Phys. 121: Thursday, 06 Nov. Written HW 10: Due by 5 pm. HW 11: ch. 13, probs. 25, 36, and ch. 14, probs. 15, 18, 36, and 43. Due in one week. Mast. Phys.: Assign. 9 due on Tuesday. Reading: Finish ch. 14 by Tuesday (You may skim sects. 14.7 and 14.8.) Exam 2: average was 12.8/20; there was one perfect score (20/20) - congratulations! I have added a curve of 1.5 points to the score shown on your exam, when calculating the scores shown on Moodle. Test corrections through the OSL are available on problems 3, 4, 10, and 14; return them to me with your original exam by Tues., 18 Nov.

Test 2: let's go over it...

Clickers: A baseball bat is cut in half at its center of mass. Which end is heavier? The handle end (left end). The hitting end (right end). The two ends weigh the same. Answer: B 3 3

Clickers: Which third force on the wheel, applied at point P, will make the net torque zero? Answer: A 4 4

Clickers: which torque vector goes with the figure in (a)? (F is into the screen and slightly to the right.) a) 1 b) 3 c) 4 d) 5 e) 6

Clickers: What does the scale read? 500 N. 1000 N. 2000 N. 4000 N. Answering this requires reasoning, not calculating. Answer: C Slide 12-91 6 6

Ch. 13: Newton's Law of Universal Gravitation: Any two objects with mass produce a gravitational force between them! The direction of the force is attractive (straight toward each other), and the magnitude is where r is the distance between the (centers of mass of the) two objects, and G is a constant. (G = 6.67 x 10^(-11) N m²/kg².)‏

Clickers: Three stars are aligned in a row. The net force on the star of mass 2M is To the left. To the right. Zero. Not enough information to answer. Slide 13-33 8 8

Notice that the usual relation holds: F_r = - dU/dr (force = negative slope)‏

Decrease of g with Distance A satellite orbits the earth at height h above the earth’s surface. The value of g at height h above sea level is: where gearth = 9.83 m/s2 and Re = 6.37  106 m.

Decrease of g with Distance

The parabolic orbit (total E = 0) has exactly (the local) escape speed at all times: (This follows from its total energy being exactly zero, with the convention that U(r) goes to zero as r goes to infinity.)

Fun Fact: putting v_esc. = c, the speed of light, gives a size that Michell and Laplace called a “dark star”... R_dark = 2 G M/c² --- this turns out to be the size of a black hole!

The Principle of Equivalence The inertial mass of an object relates the net force acting on it to its acceleration: The gravitational mass of an object appears in Newton’s law of gravity and determines the strength of the gravitational attraction: The assertion that mgrav = minert is called the principle of equivalence.

Clickers: For the non-circular orbits, which of the following is true? a) The orbiting object moves slower as it gets closer to the Sun. b) The orbiting object moves faster as it gets c) The orbiting object will have a constant speed. d) The orbiting object will constantly gain speed. e) The orbiting object will fly away if you cut the invisible cord which holds it to the Sun.