What is the difference between momentum and kinetic energy?

[aloshi]

I have read "An elementary treatise on mechanics" and i have some difficulty in understanding.


1)
“When two bodies in motion impinge, if their centers of inertia move in the same straight line perpendicular to a plane tangent to the bodies at their point of contact , the impact is said to be direct and central.”
I can not really understand:
“the same straight line perpendicular to a plane tangent to the bodies at their point of contact”
if I'm drawing a picture of how the impinge look;
[PLAIN]http://www.pluggakuten.se/wiki/images/2/22/F%C3%B6rsta.jpg

[PLAIN]http://www.pluggakuten.se/wiki/images/2/22/F%C3%B6rsta.jpg

Have I understand’t correct?

2)
I can not really understand:
“if the straight line described by the center of inertia of one of the bodies is not perpendicular to the tangent plane , the impact is said to be oblique.”

if I'm drawing a picture of how the impinge look:

[PLAIN]http://www.pluggakuten.se/wiki/images/c/c7/Andra.jpg

[PLAIN]http://www.pluggakuten.se/wiki/images/c/c7/Andra.jpg
Have I understand’t correct?



it is from 240. DEF. in "An elementary treatise on mechanics"

 

[tiny-tim]

1)
“When two bodies in motion impinge, if their centers of inertia move in the same straight line perpendicular to a plane tangent to the bodies at their point of contact , the impact is said to be direct and central.”
I can not really understand:
“the same straight line perpendicular to a plane tangent to the bodies at their point of contact”
…
2)
I can not really understand:
“if the straight line described by the center of inertia of one of the bodies is not perpendicular to the tangent plane , the impact is said to be oblique.”

Hi aloshi!

The "tangent plane" is the plane of contact between the two spheres …

imagine that, when they are touching, you put a flat piece of paper between them …

it will be tangent to both spheres at the point of contact.

Now, it's possible for one (or both) of the spheres to come towards that paper at an angle (though still hitting the same contact point) …

in that case, the centre of inertia is not moving perpendicular to the tangent plane.

 

[aloshi]

Hi aloshi!

The "tangent plane" is the plane of contact between the two spheres …

imagine that, when they are touching, you put a flat piece of paper between them …

it will be tangent to both spheres at the point of contact.

http://www.pluggakuten.se/wiki/images/8/83/Papper.jpg

Now, it's possible for one (or both) of the spheres to come towards that paper at an angle (though still hitting the same contact point) …

in that case, the centre of inertia is not moving perpendicular to the tangent plane.

http://www.pluggakuten.se/wiki/images/0/0e/Snett.jpg

like that??

 

[tiny-tim]

like that??

That's it! :tongue2:

Sphere B is approaching obliquely, and the impact is oblique.

 

[aloshi]

can you help me with this too, thanks;

"When the bodies impinge, they exert a mutual but varying pressure during the interval between contact and separation, an interval of time which is generally very short, and we suppose them to suffer a degree of compression, by wich, during a portion of this interval, their centers will approach each other, and during the remaining portion will recede by the action of an internal force rending to restore them to their original form. The force urging the approach if their centers is called the force of compression; the opposing force causing them to separate again is called the force of restitution or elasticity. The ratio of the force of restitution to that of compression is called the modulus of elastisk"

1)what is/does meant by compression?
the force that the balls come into each other, collide(the force at collide)??

2)what is/does meant by restitution? the force that removes them?
3)what is/does meant by “The ratio of the force of restitution to that of compression is called the modulus of elastisk” ?

 

[tiny-tim]

Hi aloshi!

Compression is the opposite of tension (negative tension) … it means the sphere is squashed very slightly, and there is an internal force, just like the internal force of tension in a rope, but acting inward instead of outward.

Tension and compression are stress when there are no shear forces (sideways forces).

Restitution is the restoring force when the sphere starts to expand again (back to its original size).

If the material is perfectly elastic, then the collision is also perfectly elastic, and no energy is lost. The force of restitution is then the same as the force of compression.

If the material is not perfectly elastic, then energy is lost, and the force of restitution is less than the force of compression.

The ratio is called the modulus of elasticity (or the coefficient of restitution).

See also http://en.wikipedia.org/wiki/Coefficient_of_restitution"

 

[aloshi]

Hi aloshi!

