klepner_soluciones

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INDEX: assign 2---2.11,14,17,22,29,31,34 assign 3---3.2,7 assign 4---3.6,10,14,15,19 assign 4--- 4.4 assign 5--- 4.3,11,13,21,23 assign 6--- 4.27 assign 12---5.2 assign 6---6.9 assign 7---6.11,18,20,21 assign 8---6.24,26,32,36 assign 8---7.1 assign 9---7.2,4,5 assign 10---7.5 assign 10---8.2,5,9,10 assign 11---9.6,8,10 assign 12---10.3,5

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Page 1: Klepner_soluciones

INDEX:assign 2---2.11,14,17,22,29,31,34 assign 3---3.2,7assign 4---3.6,10,14,15,19 assign 4--- 4.4assign 5--- 4.3,11,13,21,23assign 6--- 4.27 assign 12---5.2 assign 6---6.9assign 7---6.11,18,20,21assign 8---6.24,26,32,36 assign 8---7.1assign 9---7.2,4,5assign 10---7.5 assign 10---8.2,5,9,10 assign 11---9.6,8,10 assign 12---10.3,5

Page 2: Klepner_soluciones

Assignment 1. 2-Sept-2005

Please note that this problem set assumes that you remember somestuff from your cegep/U0 courses in mechanics and vector algebra

1. Kleppner and Kolenkow, chapt.1, problem 1.5.

2. Kleppner and Kolenkow, chapt.1, problem 1.11.

3. Kleppner and Kolenkow, chapt.1, problem 1.12.

4. Kleppner and Kolenkow, chapt.1, problem 1.16.

5. Kleppner and Kolenkow, chapt.1, problem 1.19. The answers areto be expressed in terms of their x and y components. Sketch theposition as a function of time.

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Assignment 2. 9-Sept-2005

1. Kleppner and Kolenkow, chapt.2, problem 2.11. In what way would thephysics be different if the bottom string is replaced by a rod?

2. Kleppner and Kolenkow, chapt.2, problem 2.14.

3. Kleppner and Kolenkow, chapt.2, problem 2.17.

4. Kleppner and Kolenkow, chapt.2, problem 2.22.

5. Kleppner and Kolenkow, chapt.2, problem 2.29.

6. Kleppner and Kolenkow, chapt.2, problem 2.31.

Page 7: Klepner_soluciones

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Assignment 3. 16-Sept-2005

1. Kleppner and Kolenkow, chapt.2, problem 2.34.

2. Kleppner and Kolenkow, chapt.3, problem 3.2

3. Find the position of the center of mass of a right circular cone of height H

and base radius R and uniform mass density λ.

4. Consider the cone of the previous problem with a hole or radius R0 = 0.5R

drilled vertically along its axis. Find the position of the center of mass of

this object.

5. Kleppner and Kolenkow, chapt.3, problem 3.7

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Assignment 4. 23-Sept-2005

1. Kleppner and Kolenkow, chapt.3, problem 3.6

2. Kleppner and Kolenkow, chapt.3, problem 3.10

3. Kleppner and Kolenkow, chapt.3, problem 3.14

4. Kleppner and Kolenkow, chapt.3, problem 3.15

5. Kleppner and Kolenkow, chapt.3, problem 3.19

6. Kleppner and Kolenkow, chapt.4, problem 4.4.

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Assignment 5. 30-Sept-2005

1. Kleppner and Kolenkow, chapt.4, problem 4.3

2. Kleppner and Kolenkow, chapt.4, problem 4.6

3. Kleppner and Kolenkow, chapt.4, problem 4.11

4. Kleppner and Kolenkow, chapt.4, problem 4.13

5. Kleppner and Kolenkow, chapt.4, problem 4.21 (part a only).

6. Kleppner and Kolenkow, chapt.4, problem 4.23

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Assignment 6. 7-Oct-2005

1. Kleppner and Kolenkow, chapt.4, problem 4.27

2. Solve problem 2.34 in Kleppner and Kolenkow, chapt.2, using the ideas ofenergy and angular momentum.

3. Kleppner and Kolenkow, chapt.6, problem 6.9

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Assignment 8. 21-Oct-2005

1. Kleppner and Kolenkow, chapt.6, problem 6.24

2. Kleppner and Kolenkow, chapt.6, problem 6.26

3. Kleppner and Kolenkow, chapt.6, problem 6.32

4. Kleppner and Kolenkow, chapt.6, problem 6.36

5. Kleppner and Kolenkow, chapt.7, problem 7.1

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Assignment 9. 28-Oct-2005(Hints added, 2005-Nov-05)

1. Kleppner and Kolenkow, chapt.2, problem 2.20.

• Solve for the accelerations of all the elements of this pedagogical ma-chine, ~a1, ~a2 and ~a3.

• If mass 3 starts at t = 0 at a height h above the bottom of its well, findthe time when it hits the bottom.

Instructions: do this problem as an exercise in correct procedure - define thecoordinate system, write every vector in terms of its components and solvefor these components.

2. Kleppner and Kolenkow, chapt.7, problem 7.2

3. Kleppner and Kolenkow, chapt.7, problem 7.4

Hint: this is not hard to solve once you see the physics that governs thesituation. You should calculate the angular momentum ~L about a suitableorigin. Then d~L/dt tells you what the torque must be, and you can determinethe normal force from the torque. The choice of origin is critical becauseyou don’t want the unknown and irrelevant forces at the vertical axle tocontribute to the torque.

4. Kleppner and Kolenkow, chapt.7, problem 7.5

Hint: this problem is not hard to solve once you see the physics that governsthe situation. The first step is to understand why the car tends to tip. To dothis, calculate the angular momentum ~L(car) about a suitably chosen originand see that d~L(car)/dt requires that the normal forces on the wheels on theright and left side of the car be different. Obviously, the origin needs so bechosen in such a way that other unknown forces don’t enter the equations.Once you undestand what is happening, it is easy to add a flywheel in sucha way that d(~L(flywheel) + ~L(car))/dt doesn’t require a torque from thenormal forces. The orientation of the flywheel is a little surprising if you arethinking symmetry (I guessed wrong when asked on Friday) and you needto make sure that it works for both left turns and right turns.

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Assignment 10. 11-Nov-2005(Reminder: this assignement will not be collected or graded.)

1. Kleppner and Kolenkow, chapt.8, problem 8.2

2. Kleppner and Kolenkow, chapt.8, problem 8.5

3. Kleppner and Kolenkow, chapt.8, problem 8.9

4. Kleppner and Kolenkow, chapt.8, problem 8.10

5. Kleppner and Kolenkow, chapt.7, problem 7.5.

Instructions: do the calculation in the rotating coordinate system in whichthe car is at rest.

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Assignment 11. 18-Nov-2005(Reminder: this assignement will not be collected or graded.)

1. Kleppner and Kolenkow, chapt.9, problem 9.6 (part 1 only).

2. Kleppner and Kolenkow, chapt.9, problem 9.8

3. Kleppner and Kolenkow, chapt.8, problem 9.10

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Assignment 12. 25-Nov-2005(Reminder: this assignement will not be collected or graded.)

1. Kleppner and Kolenkow, chapt.10, problem 10.3.

2. Kleppner and Kolenkow, chapt.10, problem 10.5

3. Kleppner and Kolenkow, chapt.5, problem 5.2

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