A block and a disk connected by a rope

[LCSphysicist]

Homework Statement

All below

Relevant Equations

All below

Basically, there is a gravitational field g and a friction force acting on the cylinder, which does not slip in the plane.
The question is, the acceleration of m'.
I solve this question basically by this:

" m*g*dh*sina + m'*g*dh = m*v1*dv1 + m'*v2*dv2 + I*w1*dw1 " {1}
w*r = v1' + v2'

So

The problem is, in {1} i suppose Δ U = - Δ T, until here okay, but i needed to say that:
Δ U = -(m*g*dh*sina + m'*g*dh)

I am trying to see why this is right.

Why not -(m*g*dh*sina) + (m'*g*dh) or +(m*g*dh*sina) - (m'*g*dh)
?

Maybe doing by the other ways, i would eliminate by absurds, or the first way already encompasses the case where one go up and another go down?

 

[BvU]

Hi,

What do you do with the kinetic energy of the rotation of the cylinder ?

Also: what do your symbols (other than the ones in the picture) represent

 

[LCSphysicist]

Hi,

What do you do with the kinetic energy of the rotation of the cylinder ?

Also: what do your symbols (other than the ones in the picture) represent

Well, dh is the distance traveled by the block hanging
v one is the velocity of the sphere
v two is the velocity of the block
I is the moment of inertia passing through the center of the sphere
w is the angular velocity

And using the fact that w1*r need to be equal to -v1, just substituting in the equation

 

[haruspex]

m*g*dh*sina + m'*g*dh

If m' descends dh, how far up the slope as m move?

w*r = v1' + v2'

Same question, and check those signs.

 

[LCSphysicist]

If m' descends dh, how far up the slope as m move?

Same question, and check those signs.

Actually the second notation that you quote is a vector notation XD are the constraint that i found.

Lo = x2 + x1 - Theta*r

" If m' descends dh, how far up the slope as m move?"
I thought it far up dh too, but, it fall by R theta later, since it is routing. That is, as result:

-dh + dtheta*r (i adopt positive down the slope.)

Exact as it previous Lo = x2 + x1 - Theta*r
dLo = 0 = dh + x - dtheta*r
x = dtheta*r - dh

The problem is yet the signal in the potential equation :C

 

[haruspex]

Actually the second notation that you quote is a vector notation XD are the constraint that i found.
Lo = x2 + x1 - Theta*r

I assume x1 and x2 are movements by m (i.e. the mass centre of the cylinder) and m' respectively.
That cannot make sense as a vector equation since the constraint is imposed by the string, and the string changes direction between the two. Clearly these are just distances.

i adopt positive down the slope

And down positive for the block too? Ok, that explains x1+x2.
It looks like you are taking clockwise as the positive direction for theta, right?
Lo, I take it, is the string length.
(It would save a lot of back and forth if you were to define all your variables in the first place.)

Since it is rolling contact, what is the relationship between theta and x1?