Compression is the opposite of tension (negative tension) … it means the sphere is squashed very slightly, and there is an internal force, just like the internal force of tension in a rope, but acting inward instead of outward.

Tension and compression are stress when there are no shear forces (sideways forces).

Restitution is the restoring force when the sphere starts to expand again (back to its original size).

I still can not understand what the difference by compression and Restitution.
So I Understand/ grasp;
1)
http://www.pluggakuten.se/wiki/images/6/63/1.JPG
2)
http://www.pluggakuten.se/wiki/images/7/75/2.JPG
3)
http://www.pluggakuten.se/wiki/images/6/6b/3.JPG
4)
http://www.pluggakuten.se/wiki/images/8/80/6.JPG

 

[tiny-tim]

compression and restitution

I still can not understand what the difference by compression and Restitution.

Hi aloshi!

I don't actually understand your first two diagrams .

Let's start again.

Tension: is irrelevant … these spheres are never under tension.

(a sphere could be under tension if, for example, it was hollow, and the pressure inside was more than the pressure outside)

Compression: when the spheres meet, they squash, so they experience compressive forces.

This happens both during the squashing and expanding periods.

Your book said …

we suppose them to suffer a degree of compression, by which, during a portion of this interval, their centers will approach each other, and during the remaining portion will recede by the action of an internal force rending to restore them to their original form.
The force urging the approach if their centers is called the force of compression; the opposing force causing them to separate again is called the force of restitution or elasticity.

What I've called squashing and expanding, your book calls approaching and receding.

In both these portions of the collision, the force is compression, but for some reason your books is distinguishing between them, and calling the first force the force of compression, and the second force the force of restitution.

The second force will always be less than the first force (unless the collision is elastic), and the ratio of the energies involved is called the coefficient of restitution.

 

[aloshi]

Hi aloshi!

I don't actually understand your first two diagrams .

Let's start again.

Tension: is irrelevant … these spheres are never under tension.

(a sphere could be under tension if, for example, it was hollow, and the pressure inside was more than the pressure outside)

Compression: when the spheres meet, they squash, so they experience compressive forces.

This happens both during the squashing and expanding periods.

have i understand it right?

Compression :
the force comes from the speed at which balls are? because the velocity is a vector. a vector has both direction and size, it is right ?

restroring force is the internal force that enables/make them to starts to expand again (back to its original size)
I'm sorry, but I am bad in English, sorry!

 

[tiny-tim]

Hi aloshi!

let's see … you got the original quotation from http://books.google.com/books?id=Wk...ient=safari&cd=62#v=onepage&q=impact&f=false" …

there's a worked example of the principle of that paragraph at para. 245, including …

Let e be the modulus of elasticity, or the ratio of the force of restitution to that of compression. Since these forces are proportional to the velocities they generate or destroy in the same mass, the velocity destroyed in m₁ by the force of restitution will be e(v₁ - v).​

(That's rather old-fashioned (1855) language … I think nowadays we'd talk of "change in velocity (or momentum)", rather than generating or destroying velocity.)

Perhaps the PF Library on coefficient of restitution (same as modulus of elasticity) puts it more clearly …

For a collision between two objects, the coefficient of restitution is the ratio of the relative speed after to the relative speed before the collision.

The coefficient of restitution is a number between 0 (perfectly inelastic collision) and 1 (elastic collision) inclusive.​

have i understand it right?

Compression :
the force comes from the speed at which balls are? because the velocity is a vector. a vector has both direction and size, it is right ?

restroring force is the internal force that enables/make them to starts to expand again (back to its original size)

Yes, force is (rate of) change of momentum, so it is proportional to change of velocity …

in that sense, the force comes from the velocity, and the velocity comes from the force.

And yes, as vectors, the force and the velocity will be in the same direction.

On the "way in", in that book, the force is called compression, and on the "way out", it is called the restoring (or restitutive) force (but I don't think a modern book would bother to make that distinction).

I don't think you really need to know how force comes into it when you have a problem like this …

In examination questions, just ignore these internal forces, and deal only with momentum before, momentum after, and coefficient of restitution. ​

 

[aloshi]

hi!
thanks for all the answers.

you have write;

If the material is perfectly elastic, then the collision is also perfectly elastic, and no energy is lost. The force of restitution is then the same as the force of compression.

