gravitation sections 9.1 – 9.3. reminders reading quiz for chapter 11 (sections 1-2) due by start...
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Gravitation
Sections 9.1 – 9.3
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Reminders
• Reading quiz for Chapter 11 (Sections 1-2) due by start of class on Tuesday.
• Lab this week: Lab A7-CE – Conservation of Energy – due by Friday at 4 p.m.
• In-class Quiz #4 on Thursday, October 23 – addresses chapters 8 and 9.
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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
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Working…
Earth acts as though all its matter is concentrated in a point at its center.
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Working…
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Newton Finds Kepler’s Third Law
• P2 = r3 (P in years; r in astronomical units)• P2 = kr3 (arbitrary units)• Newton derives this relationship
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A Note about Dark Matter
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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 of weight versus mass.
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Time for an Experiment!
• Let’s graph gravitational force (weight) versus mass to find the relationship.
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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.
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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
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Gravitational PE on Universal Scale
• PE = mgh = -GMm/r• At cosmic distances,– Etotal = KE + PE (where PE = 0 at ∞)
– Etotal = ½mv2 – GMm/r
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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!
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Sample 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
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Sample 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.