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Gravitation

Gravitation. Sections 9.1 – 9.3. Reminders. Reading quiz for Chapter 11 (Sections 1-2) due by start of class on Thursday. Lab this week: Lab A7-CE – Conservation of Energy – due by Friday at 4 p.m. In-class Quiz #5 on Thursday, March 27 – addressing chapters 8, 9, and 11. Newton’s Apple.

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Gravitation

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  1. Gravitation Sections 9.1 – 9.3

  2. Reminders • Reading quiz for Chapter 11 (Sections 1-2) due by start of class on Thursday. • Lab this week: Lab A7-CE – Conservation of Energy – due by Friday at 4 p.m. • In-class Quiz #5 on Thursday, March 27 – addressing chapters 8, 9, and 11.

  3. Newton’s Apple • Perhaps in contemplating the fall of an apple, Newton realized that its acceleration was (in modern metric terms). • He realized that the moon’s acceleration toward Earth was

  4. Working… Earth acts as though all its matter is concentrated in a point at its center.

  5. Working…

  6. Newton Finds Kepler’s Third Law • P2= r3(P in years; r in astronomical units) • P2 = kr3 (arbitrary units) • Newton derives this relationship

  7. A Note about Dark Matter

  8. Relationship Weight versus Mass • Weight is a force defined by (kg.m/s2). • Recall that 1kg.m/s2 is a Newton, N • What weighs 1 N? • A medium apple • A cooked quarter-pounder burger (meat only) • Mass is the amount of matter in a body. • To find relationship between weight and mass make a graph.

  9. Time for an Experiment! • Let’s graph gravitational force (weight) versus mass to find the relationship.

  10. Gravitational Field Strength • Wt = km where k = g; ergo, Wt = mg • g = gravitational field strength in units of N/kg • g = -9.81N/kg • When simplified, • Hence, g = -9.81m/s2 • Gravitational field strength has the units of acceleration and is directed downward.

  11. Warning! • Do not confuse g with G. • g = -9.81N/kg = -9.81m/s2 • G = 6.67x10-11Nm2/kg2 • Wt = mg = -GMm/r2 • g = -GM/r2 = -(6.67x10-11Nm2/kg2)* (5.97x1024kg)/(6,371,000m)2 = -9.81m/s2

  12. Gravitational PE on Universal Scale • PE = mgh = -GMm/r • At cosmic distances, • Etotal = KE + PE (where PE = 0 at ∞) • Etotal = ½mv2 – GMm/r

  13. Black Holes • Recall, Etotal = KE + PE = ½mv2 – GMm/r • If Etotal = 0, then vescape = √(2GM/r) • If Etotal > 0, then v > vescape • If Etotal < 0, then v < vescape • In a black hole, M is “normal” but r can be vanishingly small. Hence, when something gets close enough to a black hole it can not escape – even light!

  14. Extra Credit Problems • Four extra credit problems follow. You should search your textbook, the internet, or other resources to find necessary values. • Each problem is worth ½ point. • Problems must show all work, beginning with mathematical equations. • This optional assignment is due at the start of class on Thursday. • Clearly label each problem with its number and be certain to place a box around each answer.

  15. Problems #1 and #2 • #1 Calculate the weight of a 0.454kg loaf of bread on the surface of Earth. Give the magnitude and direction of that force. • #2 Show that the local value of “g” (the gravitational field strength) on the surface of the moon is approximately 1/6 that on the surface of Earth. Note that gEarth= -9.81N/kg

  16. Problems #3 and #4 • #3 How much gravitational force exists between two 1kg lead spheres whose centers are 1m apart from one another? • #4 Show mathematically that the acceleration due to gravity in a 300km high orbit is 91.2% that on the surface of Earth. Assume a radius of 6,371km for Earth.

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