From Autumn 99

 Real Final

1.  A merry-go-round rotates at the rate =1.2 rad/s with a man of mass m = 80 kg standing at a point ri = 2.0 m from the center-axis of rotation.
See Figure 1.

  1. (5 points) What is the new angular speed when the man walks to a point at the edge of the merry-go round? See Figure 2. Assume the merry-go-round is a solid cylinder of radius R = 4.0 m and mass M = 25 kg.
  2. (1 points) What is the kinetic energy of the system before the man's motion to the edge?
  3. (1 points) What is the kinetic energy of the system after the man's motion to the edge?
  4. (2 points) What is the change in kinetic energy of the system?
Solutions:
(a) Iiwi = Ifwf

(m(R/2)2 + ½MR2 )wi= (mR2 + ½MR2)wf 
Find   wf.
 (b)  ½Iiwi2
 (c) ½Ifwf2 
(d)  ½Ifwf  2   - ½ Iiwi2

2. (20 points)

A block of wood floats partially submerged in a lake. The cross-sectional 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/m3. Assume the lake water has density 1000 kg/m3 . See the diagram below. What is the height H of the top face of the block above the water surface?

 

 

Mg = FB

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 250C. The inner diameter of the ring is D1 = 3.196 cm at 250C. 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:

We assume that only the shaft is being cooled, to the correct diameter.
3.196 = 3.212[(1 + 19x10-6*(Tf - Ti)] 
Solve for Tf .  Note Ti = 250C

 4. (20 points)

An ice cube at initial temperature -10.0 0C and mass m is placed in water with mass M = 650 g and initial temperature 25.0 0C. The final equilibrium temperature of the mixture is 3.0 0C.

What is the mass m of the ice cube? Show all work!

Solutions:
mCi[0-(-10)] + LF*m + mCW(3 - 0)= MCW(25 - 3).  Solve for m.
Ci = specific heat of ice. Cw = specific heat of water.

 

5. (24 points)

A 6.0-kg block of aluminum is cooled from 950C to 250C at atmospheric pressure. The density of the aluminum is 2700 kg/m3. The linear expansion coefficient of aluminum is 24.0x10-6 (oC)-1 . The specific heat of aluminum is C = 900 J/kg 0C.

  1. (10 points) Find the work done by the aluminum. Is it positive or negative?
  2. (7 points) Find the heat transferred in this process. Is the heat transferred to the aluminum positive or negative?
  3. (7 points) Find the change in internal energy. Is this change positive or negative?

See hint to #20, Quiz 11.  .

 

 6. (20 points)

The motion of an object is described by the equation

  1. (3 points) What is the first time t when the value of x is 0.40 m? (Hint: What is the value of t when 
    )
  2. (8 points)What is the first time t when the value of x is 0.24 m?
  3. (3 points)What is the amplitude of the motion?
  4. (3 points)What is the period of the motion?
  5. (3 points)What is the frequency of the motion?

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.

 

  1. (10 points) At what distance from the speaker would you experience the sound at exactly 110 dB?
  2. (10 points) Suppose a skier is traveling toward the speaker at speed 20.00 m/s. What is the frequency heard by the skier?