response :)

Please have a look at the attachment . The question was asked in a prestigious national examination .The question along with the solution is given.The answer is given to be option c) .

At other places answer is given to be a) and c) . Different opinions on this question exist .

I know how to solve the problem .

Solution 1)If friction is considered to be impulsive ,then we will get option c) .We can't conserve linear momentum .By applying angular impulse angular momentum relation we find , angular velocity to be anticlockwise ,hence friction towards left .

Solution 2) If friction is considered non-impulsive, then we get both a) and c) . In this case we conserve linear momentum and get the linear speed of the center of the ring to be zero. By applying angular impulse angular momentum relation we find, angular velocity to be anticlockwise, hence friction towards left.

Now I feel there is a third case which nowhere has been discussed which is as follows –

There might not be friction present at all i.e the surface might be frictionless. The ring would have been rolling without slipping happily on a frictionless surface .The stationary ring could have been set into motion with an impulse such that it could have started rolling straightaway without slipping.

In that case the answer would be option a) and d).

Kindly give your thoughts on this problem especially the third case.

I think this was asked in IITJEE. OK as far as zero friction is considered, it is IMPOSSIBLE. You can't make a ring roll on a frictionless surface. It can move but it can't roll. To clarify it let us consider a hypothetical situation in which a ring is rolling without slipping on a frictionless horizontal surface. Let's start by drawing FBD of the ring. Can you tell me which force has a non-zero torque on the ring about CM?

 

[Tanya Sharma]

OK as far as zero friction is considered, it is IMPOSSIBLE. You can't make a ring roll on a frictionless surface. It can move but it can't roll.

Absolutely POSSIBLE...The ring can surely roll without slipping on a frictionless surface.

To clarify it let us consider a hypothetical situation in which a ring is rolling without slipping on a frictionless horizontal surface. Let's start by drawing FBD of the ring. Can you tell me which force has a non-zero torque on the ring about CM?

Place a ring and give an impulse such that the ring starts rolling without slipping immedietely with no friction required.The impulse given will provide the required rotational motion as well as translational motion.Now in order to maintain its motion it doesn't require any external force.

 

[sankalpmittal]

Absolutely POSSIBLE...The ring can surely roll without slipping on a frictionless surface.
Place a ring and give an impulse such that the ring starts rolling without slipping immedietely with no friction required.The impulse given will provide the required rotational motion as well as translational motion.Now in order to maintain its motion it doesn't require any external force.

When sphere is doing rolling without slipping on a horizontal surface, static friction is not involved, and hence it do no work on the sphere, and sphere rolls maintaining the condition of V_cm = Rω. It does not even mean that the surface was frictionless. In fact there can be pure rolling on a rough surface only(why?). If the surface was all smooth, the sphere would rather slip due to momentary impulse, and static friction could not bring the condition of pure rolling. Static friction is conservative force, remember. Same thing applies for ring.

utkarshakash is right.

Tanya, you are correct that when there is pure rolling, no external force is required to maintain it but of course "without friction" it cannot be initiated. Hint: While doing the numericals, why do you take the axis of rotation passing through contact point of sphere with surface ?

 

[ehild]

... when there is pure rolling, no external force is required to maintain it but of course "without friction" it cannot be initiated.

Imagine that the object (sphere, ring ...) rolls on a rough surface so the condition of Vcm=rω holds, and then it arrives to a frictionless surface. Do either the velocity of the CM or the angular velocity of rotation change?

ehild

 

[haruspex]

If the static friction was not great enough, that would have caused slipping during the collision, but the force of friction would be finite and the change of linear momentum would be so small in the very short time of the collision that you could consider the linear momentum to be conserved.

I disagree. Friction could be insufficient to prevent slipping yet still deliver a substantial impulse. If the coefficient of static friction is μ and the normal impulse is J then surely the frictional impulse would be μJ.

when there is pure rolling, no external force is required to maintain it but of course "without friction" it cannot be initiated

Strike the ring horizontally at the top and impulses will be just right to set the disc rolling without requiring any friction from the ground. Same applies to a disc and a sphere, but with different strike heights.
In the present question, the impact was below the top of the ring, so a frictional force in the opposite direction is required to achieve rolling. If the impulse had been above the top of the ring (through some lever arm attachment) then the friction would need to act the other way.

