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The nuclear explosion occurs. How does the radius of the fireball depend on the time? (Sedov's problem)
Pulling Strings (MIT)
A mass m is attached to the end of a string. The mass moves on a frictionless table, and the string passes through a hole in the table (see Figure P.1.9), under which someone is pulling on the string to make it taut at all times. Initially, the mass moves in a circle, with kinetic energy 
. The string is then slowly pulled, until the radius of the circle is halved. How much work was done?
Collision of Mass–Spring System (MIT)
A mass 
with initial velocity 
strikes a mass-spring system 
initially at rest but able to recoil. The spring is massless with spring constant k (see Figure P. 1.22). There is no friction.
a) What is the maximum compression of the spring?
b) If, long after the collision, both objects travel in the same direction, what are the final velocities 
and 
of and respectively?
Relativistic Rocket (Rutgers)
A rocket having initially a total mass 
ejects its fuel with constant velocity 
relative to its instantaneous rest frame. According to Newtonian mechanics, its velocity V, relative to the inertial frame in which it was originally at rest, is related to its mass M(V) by the formula
a) Derive this result.
b) Suppose the velocity of the ejecta is limited only by 
and derive the relativistic analogue of the above equation. Show that it reduces to the Newtonian result at the appropriate limit.
Compton Scattering (Stony Brook, Michigan State)
In the Compton Effect, a γ - ray photon of wavelength λ strikes a free, but initially stationary, electron of mass m. The photon is scattered an angle θ and its scattered wavelength is 
. The electron recoils at an angle φ (see Figure P.2.10).
a) Write the relativistic equations for momentum and energy conservation.
b) Find an expression for the change 
in the photon wavelength for the special case 
.
Particle Creation (MIT)
Consider a photon of energy 
incident on a stationary proton. For sufficiently large a π meson can be produced in a reaction
What is the 
threshold photon energy for this reaction to occur?
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