Physics 121 Midterm - Fall 1997

1.

  [10 marks, 5 for each part]

a)

If you have a sample of radioactive ⁶⁰Co (with a half-life of 5.3 years) what fraction of the radioactive isotopes will be left after 15.9 years?

b)

If you insert 1 kg. of stable ⁵⁹Co into a nuclear reactor to absorb neutrons and become radioactive ⁶⁰Co you find that 3.00 x 10⁶atoms of ⁶⁰Co are made per second. If you leave the sample in the reactor for a very long time (compared to 5.3 years) how many atoms of ⁶⁰Co will be present in the sample?

2.

[12 marks, 4 for each part]

In outer space a stationary astronaut (mass 60 kg) sees approaching him a long (30 m) uniform rod (mass 60 kg) which is moving toward him, as shown, with a velocity of v = 3.60 m/s. The astronaut is just able to grab the end of the rod and holds on.

a)

Regarding the astronaut as a point mass, 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?

3.

  [12 marks]

You have a flywheel - a uniform disk of mass 100 kg and radius 0.50 m mounted on an axle through its centre-of-mass - which you can accelerate electrically. If the flywheel starts from rest (at t=0) and then is subject to angular acceleration $\alpha$ = (0.31t³ - 0.11t²) rad/sec², what is the kinetic energy of the flywheel at t=2.0 sec?

4.

  [12 marks, 6 for a, 3 for b, 3 for c, plus 1 extra mark for d.]

You have 100 cars, all of the same mass m, stopped on an icy road (no friction).

They are parked quite close together, as shown, when car number zero, of the same mass, m, collides with car number one at a speed of v = 60 km/hour. The cars have perfect bumpers so that this collision, and all the subsequent impacts, are perfectly elastic.

a)

What is the speed of car 1 after it has been hit by car 0 and before it collides with car 2? (If you have ever watched a billiard ball collide head-on with another, you will know the answer.)

b)

What is the final result after each car has hit the one in front of it?

c)

If car 1 was hit, in rapid succession, by three cards, each of mass m and speed of 60 km/hour, what is the final result after all collisions have occurred?

d)

(Much harder and for 1 extra mark - try this only if you have finished the other questions.) If the situation were the same as above except that car 0 had mass 2 m, what would be the final result after all collisions had occurred?