1. Relate gravitational force to masses of objects and distance between objects.

(a) What is the approximate force of gravity on a 70kg person due to the Andromeda galaxy, assuming its total mass is 1013 than of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.

The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G.I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius rof the fireball should depend only on time since the explosion, t, the density of the air, , and the energy of the initial explosion, E. Thus, he made the educated guess that r=kEabtcfor some dimensionless constant kand some unknown exponents a,b, and c. Given that [E]=ML2T-2 , determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that k=rEabtcand that [k]=1 ). (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant khad the value 1.03. From the film reel, he was able to determine many values of rand the corresponding values of t. For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25kg/m3 , to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert yow answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-duty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)

Math Review Simplify the following expression in terms of the dimensions mass, length, and time given by [M], [L],and [T]. (See Section 1.3.) [M][L]2[T]3[T][L][T]=?

(Indicates a review question, which means it requires only a basic understanding of the material to answer. Questions without this designation typically require integrating or extending the concepts presented thus far.) . A basketball player shoots a Free throw. Make a sketch showing the basketball's velocity just after the ball leaves the player's hands. Draw in two components of this velocity, one horizontal and one vertical. Repeat the sketch for the instant just before the ball reaches the basket. What is different?

(Indicates a review question, which means it requires only a basic understanding of the material to answer. Questions without this designation typically require integrating or extending the concepts presented thus far.) . The following are speeds and headings displayed on a GPS receiver, (Heading gives the direction of motion based on north = 0°, east = 90°, south = 180°, etc,) In each case, indicate whether the receiver was accelerating during the time between the displays and, if it was, describe in what way the receiver was accelerating. (a) Initially: 60 mpht 70°; 5 seconds later: .50 mph, 70°. (b) Initially: .50 mph, 70°; 5 seconds later: 70 mph, 70°. (c) Initially: 60 mph, 70°; 5 seconds later: 60 mph, 90°.

I0 orbits Jupiter with an average radius of 421,700 km and a period of 1.769 days. Based upon these data, what is tha mass of Jupiter?

Check Your Understanding Light navels about 9 Pm in a year. Given that a year is about 3107s , what is the speed of light in meters per second?

Which of the following is a vector: a person's height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth's population, the acceleration of gravity?

Supermassive black holes are thought to exist at the center of many galaxies. (a) What is the radius of such an object if it has a mass of 109 Suns? (b) What is this radius in light years?