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ISU PHY 102 - Gravitation
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PHY 102 1st EditionOutline of Last LectureI. Worka. Definitionsb. Equationsc. Young’s ExperimentII. MotionIII. Mechanical Energya. Kinetic energyb. Elastic equationsIV. PowerV. Conservation of EnergyVI. Frictional ForceOutline of Current Lecture I. Bullet Problema. Kinematicsb. Conservation of EnergyII. Bullet in block of wooda. Conservation of EnergyIII. Newton’s Applea. Derivations of formulasThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.b. Acceleration toward earthIV. Newton Derives Kepler’s Third LawV. Dark MatterVI. Relationship of Weight v. MassCurrent LectureI. A bullet is shot upward from an initial speed of 55 m/s. How high does it go?1. Use kinematics to solve the problem.∆x = ?vI = 55 m/sa=g=−9.81 m/s2vf=0Vf = vi2 + 2a∆ x2. Use conservation of energy to solve the problem.Ei =EfKE = PEg½ mvi2 = mg∆ h (m’s will cancel because it is independent of the mass)Vi2 /2g = ∆ hII. A .0005kg bullet moving horizontally with a speed of 330 m/s hits a wooden block with amass of 2.3 kg that is suspended like a pendulum but with two v-strings. The bulletbecomes embedded in the wood. What is the speed of the block immediately after the bullet is embedded? How high do the block and bullet go?(bullet)∆ hPi = PfmVi = (m + M) VV = m Vi(m+M )Ei = Ef because we are in a frictionless situationKEBlock + bullet = PEg(Block + bullet)½ (M + M)V2 = (M+M)G∆ hV2 = 2g∆ hV = √2 g ∆ hmVi = (m + M)VVi = ((m + M)V)/MIII. Newton’s AppleA. Newton realized that an apple’s acceleration when falling is: aearth = 9.81 m/s2B. He realized that the moon’s acceleration toward Earth wasamoon = v2rV = ∆ xt = circumferenceperiod=2 πrP=2 π (384,000,000 m)2,360,000 s=1020 m/ s (VELOCITY OF THE MOON)amoon = v2r=(1020ms)2384,000,000 m=.00271ms2aearthamoon=9.81ms2.00271ms2=3,600=602NOW, RMOON ORBIT = 60REARTH RADIUSEarth acts as if all its mass is concentrated around a single point.C. Acceleration is due to v2/r, r being radius, because the moon is basically falling around the earth so the freefall acceleration equation appliesIV. Newton Finds Kepler’s Third LawA. P2 = r3 (P in years; r in astronomical units)B. P2=kr3 (arbitrary units)C. Newton derives this relationshipF = ma = mv2r=GMmr2V = 2 πrPm(4 π2r2)P2r=GMmr2V. Dark Mattera.p2=(4 π2r2)GM= kr3i. modification of the third lawb. As you get farther out from the galaxy, the period of the stars should become lessand less but the stars are moving faster than we expectc. Universal Gravitational Motion does not apply which implies that there is a large amount of matter (90%) that we cannot seeVI. Relationship of Weight versus Massa. Same proportion of Wt = mg can be shown as g=mx+ba. F = (9.81 N/kg)massb. Wt = mgb. Recall that 1kg*m/s2 is a Newton, Nc. Mass is the amount of matter in a bodyVII. Gravitational Field Strengtha. Wt = km where k = g; ergo, Wt = mgb. G= gravitational field strength in units of N/kgc. DO NOT confuse g with G.i. g = -9.81 N/kg = -9.81 m/s2ii. G = 6.67 x1011Nm2/kg2iii. Wt = mg = -GMm/r2iv. G = -GM/r2 = -(6.67 x 10-11Nm2/kg2) * (5.97x1024kg)/(6371,000m)2=


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ISU PHY 102 - Gravitation

Type: Lecture Note
Pages: 6
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