 

[sankalpmittal]

Imagine that the object (sphere, ring ...) rolls on a rough surface so the condition of Vcm=rω holds, and then it arrives to a frictionless surface. Do either the velocity of the CM or the angular velocity of rotation change?

ehild

Velocity of CM or the angular velocity of rotation does not change, because as soon as the object starts pure rolling, there is no need of any external force to maintain it. When there was pure rolling, hypothetically there was no friction at that time but the ground was rough.

I disagree. Friction could be insufficient to prevent slipping yet still deliver a substantial impulse. If the coefficient of static friction is μ and the normal impulse is J then surely the frictional impulse would be μJ.

Cannot understand.

Strike the ring horizontally at the top and impulses will be just right to set the disc rolling without requiring any friction from the ground. Same applies to a disc and a sphere, but with different strike heights.
In the present question, the impact was below the top of the ring, so a frictional force in the opposite direction is required to achieve rolling. If the impulse had been above the top of the ring (through some lever arm attachment) then the friction would need to act the other way.

WITHOUT FRICTION, pure rolling cannot be initiated, right ? How can it be ? There has to be a sort of grab at the contact point of sphere. Otherwise it would just slip.

 

[ehild]

I disagree. Friction could be insufficient to prevent slipping yet still deliver a substantial impulse. If the coefficient of static friction is μ and the normal impulse is J then surely the frictional impulse would be μJ.

I wrote about the case of non-impulsive friction which is defined that the impulse delivered can be taken zero.

ehild

 

[haruspex]

Friction could be insufficient to prevent slipping yet still deliver a substantial impulse. If the coefficient of static friction is μ and the normal impulse is J then surely the frictional impulse would be μJ.

Cannot understand.

I should have said kinetic friction, not static.
Impulses are never truly instantaneous. We just mean there was a large and probably variable force that acted for a very short time, resulting in a momentum change of ∫F.dt. If the normal force is N=N(t) over that interval and the normal impulse is J_N = ∫N.dt, and slipping occurred through most of that, then the frictional force was F(t) = μ_kN(t), so the frictional impulse was ∫μ_kN(t)dt = μ_kJ_N.

WITHOUT FRICTION, pure rolling cannot be initiated, right ?

Wrong. Calculate this: a uniform cylinder mass m radius r rests on a smooth horizontal surface. A horizontal impulse J is delivered at height 3r/2. Find the horizontal and rotational speeds thereafter. At what speed, relative to the ground, does the part of the cylinder contacting the ground move?

 

[sankalpmittal]

Wrong. Calculate this: a uniform cylinder mass m radius r rests on a smooth horizontal surface. A horizontal impulse J is delivered at height 3r/2. Find the horizontal and rotational speeds thereafter. At what speed, relative to the ground, does the part of the cylinder contacting the ground move?

Is this site wrong then ? : http://www.astro.ucla.edu/~malkan/astro8/physics1a/rolling.htm

It says that :

An important point to remember is that rolling motion cannot occur on a frictionless surface. The thing will simply slide along. In the case of something rolling down an incline if the angle of the incline is very large or the inclines coefficient of friction is very small the sphere will also slide. To get pure rolling motion the force of friction must be less than the normal force times the coefficient of friction.

Other references :

http://www.phy.davidson.edu/fachome/dmb/PY430/Friction/rolling.html
http://www.lhup.edu/~dsimanek/scenario/rolling.htm

Thanks.

 

[haruspex]

Is this site wrong then ? : http://www.astro.ucla.edu/~malkan/astro8/physics1a/rolling.htm

Yes, it's wrong. It should say that rolling motion does not usually occur on a frictionless surface, because it will only occur if the wheel happens to be rotating at exactly the right rate.

 

[utkarshakash]

WITHOUT FRICTION, pure rolling cannot be initiated, right ? How can it be ? There has to be a sort of grab at the contact point of sphere. Otherwise it would just slip.

. I think all of you should consider this statement of sankalpmittal to clarify your doubt.

