- 1.
- [9 marks, 5 for a) and 4 for b)]
We have a beam of neutrons incident on iron shielding (Number of Fe atoms per
m3 = 8.46 1028). The absorption cross section of the neutrons is
0.556 x 10-28 m2.
- a)
- What is the ``half-distance" for neutron absorption in Fe?
- b)
- If we started with 3.60 x 1012 neutrons, how many neutrons are absorbed in
the final micrometer (10-6 m) of a 2.00 m thick Fe target?
- 2.
- [9 marks, 3 marks for a) & b), 2 for c), and 1 for d)]
In outer space a stationary astronaut (mass 60 kg) sees approaching him a
heavy astronaut (mass 120 kg) moving relative to him with a speed of
v = 4.00 m/s and in such a direction that they would come within 30 m of each
other. The stationary astronaut extends a massless 30 m rope so that the moving
astronaut can grab it and hang on.
- a)
- Regarding the astronauts as point masses, where is the centre-of-mass
of the system after the astronaut hangs on?
- b)
- What is the forward speed of the centre-of-mass of the system?
- c)
- What is the angular speed of the system about its centre-of-mass?
- d)
- Is any energy lost in the ``collision"? (Prove your answer.)
- 3.
- [9 marks, 4 for a) and 5 for b)]
You have an automobile (mass = 1.23 x 103 kg) whose speed is given by
v =1.350 t + 0.412 t3, where v is in m/s and t is in seconds.
- a)
- What is the force accelerating the auto at t = 3.00 sec.?
- b)
- How much distance does the auto cover between t = 1.12 sec. and t= 4.12 sec.?
- 4.
- [9 marks, 3 for each part]
We have a rotating merry-go-round which is a solid disk of radius 3.2 meters
and mass 400 kg. A person (regarded as a point mass of 60 kg) is standing on
the outer rim of the merry-go-round while the system (merry-go-round plus
person) rotates at 0.373 revolutions per second, about an axis through the
center of the merry-go-round.
- a)
- How much force does the person exert to remain at the rim?
- b)
- If the person walks to the centre of the merry-go-round, what is then
the number of revolutions per second of the system?
- c)
- How much work does the person do in walking to the centre?
