I'm certainly not mech eng so can can someone please explain the following to
me...
A cannonball is sitting on a horizontal carpet. A horozontal acceleration is
applied to the carpet. If the acceleration is small, the cannonball stays where
it is on the carpet and moves with it. If the acceleration is sufficiently
large, the cannonball will rotate in a direction opposite to the acceleration of
the carpet. What are the conditions (value of accel.) under which this rotation
will first begin?

let me take a crack at this, but keep in mind i just got back from karting,
water polo game, and 1 pitcher of molson dry...lol...Engineering!
Okay, so you have statically a cannon ball sitting on the carpet. The only
forces acting at this point are gravity on the ball, and no forces on the
carpet. If the carpet is accelerated horizontally to the right, the ball
will eiter come with it, or roll counter-clockwise in place. I'm thinking
that you have a frictional force acting between the ball and the carpet,
being
First for the ball to move laterally with it, no rolling. The frictional
force:
F= (coeff of static fric)*(Mass of cannon ball)*(acceleration due to
gravity)
Acts in the direction of motion. I'm guessing if the force acting on the
carpet is greater than this, then the ball will rotate.
Now for rotation. This force exerts a torque T on the ball. To have an
acceleration "a"(rotational), is governed by newtons second for rotation:
T= I*a(rotational) ---or----- T=I*a(tangential)/R R=radius
I think that's a start. Up to that point i'm comfortable, but now i'm going
to have a shower. Let me know if i'm right or wrong guys, i'm not afraid to
take a crack at it.
-jp

I'll give this a shot...
Place a cannon ball on a plush carpet.
Push the top of the ball horizontally, and measure the force at which
it begins to roll.
That's the force that allows it to compress some new carpet, while
releasing some squished carpet.
Now you have a number, redo the experiment.
This time accelerate the carpet under the ball gently.
If the acceration is insufficient to generate a static friction force
on the ball sufficient to make it roll (i.e. less than the value of
force you measured earlier), it just goes along for the ride.
If the acceration is more brisk, the ball begins to roll.
The relation given by Newton was this:
the force is proportional to the balls mass and to the size of the
acceleration.
Clear as mud?
Brian Whatcott
Brian

Maybe this isn't so easy after all... :-) (like many "easy" things).
So it's the friction of the ball on the carpet that "decides" when it starts
rolling? If the carpet were instead a sheet of glass then the ball should start
rolling with a lesser force of accel needed? I was also wondering about this as
it applies to that famous trick where someone pulls the tablecloth straight out
from under a tableful of china cups! I suppose in that case the accel is so
large that the cups are slipping (skidding?) on the cloth.

LOL, it is a little involved. Since last night i've been thinking about it.
I think my attempt is halfway there, but is only the beginning. I did some
trial runs with a bowling ball and a towel(yes, i am a loser) just to get a
qualitative understanding of the system, and then i hit the physics
textbooks.
From what i saw, when the ball rolled, it stayed in the same place, so it
had no tranverse kinetic energy, just rotational energy because the center
of mass stays pretty much in the same place. When the ball dosent roll it
has only kinetic energy because it's center of mass is moving with velocity
"v" in the same direction of the carpet. Now we know from newtons second
that
F = ma ; so for the couple system of mass "m(sys)", we have: a = F/m(sys).
If this acceleration is fast enough, the ball will roll while slipping on
the carpet. So far that's what i understand.
acceleration is
sufficiently

(If this is another
Professor-using-students-for-outside-fees-because-he-can't-get-it, have your
professor send his consultant's check to Toys for Tots.)
1) you have the mass of the ball, which tends to hold the ball in place and
thus, because the original frame of reference for rotation moves to reduce
net acceleration, REDUCES the amount of available tangential force for
rotation.
the mass moment of the ball, which, with the tangential force from the
weight of the ball acting on the carpet-ball interface to resist rotation,
determines the AMOUNT of rotation
the acceleration of the carpet relative to the ball, which always produces a
rotation (this parameter is not a force which can be present and not
displace- this is an acceleration which by definition displaces)
and the discontinuous rolling resistance of the ball on the inelastic
carpet, which in its lower area does not deform and holds the ball in place
and prevents acceleration, and in its upper area deforms and allows the ball
to displace relative to the carpet, reduced by the inelastic value.
Think of this as the ball having a flat spot, the larger the inelastic
coefficient the bigger the flat spot. The input force needs to overcome the
flat, i.e., to lift the ball over the edge of the flat on the ball so that
the ball can roll, and it does that by grabbing the flat and flipping the
ball around by lifting and squeezing the edge of the ball as it turns.
(The end value here is when the ball is a block, and the force from
trying to accelerate the block's mass has to be larger than the friction
force for the block to separate from the carpet.)
The value is proportional to the inelastic constant. But above a certain
constant value, the force required to rotate is greater than static
friction, and the ball will slide rather than rotate.
So IMHO, the ball always rotates in a perfectly elastic system.
When the ball rotates in an inelastic system depends on the inelastic
value, i.e., once the force required to overcome the deformation is
achieved, the ball rotates. Little deformation, small carpet acceleration -
lot of deformation, more carpet acceleration.
When the force required to rotate the ball is greater than the force
required to slide the ball, the ball will not rotate, it will just slide on
the carpet
best guess.....

not a problem -
(perched firmly on the rectangular container for fat-alkalis compounds - the
professor syndrome of which I speak is where they will consult on a matter
for pay and then have students do all the work, work required of the
students for advancement and gratis.
I may be oversensitive to the abuse of position over students, to the
unethical conduct, and to the use of academic position as a vehicle to
circumvent laws regarding the marketing of engineering.
The results get into court and the overpaid profs spew forth rot that
wouldn't see the light of day in the real world, which wastes the court's
time and society's. )
acceleration

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