Homework Assignment #7
Please return this paper as your homework submission. You may attach additional pages if necessary.
Reading: Skim the overview to chapter 7, then read 9.1-9.2 and 9.6. Begin reading 10.1-10.2, 10.6.
Upcoming Exam: There will be an exam on March 22, assuming the "Preliminaries Unit" wraps up on or around March 15. Details will be discussed as the exam approaches.
1. Why does a bowling ball on the edge of a cliff have more potential energy than a baseball on the same cliff?
A bowling ball has more mass, and gravitational potential energy increases with mass.
2. A 100-kg satellite (call it satellite A) orbits the Earth. Satellite B (also 100-kg) orbits Jupiter. Which has more potential energy? Why?
Satellite B has more potential energy because gravitational potential energy comes from the product of the two masses involved. Here, the satellites are the same mass but the planets have different masses. Since Jupiter is more massive, the satellite orbiting it has more potential energy.
3. In a sentence or two, what does E = mc2 mean? Make sure you define each variable.
E stands for energy, m stands for the mass of an object. What the equation means is that we can convert mass into energy (or vice-versa). This is the foundation for how the sun “works” as well as nuclear reactors and hydrogen bombs.
4. How does the formula in #3 explain the destructive nature of an atom bomb?
In the above formula, the energy a piece of mass can release is proportional to the SQUARE of the speed of light (which is already a large number!). Hence, a small bit of mass can create a huge amount of energy.
5. Imagine an elevator extending all the way into space, to the level of geosynchronous satellite orbits. If you dropped an object from the top of the elevator, would it fall or orbit the Earth? Explain. Hint: skim section 4.2.
Dropping an object would just make it fall straight down to Earth. Throwing it sideways is what puts it in orbit. If you give it enough momentum, it would go into a circular orbit. More momentum puts it into an elliptical one. Even more than that can launch it into space. Enough speed to do this is called “escape speed.”
6. We saw that the moon is the largest contributor to the tides on Earth. The sun also contributes, but not as much. Do the other planets (for instance, Jupiter) contribute to the tides at all? Why or why not?
They contribute very very little. They’re simply too far away to have much effect, since gravity dies off as the SQUARE of the distance from the source object.
7. Summarize the processes by which planetary interiors get hot and cool off. Why would large planets retain their internal heat longer than smaller ones?
Planetary interiors heat up by accretion, radioactivity, and differentiation. They cool off by convecting their heat to the surface and outgassing (and through volcanic explosions). Small planets cool more quickly because it’s easier for them to cycle their heat through the middle layers of the planet.
8. What are the (3) requirements for a global magnetic field?
Fluid metallic layer, convection in that layer, and moderately rapid rotation.
9. How does this magnetic field protect the earth? (From what?)
The magnetic field deflects cosmic rays (charged particles) from the sun around the Earth. This form of radiation can be harmful.
10. How is having too much greenhouse gas in an atmosphere bad? How is not having enough bad?
Having too much would overheat the planet because infrared light would be trapped on the planet for too long (see: Venus). Having too little would cause the planet to be unable to heat up enough because most of the infrared light the planet emits would escape right into space (see: Mars).