From Autumn 99 
1. (20 points)
A solid cylindrical pulley of mass M = 5.50 kg and radius R = 0.660 m is used to lower a bucket of mass m = 3.10 kg into a well. See the schematic of the system below.
Solution Outline: This problem is so easy, I am almost tempted not to
post a solution. (I say this with a SMILE !

2. (20 points)
A sphere of mass m = 24 kg and radius R = 0.20 m rolls without slipping up a ramp that is inclined at an angle with the horizontal. A schematic of the system is shown on the diagram below. Suppose that the angular speed at the bottom of the hill is 36 rad/sec.
What is the vertical height h that the sphere reaches before momentarily coming to rest?
Hint: Use conservation of energy in the presence of rolling!
The moment of inertia of the sphere is I =
.
Solution Outline: Guess what ?

3. (20 points)
A 5.00kg block of wood (density 635 kg/m^{3} ) is connected to a light string that is connected to the bottom of a large beaker filled with water. Assume the density of water is 1000 kg/m^{3}. A diagram of the system is below.
What is the tension T in the string?
Solution Outline: Guess what ?

4. (20 points)
A liquid () flows through two horizontal sections of tubing joined end to end. In the first section the crossectional area is A_{1} = 9.5 cm^{2} , the fluid speed is 265 cm/s and the pressure is P_{1} = 1.2x10^{5} N/m^{2}. In the second section the crossectional area is A_{2} = 9.0 cm^{2}.
Find the pressure P_{2} in the second (smaller) section.
Note: v_{2 }= A_{1}·v_{1}/ A_{2} You know v_{1}. Find v_{2} from the above equation and solve for P_{2} from the equation below. Note that y_{1} = y_{2} and so they cancel !: 
5. Extra Credit
An automobile fuel tank has volume =12.000 gallons. It is filled with 11.125 gallons of gasoline when the temperature is 10^{0}C . The vehicle is left in the sun and the temperature rises to 35^{0}C. The expansion coefficient for gas is 9.6x10^{4} (^{o}C)^{1}
Does any gas overflow from the tank? Answer yes or no and prove your answer!