PHYSICS 1403-003 (MWF), QUIZ 3, Chapter 5, March 4, 2005
Partial credit will be LIBERAL, provided that you show your work! USE BACK IF NECESSARY!
Name: ______
1. (10 points) CONCEPTUAL QUESTION. See figure. A ball, mass m, is twirled at the
end of a string in a vertical circle of radius r at constant speed v. Free body diagrams for
the ball at the top & at the bottom of the circle are shown. Is the string tension FTA that
the string exerts on the ball at the top (point A) less than, more than, or the same as the
tension FTB at the bottom (point B)? Why? Explain (using WORDS, as well as
equations!) your answer using Newton’s 2nd Law with centripetal acceleration!
2. (20 points). See figure. A planet, mass m = 4.0 ´ 1024 kg, is in a circular orbit at a constant speed v around a star, which is assumed to be a uniform sphere of constant density. The radius of the orbit (measured from the star’s center) is r = 1.8 ´ 1011 m. The mass of the star is M = 2.5 ´ 1030 kg. The gravitational constant is G = 6.67 ´ 10-11 N m2/kg2.
a. Compute the gravitational force between the planet & the star. What is the “centripetal force” on the planet? (Hint: You don’t need to know the planet’s speed to answer this!)
b. Compute the centripetal acceleration experienced by the planet. What is the direction of this acceleration? (You don’t need to know the planet’s speed to answer this!)
c. Compute the speed of the planet. Note: Einstein told us that the largest speed possible for any object is the speed of light c = 3 × 108 m/s. If you get a v larger than this, something is wrong!
d. Compute the period of the planet’s orbit. Note: This should be something reasonable for a planet’s period. If you find only a few seconds (or less!) or billions of years, something is wrong!