Problem Set 9

These problems on oscillations, waves, and thermo are due November 28 at 4 PM. The reading for uncoming material is in chapters 13, 14, and 15.

(1) Ch 11 P 20 A block of mass m is supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

(2) Ch 11 P 51 The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

(3) Ch 11 P 58 A particular guitar string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?

(4) Follow this link to the Phet wave demonstrator. Once you have played with it a bit to get an idea of how it works set the damping to "4" and the frequency to "56". (a) What do you see? Make a sketch. (b) What is the wave speed? (c) What is the frequency of the fundamental? Sketch what it would look like. (d) Check your result for part (c) by finding another harmonic. Hint: The demo has rulers and a timer.

(5) Ch 13 P 9 The Eiffel Tower is built of wrought iron approximately 300 m tall. Estimate how much its height changes between July (average temperature of 25°C) and January (average temperature of 2°C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.

(6) Ch 13 P 37 A hot-air balloon achieves its buoyant lift by heating the air inside the balloon, which makes it less dense than the air outside. Suppose the volume of a balloon is 1800 m^3 and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0°C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.)

(8) Ch 13 P 80 A space vehicle returning from the Moon enters Earth’s atmosphere at a speed of about 40,000 km/hr. Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)