Help with mechanics problem from images

[winichris]

~~~~URGENT, Question about mechanics~~~~~~~

http://imageshack.us/f/685/19897974.png/
http://imageshack.us/photo/my-images/152/12617395.png/

Anyone got some ideas about the questions?

Thanks.~~

 

[tiny-tim]

welcome to pf!

hi winichris! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[winichris]

hi winichris! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

My teacher taught some very easy notes.
But he gave us this kind of so difficult problems.
I don't have ideas about that.

For Q1,
velocity of mass m = 2a x (g/a)^0.5

By conservation of momentum, m x 2a x (g/a)^0.5 = m x (velocity of ring)
velocity of ring will be = 2a x (g/a)^0.5

But I think this solution is wrong since by using conservation of energy:

0.5 x m x (velocity of mass)^2 = 0.5 x m x (velocity of ring)^2 + mgh

This will make h=0

So can you help me to think of this question?

 

[tiny-tim]

you need to start by finding expressions for the momentum and the energy at a general speed v (of the ring) and angle θ

for horizontal momentum of the rod, you must use the velocity of the centre of mass of the rod

for kinetic energy of the rod, you must add the rotational kinetic energy (using moment of inertia about the centre of mass) to the "translational" kinetic energy of the centre of mass

start again! ​

 

[winichris]

you need to start by finding expressions for the momentum and the energy at a general speed v (of the ring) and angle θ

for horizontal momentum of the rod, you must use the velocity of the centre of mass of the rod

for kineticenergy of the rod, you must add the rotational kinetic energy (using moment of inertia about the centre of mass) to the "translational" kinetic energy of the centre of mass

start again! ​

When the mass is at its highest point, its velocity and angular velocity are both zero?

 

[tiny-tim]

When the mass is at its highest point, its velocity and angular velocity are both zero?

when the rod is at its greatest angle, its angular velocity is obviously zero

but why would its ordinary velocity also be zero?

 

[winichris]

when the rod is at its greatest angle, its angular velocity is obviously zero

but why would its ordinary velocity also be zero?

http://imageshack.us/photo/my-images/823/phy.png/
When it is in the highest point, is the tangential velocity is zero? because v=rw, where w=0. (red blanket in the picture)

As the whole system is moving to right, so there should be a radial velocity of the mass ??(blue blanket in the picture)

But there is a question, there are 3 unknowns (angle theta, velocity of mass and velocity of ring) but there are only 2 equations.
So whether the radial velocity of the mass is equal to initial velocity of the mass?

Thanks a lot!

 

[tiny-tim]

When it is in the highest point, is the tangential velocity is zero? because v=rw, where w=0. (red blanket in the picture)

As the whole system is moving to right, so there should be a radial velocity of the mass ??(blue blanket in the picture)

why are you using "radial" and "tangential"? there's no origin here (the ring is moving)

But there is a question, there are 3 unknowns (angle theta, velocity of mass and velocity of ring) but there are only 2 equations.

no, there are only 2 unknowns … position of ring, and angle of rod

 

[winichris]

why are you using "radial" and "tangential"? there's no origin here (the ring is moving)


no, there are only 2 unknowns … position of ring, and angle of rod

radial and tangential is for the rod (not the ring above).
Because when it is at highest point, w=0, can i conclude that tangential velocity=0?

Position of ring means velocity of ring?

 

[tiny-tim]

radial and tangential is for the rod (not the ring above).
Because when it is at highest point, w=0, can i conclude that tangential velocity=0?

yes of course

Position of ring means velocity of ring?

you can use either

 

[winichris]

yes of course


you can use either

So with tangential velocity=0, the rod only consist of radial velocity.
Is the radial velocity (blue blanket in the last photo) = initial velocity of rod ( radius x angular velocity)

 

[tiny-tim]

can you please type your equations directly into the post, instead of photocopying them?

and what is y? and remember that there's no mass at the free end of the rod

 

[winichris]

can you please type your equations directly into the post, instead of photocopying them?

and what is y? and remember that there's no mass at the free end of the rod

Let y be the radial velocity of the rod at highest point, x be the velocity of the ring when rod at highest point, v be initial velocity of the rod.
v=rw=2a(g/a)^0.5, right?
Will y and v be equal?

Momentum: mv = my cos(theta) + mx
Energy: 0.5mv^2 + 0.5Iw^2 = mg2a(1-cos theta) + 0.5mx^2 + 0.5my^2

 

[tiny-tim]

Let y be the radial velocity of the rod at highest point

the radial velocity is always 0

, x be the velocity of the ring when rod at highest point, v be initial velocity of the rod.

