Lect15_[Compatibility_Mode]

Lect15_[Compatibility_Mode] - Physics 344 Foundations of...

This preview shows pages 1–5. Sign up to view the full content.

Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Notices: Help session Tuesday 1:30 to 3:30 in room 160. Exam I will be at 8:00pm Thursday, October 7 in MTHW 210

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
After introducing the 4-momentum vector of a particle last lecture we looked back at the recitation problem involving a particle of mass m = 3 kg moving at speed v = 4/5 in the y direction relative to a Home-frame coordinate system. The problem asked what energy an observer in an Other frame oving in the x direction at speed 3/5 relative to the Home frame would moving in the x direction at speed V = 3/5 relative to the Home frame would measure the particle to have. We considered this highly relativistic situation to illustrate the way in which orking with 4- ectors can be used to make physical predictions and to solve working with 4 vectors can be used to make physical predictions and to solve problems. In the process, we obtained an expression for the Other-frame energy of the article that was correct for any speeds nd I meant to use this to show particle that was correct for any speeds v and V . I meant to use this to show the result reduces to the expected Newtonian result in the limit that both speeds are small compared to c , but forgot to do this.
We saw that the Home-frame components of the particle’s 4-momentum 5/ 3 m m γ ⎡⎤ vector were related to its relativistic energy and momentum components measured in that frame and that in this particular case they were 0 4/ 3 p px py mv P m v ⎢⎥ = ± where 22 11 5 3 ( 4 / 5 ) p v == = −− 0 pz ⎣⎦ We determined the Home-frame components of the Other observer’s 4-velocity nd used its relationship to the dimensionless unit vector parallel to the t’ axis and used its relationship to the dimensionless unit vector parallel to the t axis of the Other coordinate system to solve the problem. 5/4 3/4 00 0 obs V u = ± where 5 4 ( 3 / 5 ) V =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Specifically, this particle’s energy measured in the Other frame is 0 ˆ p m V E Pt m γγ γ ⎡⎤ ⎢⎥ = ⋅= ±i 0 00 p p mv
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

Lect15_[Compatibility_Mode] - Physics 344 Foundations of...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online