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supperking
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Homework Statement
A homogeneous disk A of a radius R is resting on a cart B (on wheels, assume no work against friction) when a force F is applied to the cart. Assuming the slip does not slip, determine:
(a) minimum coefficient of static friction required to prevent slipping
(b) acceleration of the cart
(c) angular acceleration of the disk
(d) linear acceleration of the disk
Mass of A and B are also known. Let mass of A be Ma and mass of B be Mb.
Actual numerical values are as follow:
Ma=20kg
Ma=30kg
R=0.6m
F=60N
Homework Equations
F=ma=umg (where u is coefficient of friction, static)
I=mr2/2 (where I is moment of inertia of a disk)
FR=I*alpha (where alpha is angular acceleration)
No slip: v=rw, a=R*alpha (where w is angular velocity)
The Attempt at a Solution
Attempt 1
(a) F=umg, so u=F/Mag
I'm already skeptical about this, since I have the impression that F is exerted on the cart, not on the disk. So I should not be applying it to the disk.
(b) F=(Ma+Mb)a, find a
This in itself make no sense. If I draw a free body of the cart, the cart experiences zero resultant force. Moreover, N2L should not be applied to a non-rigid body and I should not add in 2 masses.
(c) Fr=I*alpha. Find alpha.
(d) a=r*alpha. Find a.
Something is really wrong with my understanding. Any instructions that can guide me to the correct direction will be appreciated. I will like to understand it in terms of classical Newton laws (2nd and 3rd law) and also freebody diagrams. More fundamentally, I will like to question if the only contact between a body and another is by friction (be it kinetic or static), when a force is applied to the formal body, isn't the force that is felt by the latter limited by friction? I also have an inkling this is about using of N2L in non-inertia frame.
Attempt 2
This attempt is based on 'friction force = 0 under rolling'.
(a) Same as attempt 1.
(b) F=mbab, find ab
(c) rF=I*alpha, find alpha
(d)
Due to rolling, arolling=r*alpha
Due to pseudo force in non-inertia frame, apseudo=F/ma
Acceleration in inertia frame = apseudo-arolling
In numerical answers, (b) 2ms-2 (c) 10rad/s2 (d) -3ms-2
I find this attempt slightly better, but it does not answer my previous doubt about whether the force on the disk is limited by the friction.
Attempt 3
I modified how I apply the psuedo force concept in part (c).
(c) Fpsuedo=maab
(since point of contact moves with cart)
rFpsuedo=I*alpha, find alpha
(d) Linear acceleration = 0
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