Practice Problems for final:

1) I recommend you go over the previous exams - be sure you understand how to do all the problems you got wrong. There will be a couple of old problems reappearing (and they won't be the easiest ones...)

2) If you didn't look at the two "optional" problems on CAPA set #12 (the one on fluids), it would be prudent to do so while studying for the final.

3) You have a gold crown (density 19E3 kg/m^3) that weighs 100N. What is its apparent weight when immersed in water?

More generally, can you derive a formula that tells the density of an unknown material, simply by weighing it before and after immersion in water (like my demo in class with the crown?)

4) How high would the level be in a barometer made of a fluid with density 2.5E3 kg/m^3, if the pressure outside were 0.9 atm?

5) A pendulum with length L, mass M, and total energy E, swings from a maximum angle theta. It has a maximum speed at the bottom of the swing of V. If you increase the total energy by a factor of four, what happens to V? To the period? The frequency?

6) A rope of length 2m has a standing wave on it with one node. The frequency of vibration is 100 Hz. What is the speed of the wave? If the tension in the rope is 1000N, what is the mass of the rope? What other frequencies make standing waves on this rope?

7) A stereo speaker 10 meters away makes a sound level at your ear of 55 dB. What is the intensity of the sound at your ear in W/m^2? How much total power is the speaker putting out, assuming no losses? (Hint: the sound energy spreads out in spherical waves, the area of a sphere is 4 Pi R^2) If you walk out another 10 meters farther, how loud does it sound?

8) A 30 g glass thermometer (heat capacity of glass is 840 J/(kg C)) reads 21 C before being placed in 1000 cm^3 of water. When the water and thermometer reach equilibrium, the temperature is now 24 C. How hot was the water, originally? If you start heating this 1000 cm^3 of water, how much energy would it take to boil it all away? (Latent heat of water to steam is 22.E5 J/kg)