Physics 581 Homework #6
Due Thursday 4:30 p.m.
1. I make salad dressing in a conical bottle, wide at the base, steadily narrowing up to the neck. I pour in 100 cc of vinegar, then add 100 cc of olive oil. The oil is a layer on top of the vinegar. Then I shake it vigorously, so the two liquids are completely mixed together.
How (if at all) does the pressure on the bottom after shaking differ from the pressure on the bottom before shaking?
2. If an ice cube is floating in a glass filled to the brim with water, what happens to the water level as the ice cube melts? Would your answer be the same if the ice cube were stuck to the glass and was fully submerged? What about an ice cube in a glass of pure alcohol?
3. Weather balloons lift about a kilogram (I think) about 20 miles. Assume the density of the atmosphere varies as exp(-h/h0), where h0 = 8.5km. How big are these balloons?
4. If youíre swiveling around in a chair with weights in your outstretched hands, then you pull them in, there is a definite angular acceleration. But thereís no external torque acting. How can there be an acceleration without a torque acting. Isnít that the same as a mass accelerating in a straight line without an external push? Explain the difference, if any.
5. If you form a cylindrical soap film between two rings, and there are also spherical soap film caps on the rings, how are the radii of the spherical caps related to the radius of the cylinder?
If you now pop one of the spherical caps, and the other films survive, what shape do they take? Explain why.
6. Suppose we repeated the experiment of the two unequal bubbles at opposite ends of a tube with balloons instead of bubbles. Would you expect the same result? Explain.