Two questions (1st: Rigid body, 2nd: Inelastic collisions)

Hi all.
É have two questions about two different things that I have been bothering
me.

1st question concerning rigid body:
We have a circular, horizontal, flat, solid disc with mass Ì, which is
resting on a frictionless horizontal surface. If we tangentially apply to
the the circumference of the disc, a steady horizontal force (parallel to
the surface), will the disk do a combined motion of translation and rotation
or will it do only a translational motion?

2nd question concerning inelastic collision:
We have a wedge with mass m1 and if we want to push it with our hands in
another body with mass m2, so that the whole wedge just enters the other
body, we have to spend an amount of energy (E1). Now, the same wedge has an
horizontal velocity and hits the same body m2 which is resting at a
frictional horizontal plane, free to move. When the collision ends, the
whole wedge has just entered the body m2 and the whole body (m1+m2) has a
final velocity. The question is:
Is the amount of the energy E1 equal to the heat that is produced from the
inelastic collision of the wedge and the body with mass m2?

"George Panagiotakopoulos" <[Only registered users see links. ]> wrote in message
news:1118325310.218406@athnrd02...

Hi George:
The disk will do the combination. The acceleration of the centre of mass is
given by
F = ma
and the angular accleration is given by
(Torque, which is the force times the radius) = moment of inertia times
angular acceleration.

This separation of the 'motion of the centre-of-mass and the motion about
the centre-of-mass' is a standard problem in intermediate mechanics.

Have you ever shot a cue ball with lots of side-English? You will note that
the ball translates and spins at the same time.

Put a stick on the ground. Whack its end sideways. Watch it rotate and
translate. Works better on ice.



When you originally shoved the wedge into the second lump, some of your
energy went into creating heat and some went into pulling the lump apart -
creating more surface energy, if you like. So, E1 is more than just the
heat that is produced.

In the second scenario, the energy of the wedge is equal to E1 plus the
kinetic energy of the body after the collision.

What made you think of this?

Ron Verrall

Hi Ron, thanks for your answer.

1st problem:

I know that when we have friction will happen everything you said. But here
we didn't have friction.
The problem could be restated as this:
You have a resting free body (with no any axis of rotation) to which no
forces at all are applied (no friction, no gravitational or other forces)
and someone applies an external force that its line doesn't pass through the
center of the mass.
Is the motion that occurs, a combined motion? This is my problem.

2nd problem:

I want to compare:

i) the minimal energy (E1) I need to spend in order to put with my hands
entire the wedge in the other body, pushing him two bodies from the one and
the other side,

ii) the loss of energy due to the plastic collision of wedge and body, if
due to this plastic colission the wedge enters just entire in the body.



I didn't think of this scientific freak. The ministry of education did :-))


"Ron Verrall" <[Only registered users see links. ]@#$spam.ca> wrote in message
news:FWYpe.1616738$Xk.92486@pd7tw3no...

George Panagiotakopoulos wrote:

Friction or not, there *will* be a torque, and there *will* be a net
force to displace the body.

Tom Davidson
Richmond, VA

"George Panagiotakopoulos" <[Only registered users see links. ]> wrote in message
news:1118340322.793167@athnrd02...

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What I said did not assume any friction. I assure you that the motion is
combined. Didn't you like my two examples? Imagine the stick on the ice.
No friction there - not much, anyway. If you hit the stick at its center of
mass, it slides without rotating. If you hit it off center - at the end,
say, it will slide and rotate.
Ron
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What didn't you like about my answer? You have just restated the question.
Ron
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snip the rest...