Monday, March 29th, 2010
TA: Tomoyuki Nakayama
PHY 2048: Physic 1, Discussion Section 3705
Quiz 8 (Homework Set # 11)
Name:
UFID:
Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator.
You need to show all of your work for full credit.
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Two concentric spherical shells with uniformly distributed masses M1 and M2 are situated as shown
in the figure below right.
a) Find the magnitude of the net gravitational force on a particle of mass
m, due to the shells, when the particle is located at radial distance a.
If a particle is outside of a shell with mass M, the force due to the shell
is the same as that due to a particle with all the mass M concentrated at
the center of the shell. Since the particle m is outside of the shell M1 and
M2, both exert gravitational forces that equal the forces due to particles
M1 and M2 concentrated at the center of the shells, thus the force is
F(a) = G(M1+M2)m/a2
b) Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when
the particle is located at radial distance b.
If a particle is inside a shell, the net force exerted on the particle by the shell is zero. Now the
particle is inside of shell M2 and outside of shell M1, so only shell M1 exerts force on the particle. We
obtain
F(b) = GM1m/b2
c) Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when
the particle is located at radial distance c.
Now the particle is inside of shell M1 and M2. Neither of them exerts force on the particle.
F(c) = 0