1) ( 25 pts) Open book
A book containing 100 square pages each of mass m=0.5 gram and sidea = 10 cm lies on a frictionless table open to page 50. A massless bug crawling around the book flips pages until the book is open to page75. a) 10 pts What is the (vector) displacement of the binding?b) ( 15 pts ) If the book (open to page 75) was frozen solid, what would be the moment of inertia for rotations about the left edge?

a: The cm relative to the binding is at [(R - L)/(R+L)]a/2 where R and L arethe number of pages to the left and to the right and does not move. Does the book neccessarily have the same orientation? I is an integral of dm x^2 as for a rod but the mass per unit length changes halfway across.

2) ( 25 pts ) Nancy and Tonya
a) ( 10 pts ) Nancy (M=50 kg) with initial speed v= 2 m/s collides head-on into Tonya (M=50 kg) who is initially stationary, and the pair slide without friction together (no rotation) having some heated discussion. How much mechanical energy is dissipated? Assume Nancy and Tonya are pointlike.b) ( 15 pts ) Suppose Nancy would have missed Tonya byb = 1 meter but they join hands and thereafter remain rigidly separated by distance b. How much energy is converted to heat in this case and how long does it take Tonya to rotate by 180 degrees in the cm frame?

a: The inelastic case was solved in lecture. See practice exam problem on billiard balls for the rotational case. Here the moment of inertia about the cm is 2MR^2 and there is no energy loss! What has changed?

3) ( 25 pts ) Escapes
An atom of mass 2 stones is attracted to a plane surface by a conservative force |F| = k/x^6 where x is the distance from the surface in yards and k= 5 in the yard-stone-second (YSS) system.
a) ( 10 pts ) Express the units of k in stones, yards, and seconds. Give the value and units in the YSS system for the work required to move an atom initially at a distance x_1=10^{-10} yards to distance x_2= 2\times 10^{-10} yards.b) ( 15 pts ) What is the minimum speed required for the atom initially at distance x_1 to excape to x= infinity?

a: [k] = [F][L]^6 = [m][L][T^{-2}][L^6] = stone- yard^7 - s^{-2} The work is the integral of force over distance. The escape speed follows from energy conservation - the initial KE must amount to the change in potential energy.

4) ( 25 pts }) Trapdoor
A square door of side a = 1 m and mass m = 30 kg is mounted in the ceiling and latched closed. Pointlike Pat (mass 60 kg) stumbling around upstairssteps onto the edge of the door and sticks. a) (10 pts) What is total moment of inertia about the hinge? b) ( 15 pts ) If the latch is released so the door swings down,what will be Pat's maximum speed?

a: Worked example in the text except add Pat at the edge.