1. Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons (mass 1.0 u) and deuterons of mass 2.0 u. a) What is the speed of a neutron, expressed as a fraction of its original speed, after a head-on, elastic collision with a deuteron which is initially at rest? Express your answer using three decimal places. b) What is its kinetic energy, expressed as a fraction of its original kinetic energy? Express your answer using three decimal places. c) How many such successive collisions will reduce the speed of a neutron to 1/2190 of its original value? Express your answer as a number of collisions.

2. A uniform cube with mass 0.700 kg and volume 0.0270 m3 is sitting on the floor. A uniform sphere with radius 0.400 m and mass 0.800 kg sits on top of the cube. a) How far is the center of mass of the two-object system above the floor? Express your answer with the appropriate units.

3. James (mass 85.0 kg) and Ramon (mass 69.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. Ramon pulls on the rope to give himself a speed of 1.10 m/s. a) What is James's speed? Express your answer with the appropriate units.

4. Two friends, Burt and Ernie, are standing at opposite ends of a uniform log that is floating in a lake. The log is 3.1 m long and has mass 290 kg. Burt has mass 34.5 kg and Ernie has mass 33.5 kg. Initially the log and the two friends are at rest relative to the shore. Burt then offers Ernie a cookie, and Ernie walks to Burt's end of the log to get it. a) Relative to the shore, what distance has the log moved by the time Ernie reaches Burt? Neglect any horizontal force that the water exerts on the log and assume that neither Burt nor Ernie falls off the log. Express your answer with the appropriate units.