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**Write the following text on the front cover of your homework
assignment and sign it. If the text is missing, 20 points will be subtracted
from your homework grade.**

1.
The
center of gravity of a system of particles is the point about which the
external gravitational forces exert no net torque. For a uniform gravitational force, show
that the center of gravity is identical to the center of mass for the system of
particles.

2.
A
projectile is fired at an angle of 45° with initial kinetic energy *E*_{0}. At the top of its trajectory, the
projectile explodes into two fragments (an additional energy *E*_{0} is released during the
explosion). One fragment of mass *m*_{1} travels straight
down. What is the velocity (specify
both magnitude and direction) of the second fragment of mass *m*_{2}, and the velocity of the
first?

3.
A
fixed force center scatters a particle of mass *m* according to the force law *F*(*r*) = *k*/*r*^{3}. If the initial velocity of the particle
is *u*_{0}, show that the differential scattering
cross section is

4.
The
most energetic *a*-particles
available to Ernest Rutherford and his colleagues for the famous Rutherford
scattering experiment were 7.7 MeV. For the scattering of 7.7 MeV *a*-particles
from ^{238}*U* (initially at
rest) at a laboratory scattering angle of 90°, find the following:

a.
The
recoil scattering angle of ^{238}*U* in the laboratory frame.

b.
The
scattering angles of the *a*-particle
and ^{238}*U* in the
center-of-mass frame.

c.
The
laboratory kinetic energy of the scattered *a*-particle and ^{238}*U*.

d.
The
impact parameter *b*.

e.
The
distance of closest approach *r*_{min}.

f.
The
differential cross section at a laboratory scattering angle of 90°.

g.
The
ratio of the probabilities of scattering at 90° to that of 5° in the laboratory
frame.

5.
A
rocket in outer space, in a negligible gravitational field, starts from rest
and accelerates uniformly with an acceleration *a* until it reaches its final speed *v*. The initial mass of
the rocket is *m*_{0}. How much work does the rocket's engine
do?

This set covers the material discussed in Chapter 9.