the rod doesn't have a velocity, it only has an angular velocity

Energy: 0.5mv^2 + 0.5Iw^2 = mg2a(1-cos theta) + 0.5mx^2 + 0.5my^2

(try using the X² button just above the Reply box )

kinetic energy = 0.5mv² for the ring + 0.5mv² for the centre of mass of the rod + 0.5Iω² for the rod

(and at the top of the swing, ω = 0)

 

[winichris]

the radial velocity is always 0 the rod doesn't have a velocity, it only has an angular velocity

"when the rod is at its greatest angle, its angular velocity is obviously zero
but why would its ordinary velocity also be zero? "<-- you said that the rod should have zero velocity before.
Or maybe i misunderstand your meaning.
So the ordinary velocity of the rod should be zero at highest point?

 

[tiny-tim]

"when the rod is at its greatest angle, its angular velocity is obviously zero
but why would its ordinary velocity also be zero? "<-- you said that the rod should have zero velocity before.

no, i said the opposite ...

when the rod is at its greatest angle, its angular velocity is obviously zero

but why would its ordinary velocity also be zero?

 

[winichris]

no, i said the opposite ...

the radial velocity is always 0


the rod doesn't have a velocity, it only has an angular velocity

Sorry i type wrongly.
You say the rod does not have an ordinary velocity here..

 

[winichris]

Or maybe can you just tell me what will be the ordinary velocity of the rod when it is at highest point? thanks a lot, you are so helpful:)

 

[tiny-tim]

Or maybe can you just tell me what will be the ordinary velocity of the rod when it is at highest point? thanks a lot, you are so helpful:)

the rod does not have an ordinary velocity, the rod has an angular velocity, and the centre of mass of the rod has an ordinary velocity

at its highest point, the angular velocity is 0, and therefore the velocity of the centre of mass of the rod is the same as the velocity of the ring

 

[winichris]

the rod does not have an ordinary velocity, the rod has an angular velocity, and the centre of mass of the rod has an ordinary velocity

at its highest point, the angular velocity is 0, and therefore the velocity of the centre of mass of the rod is the same as the velocity of the ring

At the highest point, the direction of the velocity of the center of rod is towards right or towards right upwards direction?

If the direction is towards right,

m(2aw) = m(velocity of ring) + m(velocity of center of mass of rod)
As velocity of ring and velocity of center of mass of rod is same,
so velocity of ring= aw

right?

 

[tiny-tim]

If the direction is towards right,

m(2aw) = m(velocity of ring) + m(velocity of center of mass of rod)
As velocity of ring and velocity of center of mass of rod is same,

yes, your RHS (total final horizontal momentum) is correct

but your LHS (total initial horizontal momentum) is wrong

 

[winichris]

yes, your RHS (total final horizontal momentum) is correct

but your LHS (total initial horizontal momentum) is wrong

Initially, only the rod is moving while the ring is at rest.
And the velocity of the rod is (radius)x(w), so what's wrong?

 

[tiny-tim]

And the velocity of the rod is (radius)x(w), so what's wrong?

you keep saying "the velocity of the rod" !

the rod does not have a velocity, its centre of mass has a velocity

 

[winichris]

you keep saying "the velocity of the rod" !

the rod does not have a velocity, its centre of mass has a velocity

Ok sorry, actually I don't quite understand what is the difference between velocity of rod and center of mass of rod..

So what's wrong of my LHS part(the initial momentum)?

 

[tiny-tim]

m(2aw) =

why m? why 2? why a? why w?

 

[winichris]

why m? why 2? why a? why w?

momentum = mass x velocity

velocity = radius x angular velocity

mass=m
radius=2a (the length of rod)
angular velocity = w =(g/a)^0.5 (from question)

am i correct

 

[tiny-tim]

momentum = mass x velocity

velocity = radius x angular velocity

you need the velocity of the centre of mass

 

[winichris]

you need the velocity of the centre of mass

I think I don't know how to find the velocity of center of mass:(

2aw/2??

Really no idea:(

 

[tiny-tim]

get some sleep :zzz:

 

[winichris]

get some sleep :zzz:

ok, have a good sleep:)

thanks a lot:)

I will think of it, but i think i still need your help since i really do not have ideas about that-_-