Lesson 18

**Law of Universal Gravitation, Potential**

Name:faculty |
Section:M2 |
Start Time:12:15:32 |
Instructor:pate |
Course:355 |

**1)** We can think of the gravitational field vector **g** as being the gradient of a scalar function F called the *gravitational potential*. The gravitational force is given by **F** = m**g**. We can also think about the gravitational potential energy of a body in the gravitational field, and can express that potential energy in terms of the gravitational potential F. We can even think about equipotential surfaces, which are surfaces of constant gravitational potential.

You've seen all of this before, but in the context of electric fields and electric potentials rather than gravity. What are all of the analogous quantities and equations from the electricity context? Is there anything whose analog you don't know or understand?

**2)** Suppose you are stranded on the surface of a small asteroid. (The image to the right is an image of the asteroid Vesta3, taken by the Hubble Space Telescope!) Estimate how fast you'd have to jump off its surface in order to be able to escape from its gravitational field. (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Please be sure to explain your assumptions, as usual.

**3)** The Acme engineering company has been hired by a wealthy person to investigate the feasibility of a train that travels in a tunnel through the center of the Earth. The Acme engineers have programmed a simulation of this into a Physlet page so that you can better take a look. The physlet shows the train (modeled by Acme as a spherical black ball) moving through the tunnel, and four possible graphs (one for each simulation) to represent the train's acceleration versus time.

Which of the four physlet animations correctly shows the train's acceleration versus time?

**Note: To obtain your answer, you'll need to give another Physlet page a try. Important: This page will open in a NEW window, so you'll need to come back to THIS window (using the taskbar) to submit your preflight. Once again, if the physlet page does NOT load properly, please tell me what happens, including any error messages it displays, in the comments box below. Thanks. Click this link to get to the physlet page.**

Animation 1 Animation 2 Animation 3 Animation 4

Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

**You may change your mind as often as you wish. When you are satisfied with your responses
click the SUBMIT button.**