Physics 152 Homework #2

1. An evil genius puts a spherical rock (made of ordinary stone) in the earth’s orbit, but moving around the sun the other way. It collides with the earth, landing in the desert. It is estimated that the crater is about the same as would have been caused by a one-megaton hydrogen bomb. How big was the rock?

2. Open the GeneralPlanet Spreadsheet. By scrolling down the columns of numbers, you can see how the components of position and velocity vary with time. For example, going down the x column until x changes sign tells you when the planet is crossing the y axis, that is, for our given initial values, when it is closest to the Sun. Take the mass of the “planet” to be one, but don’t worry about units: this is a model.

(a) Show that, with reasonable accuracy, both total energy and angular momentum are the same at the closest approach to the “Sun” as they were at the beginning.

(b) Measure the semimajor axis of the elliptical path. Now change the initial variables until you have a circular orbit with the radius equal to the original ellipse semimajor axis.

Is the total energy in this new orbit is the same as the original orbit?

(c) Is the angular momentum in this new orbit is the same as the original orbit?

(d) Is the time for one complete revolution (planet year) in this new orbit is the same as the original orbit?

3. 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?

  4. 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?

5. Atmospheric pressure varies from day to day, but 1 atm is defined as 1.01 x 10⁵ N/m². Calculate how far upwards such a pressure would force a column of water in a “water barometer”. (That is, a long inverted glass tube, the top end sealed and having vacuum inside above the water surface, the bottom end immersed under water in a bowl of water, the other water surface in the bowl being open to the atmosphere.)

6. You have a solid metal cylinder, of height h, cross section area A, and density r, standing on its end on a table. What is the pressure on the table underneath the cylinder? Suppose you now heat the cylinder, and it expands by the same percentage in all directions (so the shape and proportions are unchanged), the height increasing to h + Dh. What is the pressure on the table now?

7. A ball is floating in water in a tub. The ball is half submerged. Now oil is poured carefully into the tub, so it forms a layer on top of the water, and the ball lies completely below the top of the oil layer. Is the center of the ball now above or below the water-oil boundary?