Conservation of Energy

Transcription

1 Conservaton o nergy The total energy o a system can change only by amounts o energy that are transerred nto or out o the system W mec th nt Ths s one o the great conservaton laws n nature! Other conservaton laws to ollow: Lnear Momentum Angular Momentum Charge Baryon Number

2 Law o Conservaton o nergy Count up the ntal energy n all o ts orms. K U nternal Count up the nal energy n all o ts orms. K U These two must be equal. K K U U nternal nternal nternal

3 Law o Conservaton o nergy K K U U nternal nternal ( ) Rearrange terms. ( K K ) ( U U ) ( ) ( ) nternal nternal ( K U) nternal mechancal nternal

4 The change n mechancal energy must equal the energy converted to energy. mechancal ( ) mec, mec, mec, mec, Intal mechancal energy, mec, K U mv U mv Fnal mechancal energy, K U mv U mec, kd

5 The change n mechancal energy must equal the energy converted to energy. ( ) ( ) mec, mec, kd mv ( kd mv ) d kd k k d d mv k d.55m k d Intal mechancal energy, mec, K U mv U mv Fnal mechancal energy, K U mv U mec, kd

6 Daly Quz, September 7, 4 A hydrogen atom wth knetc energy o 4 ev s approachng another hydrogen atom n ts ground state. The potental energy s shown to the rght. nlarge

7 Notce a Sprng potental? Ths potental wll be used n understandng molecular structure and condensed matter.

8 Sample Problem 8-33 Two atoms o masses M and m wth M>>m. Total energy > and <. Total energy >. m s unbound. It wll approach M untl r.75nm and then be repelled back to nnty. The knetc energy wll ncrease up to a maxmum at a separaton dstance o about r. nm Total energy <. m s bound to M and ther separaton oscllates between.5nm < r <.9 nm.

9 Sample Problem 8-36 A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons.

10 Sample Problem 8-36 A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons. U at top h R θ F N v mg F N θ mg y x Key ponts: The normal orce wll decrease as the angle o the surace approaches 9 o and as hs speed ncreases.

11 Sample Problem 8-36 Soluton A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons. F N mg cos θ θ mg Key ponts: The normal orce wll decrease as the angle o the surace approaches 9 o and as hs speed ncreases.

12 Sample Problem 8-36 Soluton A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons. F N mg cos θ θ mg Newton s Second Law: mg cos θ F N mv /R g cos θ v /R when just leavng the ce. v gr cos θ

13 Sample Problem 8-36 Soluton A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons. F N mg cos θ θ mg Knetc nergy at top: K ½mv o Potental nergy at top: U Knetc nergy at angle: K ½mv ½mgR cos θ Potental nergy at angle: U mg(r h) mgr( cos θ)

14 Sample Problem 8-36 Soluton A boy s seated on top o a hemsphercal ce mound o radus R 3.8m. Startng rom rest, he begns to slde down the mound. At what heght does he lose contact wth the mound? Assume rctonless condtons. Intal Conservaton o nergy Fnal ½mv mgr( cos θ) Conservaton o nergy: v gr( cos θ) Newton s Second Law: v gr cos θ Thus, cos θ /3 and h R cos θ R/3 9.m