From Autumn 99 
Real Final 
1. A merrygoround rotates at the rate =1.2 rad/s with a man of mass m = 80 kg standing at a point r_{i }= 2.0 m from the centeraxis of rotation.
See Figure 1.
Solutions: (a) I_{i}w_{i} = I_{f}w_{f} (m(R/2)^{2} + ½MR^{2} )w_{i}= (mR^{2}
+ ½MR^{2})w_{f
}Find w_{f}. 
2. (20 points)
A block of wood floats partially submerged in a lake. The crosssectional area of the block is A, the total height of the block is 2.0 m and the density of the wood is 650 kg/m^{3}. Assume the lake water has density 1000 kg/m^{3 }. See the diagram below. What is the height H of the top face of the block above the water surface?
Mg = F_{B} 650*A*2.00*g = 1000*A*(2  H)g. Solve for H. 
3. (20 points)
A brass ring is to be fitted over a cylindrical brass shaft whose diameter is D2 =3.212 cm at 25^{0}C. The inner diameter of the ring is D1 = 3.196 cm at 25^{0}C. See the diagram below.

To what temperature must the shaft be cooled before it will slip into the ring? The linear coefficient expansion of brass is
Solutions: 
4. (20 points)
An ice cube at initial temperature 10.0 ^{0}C and mass m is placed in water with mass M = 650 g and initial temperature 25.0 ^{0}C. The final equilibrium temperature of the mixture is 3.0 ^{0}C.
What is the mass m of the ice cube? Show all work!
Solutions: 
5. (24 points)
A 6.0kg block of aluminum is cooled from 95^{0}C to 25^{0}C at atmospheric pressure. The density of the aluminum is 2700 kg/m^{3}. The linear expansion coefficient of aluminum is 24.0x10^{6} (^{o}C)^{1 }.^{ }The specific heat of aluminum is C = 900 J/kg ^{0}C.
See hint to #20, Quiz 11. . 
6. (20 points)
The motion of an object is described by the equation
See hint to #23, Quiz 12. . 
7. ( 20 points) An outside stereo speaker at a ski resort emits sound waves with a power output of 90.00 W and frequency 1100.00 Hz.