Klepner_soluciones

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

Assignment 1. 2-Sept-2005 Please note that this problem set assumes that you remember some stu 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 are to be expressed in terms of their x and y components. Sketch the position as a function of time.

Assignment 2. 9-Sept-2005

1. Kleppner and Kolenkow, chapt.2, problem 2.11. In what way would the physics be dierent 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.

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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 .

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


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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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

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 of energy 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 machine, a1 , a2 and a3 . If mass 3 starts at t = 0 at a height h above the bottom of its well, nd the time when it hits the bottom. Instructions: do this problem as an exercise in correct procedure - dene the coordinate system, write every vector in terms of its components and solve for 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 the situation. You should calculate the angular momentum L about a suitable origin. Then dL/dt tells you what the torque must be, and you can determine the normal force from the torque. The choice of origin is critical because you dont want the unknown and irrelevant forces at the vertical axle to contribute 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 governs the situation. The rst step is to understand why the car tends to tip. To do this, calculate the angular momentum L(car) about a suitably chosen origin and see that dL(car)/dt requires that the normal forces on the wheels on the right and left side of the car be dierent. Obviously, the origin needs so be chosen in such a way that other unknown forces dont enter the equations. Once you undestand what is happening, it is easy to add a ywheel in such a way that d(L(f lywheel) + L(car))/dt doesnt require a torque from the normal forces. The orientation of the ywheel is a little surprising if you are thinking symmetry (I guessed wrong when asked on Friday) and you need to make sure that it works for both left turns and right turns.

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 which the car is at rest.


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


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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