Potential energy of a spring

Transcription

1 PHYS 7: Modern Mechanic Spring 0 Homework: It i expected that a tudent work on a a homework #x hortly after lecture #x, ince HWx i on material of LECx. While the due date for HW are typically et to about a week after the repective lecture, thi extra time hould be conidered a a grace period for emergencie and not a a uggetion to work on the aignment on that lat day. Lecture 3 Energy in Macrocopic Sytem Read y Potential energy of a pring x F F, x, x U k x U x kx U k Potential energy of a pring: U k Aume U 0 for relaxed pring

2 Energy of an ocillating pring-ma ytem -x max K 0 U k x y mv K U 0 max x max max v << c x Neglect friction: ( ) Ey mc + K + U 0 γ mv + k x 0 Maximum peed: mvmax k x max Speed at any point: mv + kx k x max ( / )( max ) v k m x x HOME STUDY: Example, a rebounding block L 0 m v i k 000 N/m y i y? f. What i the lowet point reached by the block? Sytem: block, pring, Earth Aume: no interaction with urrounding γ E i E mgy + mv mgy + k L y f ( ) 0 i i f f One equation, one unknown. What i the highet point reached by the block? mgy + mv mgy i i f One equation, one unknown See detail in the book (7.3), p

3 Temperature and energy: the connection Jame Precott Joule : 4.4 J/K. g Today: 4.86 J/K. g Heat capacity: amount of energy required to heat up unit of ma by unit of temperature Specific heat capacity Specific heat capacity C: amount of energy required to heat up unit of ma by unit of temperature E Cm T thermal C m T E thermal Uually expreed per gram: J/(g. K)

4 Demo: fire yringe Convert mechanical (kinetic) energy into heat 7 Example: heat capacity Niagara fall what i the water temperature rie due to gravity if there would be no loe of energy? Solution: T gh / C Cm T mgh ( 9.8 N/kg)( 50 m) ( 4.86 J/ ( K g) ) N m K g 7 J kg N m K g 7 N m kg K g g 0.7 K C water 4.86 J/(K. g) h 50 m

5 Thermal energy mivi E m ic + + k, ii i K 0-3 J/molecule Entropy degree of chao and temperature are related (will addre later) Thermal energy tranfer: Thermal tranfer of energy A proce in which energy move between a ytem and urrounding with which it i in contact, due to a temperature difference Ey Q + W Work done on the ytem Heat tranferred to the ytem (microcopic work) Reerve the word heat pecifically to denote thermal energy tranferred from one object to another Flow of electromagnetic radiation can alo change the energy Sign of Q: + - tranfer to ytem - tranfer from ytem

6 Example: heat A perfectly inulated houe ha volume of 500 m 3 (~500 ft houe) and air temperature 0 0 C. You bring in a cloed bucket of water (0 l) at temperature 00 0 C. What will be the temperature in the houe after equilibration? Solution: E + E 0 w a ( ) + ( ) 0 C m T T C m T T w w f wi a a f ai ( ) C m + C m T C m T + C m T w w a a f w w wi a a ai Water bucket T wi 00 o C 373K m 0 kg C w 4. J/(K. g) T f C m T C m + C m T + C m w w wi a a ai w w a a o T f 79.4 K5.4 C m 65 kg a Air T ai 0 o C 73K V 500 m 3 C a J/(K. g) ρ.3 kg/m 3 Ignored: wall, yourelf, heat capacity dependence on T Power (P) Energy per unit time de P Unit: Watt, dt dr P F F v dt dt dt dw P F v dt dw d ( F r ) Power aociated with work: W J/ Clicker: If a car engine run at contant power, which would take longer time to accelerate from 0 to 0 m/, or from 0 to 30 m/? (~0-0 mph) (~40-60 mph) A) Need more time to accelerate from 0 to 0 m/ B) Need more time to accelerate from 0 to 30 m/ C) The ame

7 Open and cloed ytem Cloed ytem: there i no energy flow between the ytem and urrounding E E 0; E 0 out in y Open ytem: there i energy flow between the ytem and urrounding E 0, and/or E 0; out in CLICKER: I the univere a a whole a cloed or an open ytem? A) Cloed B) Open Volume and temperature When energy rie the average ditance between atom in general mut leading to increae in volume. The pring law doe not explain: - volume change with temperature! - breaking

8 Interatomic More potential energy between two atom The More potential energy function i a realitic approximation α ( r r 0 ) 0 0 U M E e E Spring approximation: U M kr E0 When energy rie the average ditance between atom in general increae leading to increae in volume. Thermometer baed on expanion mercury Bi-metallic Galilean (buoyancy)

9 The choice of ytem and energy ytem Ball fall ditance h toward Earth ytem mg E K + U 0 y g ( mgh) 0 K + E K + mgh Analyze tatement: The Earth exert a force mg through a ditance h and doe work mgh, and there i alo decreae in the potential energy mgh, o the kinetic energy increae by mgh. WRONG! E K + ( mgh) + mgh y Avoid double counting! y HOME READING: 7.9 Work!