PHY 102 1st Edition Outline of Last Lecture I Work a Definitions b Equations c Young s Experiment II Motion III Mechanical Energy a Kinetic energy b Elastic equations IV Power V Conservation of Energy VI Frictional Force Outline of Current Lecture I Bullet Problem a Kinematics b Conservation of Energy II Bullet in block of wood a Conservation of Energy III Newton s Apple a Derivations of formulas These 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 earth IV Newton Derives Kepler s Third Law V Dark Matter VI Relationship of Weight v Mass Current Lecture I 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 v I 55 m s a g 9 81 m s 2 v f 0 Vf vi2 2a x 2 Use conservation of energy to solve the problem Ei Ef KE PEg mvi2 mg h m s will cancel because it is independent of the mass Vi2 2g h II A 0005kg bullet moving horizontally with a speed of 330 m s hits a wooden block with a mass of 2 3 kg that is suspended like a pendulum but with two v strings The bullet becomes 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 h Pi P f mVi m M V V mVi m M Ei Ef because we are in a frictionless situation KEBlock bullet PEg Block bullet M M V2 M M G h V2 2g h V 2 g h mVi m M V Vi m M V M III Newton s Apple A Newton realized that an apple s acceleration when falling is aearth 9 81 m s2 B He realized that the moon s acceleration toward Earth was 2 amoon V x t amoon v r circumference 2 r 2 384 000 000 m 1020 m s VELOCITY OF THE MOON period P 2 360 000 s m 2 v s m 00271 2 r 384 000 000 m s 1020 2 m a earth s2 3 600 602 amoon 00271m s2 9 81 NOW RMOON ORBIT 60REARTH RADIUS Earth acts as if all its mass is concentrated around a single point C IV Acceleration is due to v2 r r being radius because the moon is basically falling around the earth so the freefall acceleration equation applies Newton Finds Kepler s Third Law A P2 r3 P in years r in astronomical units B P2 kr3 arbitrary units C Newton derives this relationship F ma V 2 r P mv 2 GMm 2 r r m 4 2 r 2 GMm 2 2 P r r V Dark Matter a p2 4 2 r2 GM kr 3 i modification of the third law b As you get farther out from the galaxy the period of the stars should become less and less but the stars are moving faster than we expect c Universal Gravitational Motion does not apply which implies that there is a large amount of matter 90 that we cannot see VI Relationship of Weight versus Mass a Same proportion of Wt mg can be shown as g mx b a F 9 81 N kg mass b Wt mg b Recall that 1kg m s2 is a Newton N c Mass is the amount of matter in a body VII Gravitational Field Strength a Wt km where k g ergo Wt mg b G gravitational field strength in units of N kg c DO NOT confuse g with G i g 9 81 N kg 9 81 m s2 ii G 6 67 x1011Nm2 kg2 iii Wt mg GMm r2 iv G GM r2 6 67 x 10 11Nm2 kg2 5 97x1024kg 6371 000m 2 9 81
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