If the material is not perfectly elastic, then energy is lost, and the force of restitution is less than the force of compression.

in that sense, the force comes from the velocity, and the velocity comes from the force.

And yes, as vectors, the force and the velocity will be in the same direction.
. [/INDENT]

So if the vector is equal before (compression vector) and after (restitution vector) collision , This means the material is perfectly elastic.
And if the vector is not equal before (compression vector) and after (restitution vector) collision , This means If the material is not perfectly elastic.

that must be right!

 

[tiny-tim]

Hi aloshi!

(btw, it's "you have written" … it's one of those verbs that come from old German, and whose past participles end in "en" instead of "ed", like forgotten, driven, stricken, given … )

So if the vector is equal before (compression vector) and after (restitution vector) collision , This means the material is perfectly elastic.
And if the vector is not equal before (compression vector) and after (restitution vector) collision , This means If the material is not perfectly elastic.

that must be right!

It is right!

 

[aloshi]

what is it that makes the vector is not equal before (compression vector) and after (restitution vector) collision?

 

[tiny-tim]

Mechanical energy is lost, and converted into heat, vibration, and sound.

 

[aloshi]

why is the force F=m_1*v_1??
is There a formula that says the force is F=m_1*v_1??
I have not seen that, but in the book you find it.

 

[tiny-tim]

why is the force F=m_1*v_1??

ah, that's not ordinary force (= rate of change of momentum),

that's impulsive force (= total change of momentum) …

see the definition at para. 233 on page 137 of Smith.

Nowadays, we say "impulse" instead of "impulsive force", and the impulse obviously is the extra momentum, m₁v₁.

 

[aloshi]

Hello!
English is too difficult to comprehend
I have read the definition at para. 233 on page 137 of Smith.
could not really understand how he came to the F = mv.

 

[tiny-tim]

impulse

Hello aloshi!

could not really understand how he came to the F = mv.

It's a definition …

an impulse (an impulsive force, in old language) is defined as the amount of momentum that it will give something.

So if an impulse F is applied to a mass m, it gives it a momentum F, and so its speed is F/m.

If the same impulse is applied to a mass 2m (twice as massive), it also gives it a momentum F, but this time its speed is F/2m.

Impulse = increase in momentum.

 

[aloshi]

excuse me for (excuse my) disturbing you, doesn't admit of [any] solution.
is still being discussed what is the meaning of momentum?

 

[tiny-tim]

momentum is mass times velocity.

momentum = mv.

 

[aloshi]

but it inconceivable, mathematically is momentum the mass times velocity.momentum = mv.

 

[tiny-tim]

but it inconceivable, mathematically is momentum the mass times velocity.momentum = mv.

I'm not sure I understand you …

you seem to be repeating what I've just said.

What do you mean by "inconceivable"?

 

[aloshi]

What do you mean by "inconceivable"?

incomprehensible, /inconceivable, /unimaginable


mathematically, I can understand. but physically, I can not understand what means whith momentum

 

[tiny-tim]

Well, momentum is a very easy concept.

Momentum is fundamental to dynamics.

It's even more fundamental than energy, since total momentum is conserved even when total mechanical energy isn't.

A standard equation in collisions is m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(where u is velocity before, and v is velocity after)

 

[hsnhajiani]

what do you mean when you say the energy doesn't change the motion and it only makes some heat or some voice?
and please check whether the following statements are true or not:
the Force changes the velocity, the the impulse changes the momentum, the Work changes the energy(or the work is a method of changing the type of energy from potential to kinetic and vice versa), the momentum changes the motion, and..

i had another question too, please answer:
what is the exact definition of work(i know that Work=Force*Distance)?
well, i think there are two possible, exact definitions;
1. the work is the pure force, multiplied by the distance along which the force is being applied to the object.
2. the work is the pure force, multiplied by the distance the object has traveled (or has been displaced).

 

[danielatha4]

"mv = d/dt (1/2 mv^2)"

Do you mean...

mv = d/dv (1/2 mv^2) ??

wouldn't d/dt (1/2 mv^2) = mv(dv/dt) ?