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Unformatted text preview: hermore, the moment of inertia for a sphere is I = 2 M R2 . So,
nd
5
Newton’s of law to the sphere and
we ﬁnd the following system2 equations
and the hanging object: 2
T=
Ma
5
T = m ( g − a) . ∑F x I sphereα = mg − T = ma ( Setting these two ubstitute for Isphere andother and solving for the acceleration2
S expressions equal to each α in
2
TR = 5 MR
gives
equation (1) to obtain:
g
a=
.
1 + 2M
5m a
)R 2
Eliminate T between equations (2)
g
(b) Now we just substitute this result back in to the expression T = 5 M a to ﬁnd and (3) and solve for a to obtain: a= 1+ 2 Mg
2M mg
T=
=
.
2M
5 1 + 5m
5m + 2M (b) Substitute for a in equation (2)
4
and solve for T to obtain: T= 2M
5m 2mMg
5m + 2 M 5. A basketball rolls without slipping down an incline of angle θ. The coeﬃcient of static
friction is µs . Model the ball as a thin spherical shell. Find Picture center of mass of the ball,
(a) the acceleration of the the Problem The three forces acting on the basketball a
the ball, the the ball, force, and the force of friction....
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This document was uploaded on 03/14/2014 for the course PHYS 18 at UC Merced.
 Spring '10
 collins
 Physics, Work

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