 

[utkarshakash]

I would suggest everyone to take a look at this site

http://www.lhup.edu/~dsimanek/scenario/rolling.htm

 

[utkarshakash]

Place a ring and give an impulse such that the ring starts rolling without slipping immedietely with no friction required.The impulse given will provide the required rotational motion as well as translational motion.Now in order to maintain its motion it doesn't require any external force.

You cannot give an impulse such that the ring starts rolling without slipping on a frictionless surface. I would rather like to suggest you refer to HC Verma Part 1. I have sorted out some problems that might make you think on your reasoning once again. Worked Out Examples- Q.No- 25, 29. Exercises- Q.No. - 80, 81, 82.

 

[haruspex]

I would suggest everyone to take a look at this site

Pls quote the passage you wish to bring to our attention. (Mostly the article seems to be about speaking of friction as opposing motion instead of as opposing relative motion of the surfaces. Indeed, is that error at the root of your objection? You understand that once rolling is established on a horizontal surface there is no frictional force, right?)

You cannot give an impulse such that the ring starts rolling without slipping on a frictionless surface.

As ehild pointed out, you could have rolling occurring on a frictionless surface in consequence of the ring first rolling on a frictional surface then transiting to a smooth one. I suspected that would not satisfy you because friction was still involved in establishing the rolling motion, but it does demonstrate that if the linear velocity just happens to be rω, by whatever means, then you have frictionless rolling. So I set up an example of how exactly the right combination can occur merely by judicious application of an impulse. Did you do the algebra?

 

[haruspex]

I wrote about the case of non-impulsive friction which is defined that the impulse delivered can be taken zero.

That's not how I read you prior post:

If we consider the normal force between the ball and ring impulsive so should be the normal force between the ground and the ring. So the force of static friction is as big as needed: it is impulsive. The ball will roll after the collision.

If the static friction was not great enough, that would have caused slipping during the collision, but the force of friction would be finite and the change of linear momentum would be so small in the very short time of the collision that you could consider the linear momentum to be conserved.

I read that as saying that either the impulsive friction is enough to produce rolling immediately, or it can be neglected. I'm saying that there is a third possibility between the two, and you can prove this by starting with a realistic scenario in which the impact occurs over a short period of time, then letting that period tend to zero.

 

[utkarshakash]

So I set up an example of how exactly the right combination can occur merely by judicious application of an impulse. Did you do the algebra?

Consider this question
"A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?"

What do you have to say about this?Why it mentions the word "rough surface"?

 

[utkarshakash]

Pls quote the passage you wish to bring to our attention.

"That last sentence is important. The force due to friction doesn't necessarily act to oppose the motion of the body but acts to oppose slipping or sliding along the contact surface."

When an impulse is given the part of the body which is in contact with the ground has a tendency to slip. This is where frictional force comes into play by opposing the tendecy to slip along the surface. If there were no friction the tendency to slipping couldn't have been countered.

 

[haruspex]

"That last sentence is important. The force due to friction doesn't necessarily act to oppose the motion of the body but acts to oppose slipping or sliding along the contact surface."

I agree entirely, and it supports my argument. In the special circumstances I've described, there is no tendency to relative motion of the two surfaces, hence no friction.

"A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?"

What do you have to say about this?Why it mentions the word "rough surface"?

Because the impulse is purely horizontal. This means there is no impulsive downward force, so no impulsive normal reaction. The author of the question appears to be testing the reader's ability to deduce that no matter how rough the surface is it would be unable to prevent slipping if the ball were struck at just any old height. Only if it is struck at exactly the right height will the resulting horizontal impulse and angular impulse be so as to produce rolling motion straight away. In short, the surface might just as well be smooth, but it's up to the reader to figure that out.

 

[ehild]

That's not how I read you prior post:
I read that as saying that either the impulsive friction is enough to produce rolling immediately, or it can be neglected. I'm saying that there is a third possibility between the two, and you can prove this by starting with a realistic scenario in which the impact occurs over a short period of time, then letting that period tend to zero.

You are right, I did not think it over. Friction means finite change of momentum even in case of non-impulsive impact. ehild