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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 E0. At the top of its trajectory, the
projectile explodes into two fragments (an additional energy E0 is released during the
explosion). One fragment of mass m1 travels straight
down. What is the velocity (specify
both magnitude and direction) of the second fragment of mass m2, 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/r3. If the initial velocity of the particle
is u0, 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 238U (initially at
rest) at a laboratory scattering angle of 90°, find the following:
a.
The
recoil scattering angle of 238U in the laboratory frame.
b.
The
scattering angles of the a-particle
and 238U in the
center-of-mass frame.
c.
The
laboratory kinetic energy of the scattered a-particle and 238U.
d.
The
impact parameter b.
e.
The
distance of closest approach rmin.
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 m0. How much work does the rocket's engine
do?
This set covers the material discussed in Chapter 9.