Classical Mechanics - Assignment 9 - Physics, Exercises of Physics

Prof Walter Lewin, Massachusetts Institute of Technology (MIT) (MA), Physics, Classical Mechanics, Assignment 9, Simple Harmonic Oscillations, Delicate Balance, Compression of a Femur, A Suction Pump, Dangerous Icebergs.

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Massachusetts Institute of Technology - Physics Department
Physics - 8.01 Assignment #9 November 17, 1999.
It is strongly recommended that you read about a subject before it is covered in lectures.
Lecture Date Material Covered Reading
#29 Fri 11/19 Exam Review Lectures 16 thru 24
Mon 11/22 Exam #3 Handout of 11/15
#30 Wed 11/24 Simple Harmonic Oscillations - Energy Considerations Page 389 395
Torsional Pendulum Page 396 397
#31 Mon 11/29 Forced Oscillations - Normal Modes - Resonance Page 399 403
Natural Frequencies - Musical Instruments Page 438 445
Take Notes!
#32 Wed 12/1 Heat - Thermal Expansion Page 515 527
Due Wednesday, Dec 1, before 4 PM in 4-339B.
9.1 Short Questions
a) John is holding a computer monitor, with a mass of 25 kg, at a constant height. He complains
that he is becoming exhausted. Nancy tells him that since there is no displacement in the
direction of the applied force, he is not doing any work, and therefore should not be tired. Who
is right and why?
b) A fly is resting on the bottom of a closed jar. The jar is placed on a very accurate balance, and
there is equilibrium. The fly starts flying. Will there be equilibrium again?
c) Same question, but now with the jar open.
d) You are in orbit around the Earth. Your orbit is very elliptical. You are running very very low
in fuel, and it is touch and go whether you will have enough fuel left to reenter and return to
Earth. When should you fire your rockets for reentry, when you are farthest away from Earth
or when you are very close? Explain your answer.
e) I am sitting in a boat in a swimming pool. There is a heavy rock in my boat. I carefully mark
the water line on the tiles of the swimming pool. I then throw the rock over board. Will the
water line go up, or down, or will it stay the same? Give your reasoning. PIVoT
f) A block of pure ice is floating in a swimming pool. I mark the water line of the swimming pool,
as above. The ice melts. What will happen with the water line? Give your reasoning.
9.2 Delicate Balance page 372, problem 16
9.3 An Overhang of Books page 372, problem 18
9.4 Compression of a Femur page 377, problem 50
9.5 A Torsional Pendulum in a Watch page 408, problem 31
9.6 High Blood Pressure? page 488, problem 17
9.7 A Suction Pump page 489, problem 18
9.8 Dangerous Icebergs page 489, problem 24
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Massachusetts Institute of Technology - Physics Department

Physics - 8.01 Assignment #9 November 17, 1999.

It is strongly recommended that you read about a subject before it is covered in lectures.

Lecture Date Material Covered Reading #29 Fri 11/19 Exam Review Lectures 16 thru 24

Mon 11/22 Exam #3 Handout of 11/

#30 Wed 11/24 Simple Harmonic Oscillations - Energy Considerations Page 389 – 395 Torsional Pendulum Page 396 – 397

#31 Mon 11/29 Forced Oscillations - Normal Modes - Resonance Page 399 – 403 Natural Frequencies - Musical Instruments Page 438 – 445 Take Notes!

#32 Wed 12/1 Heat - Thermal Expansion Page 515 – 527

Due Wednesday, Dec 1, before 4 PM in 4-339B. 9.1 Short Questions a) John is holding a computer monitor, with a mass of 25 kg, at a constant height. He complains that he is becoming exhausted. Nancy tells him that since there is no displacement in the direction of the applied force, he is not doing any work, and therefore should not be tired. Who is right and why? b) A fly is resting on the bottom of a closed jar. The jar is placed on a very accurate balance, and there is equilibrium. The fly starts flying. Will there be equilibrium again? c) Same question, but now with the jar open. d) You are in orbit around the Earth. Your orbit is very elliptical. You are running very very low in fuel, and it is touch and go whether you will have enough fuel left to reenter and return to Earth. When should you fire your rockets for reentry, when you are farthest away from Earth or when you are very close? Explain your answer. e) I am sitting in a boat in a swimming pool. There is a heavy rock in my boat. I carefully mark the water line on the tiles of the swimming pool. I then throw the rock over board. Will the water line go up, or down, or will it stay the same? Give your reasoning. PIVoT f) A block of pure ice is floating in a swimming pool. I mark the water line of the swimming pool, as above. The ice melts. What will happen with the water line? Give your reasoning.

9.2 Delicate Balance – page 372, problem 16

9.3 An Overhang of Books – page 372, problem 18

9.4 Compression of a Femur – page 377, problem 50

9.5 A Torsional Pendulum in a Watch – page 408, problem 31

9.6 High Blood Pressure? – page 488, problem 17

9.7 A Suction Pump – page 489, problem 18

9.8 Dangerous Icebergs – page 489, problem 24

9.9 A Submerged Block of Wood – page 491, problem 35

9.10 A Hole in a Water Tank – page 493, problem 50 PIVoT

9.11 A cylindrical container of length L is full to the brim with a liquid which has mass density ρ. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.

rigid rod

L

a) What is the mass of the liquid which overflowed while the ball was being pushed into the liquid? b) What is the reading of the scale when the ball is fully immersed after the water that overflowed has been removed from the scale? c) If instead of being pushed down by a rod, the ball is held in place by a thin string attached to the bottom of the container as shown on the right. What is the tension T in the string, and what is the reading on the scale after the water that overflowed has been removed from the scale?