Due Wednesday April 23, 9:00am.
Write and sign the pledge! This means that you are pledging not to discuss the content of this homework with each other, or with anyone else. You are allowed to use books or internet resources, but must acknowledge in writing any which have been of significant help (not counting my notes or the textbook). You can e-mail questions to me—I might or might not answer. If I do, your question plus my answer will go to the whole class.
Note: clarity and legibility of presentation count
towards the grade on this pledged set.
1. Estimate how important changes in barometric pressure
would be compared to changes in temperature in observing the height of water in
Galileo’s thermometer (with a bulb containing air connected to a pipe going
down, with its end immersed in water, and a few centimeters of water in the
pipe). Points to consider: what would
you expect the daily temperature range in an unheated house to be? How much would that change the volume of the
gas? What is the normal variation in
atmospheric pressure over a few days?
How would that affect the volume of the gas?
2. In Count Rumford’s account of his cannon-boring
experiment, he stated:
“total quantity of ice-cold water which with the heat actually generated by friction, and accumulated in 2 hours 30 minutes, might have been heated 180°F, or made to boil, = 26.58lb.”
(The water was absorbing the heat generated by boring the cannon barrel, and was in a wooden sided container for insulation.)
He goes on: “the machinery used in the experiment could easily be carried round by the force of one horse (though, to render the work lighter, two horses were actually employed in doing it).”
Joule actually quotes the data above, then goes on to observe that Watt claimed the power of a horse was 33,000 foot pounds per minute, so assume this is the total rate of working of the two horses.
(a) Following Joule, use these data to calculate the number of Joules in one calorie.
(b) Assuming heat loss at the same rate as before, how much longer would the horses have to work to boil the water dry?
3. A uniform wire one meter long is held at tension 500N. It has a mass of 0.05kg. It is vibrating in its fundamental mode with an amplitude of 0.5cm.
(a) What is its maximum kinetic energy? What is its instantaneous shape at the moment of maximum kinetic energy?
(b) What is its maximum potential energy? What is its instantaneous shape at the moment of maximum potential energy?
(c) How are your answers to (a), (b) changed if the wire is vibrating in its first harmonic with the same amplitude?
Do also Halliday: page 452: 50, 52, 58.