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Physics 131 Homework Set, Lafayette College - April 2009, Assignments of Mechanics

A homework assignment from the physics 131 course at lafayette college, issued on april 15, 2009. It includes four problems covering various topics such as stellar collapse, rotation periods, vector calculus, and colliding objects. Students are expected to solve the problems individually and submit their answers by the due date.

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Pre 2010

Uploaded on 08/19/2009

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Lafayette College
Department of Physics
April 15, 2009
Physics 131 LevelIIHomework Set Section 1
Youmay discuss these problems with one or twoother students (or with your instructor), but
your final solutions should be written out by you alone. Under no circumstances should you see
another student’swritten solutions. If you have discussed these problems with anyone you must
acknowledge the collaboration at the beginning of the corresponding problem. Homework is due
in my office by 3:30 PM on the due date and solutions will then be made available on the course
web site. No homework will be accepted after this time.
Youare expected to carefully explain how, starting from basic principles, you have arrivedat
your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound
notebook. If the papers are illegible or disorganized, we reservethe right to return these papers
without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig.
figs.
Assignment 11: Due Monday,April 20, 2009
Problem 1: Consider a star that has a mass of 27 solar masses and a radius that is twice the
solar radius. Assume that the star has a rotation period of 30 days. Suppose that this star under-
goes a supernova event causing it to collapse to a neutron star with a radius of 25 kmand retain-
ing all of its mass (It actually retains only about 10%ofits mass, but this makes the calculation
much more difficult. Assume (not realistic) that the mass is uniformly spread throughout the
body,both before and after.What is the newrotation period. Actually rotation periods for a neu-
tron star can be as small as a fewmilliseconds (but can be much larger). Howrealistic is your
value?
Problem 2: What must be the rotation speed of the Earth in order that it would begin to fly
apart? Assume that the only force holding it together is the gravitational force.
Problem 3: Consider the vector AA =4ˆ
i+9ˆ
j+5ˆ
kand the vector BB =3ˆ
i+4ˆ
j7ˆ
k.Ifthe vector
CC =AA ×BB ,find CC .
Problem 4: Two skaters each with mass mand speed vare headed towards each other along
parallel paths separated by some distance D.Astheypass each other,theystretch out their arms
and grab each others hands and hold tight. The result is that theyspin in a circle of diameter D.
Find the final angular speed of the twoskaters. What fraction of the initial kinetic energy is lost
in this ignore the mass of their arms.

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Lafayette College

Department of Physics

April 15, 2009

Physics 131 Level II Homework Set Section 1

You may discuss these problems with one or two other students (or with your instructor), but your final solutions should be written out by you alone. Under no circumstances should you see another student’s written solutions. If you have discussed these problems with anyone you must acknowledge the collaboration at the beginning of the corresponding problem. Homework is due in my office by 3:30 PM on the due date and solutions will then be made available on the course web site. No homework will be accepted after this time.

You are expected to carefully explain how, starting from basic principles, you have arrived at your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound notebook. If the papers are illegible or disorganized, we reserve the right to return these papers without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig. figs.

Assignment 11: Due Monday, April 20, 2009

Problem 1: Consider a star that has a mass of 27 solar masses and a radius that is twice the solar radius. Assume that the star has a rotation period of 30 days. Suppose that this star under- goes a supernova event causing it to collapse to a neutron star with a radius of 25 km and retain- ing all of its mass (It actually retains only about 10% of its mass, but this makes the calculation much more difficult. Assume (not realistic) that the mass is uniformly spread throughout the body, both before and after. What is the new rotation period. Actually rotation periods for a neu- tron star can be as small as a few milliseconds (but can be much larger). How realistic is your value?

Problem 2: What must be the rotation speed of the Earth in order that it would begin to fly apart? Assume that the only force holding it together is the gravitational force.

Problem 3: Consider the vector AA = 4ˆ i + 9 ˆ j + 5 ˆ k and the vector BB = 3ˆ i + 4 ˆ j − 7 ˆ k. If the vector CC = AA × BB , find CC.

Problem 4: Two skaters each with mass m and speed v are headed towards each other along parallel paths separated by some distance D. As they pass each other, they stretch out their arms and grab each others hands and hold tight. The result is that they spin in a circle of diameter D. Find the final angular speed of the two skaters. What fraction of the initial kinetic energy is lost in this ignore the mass of their arms.