Calculating Force in System S' Using Lorentz Transformation

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SUMMARY

The discussion focuses on calculating the force in a system S' using Lorentz transformations. It establishes that for an object of mass m at rest in system S, the force components are defined as F'x = Fx and F'y = Fy/gamma, where gamma is the Lorentz factor. The participant also questions the validity of approximating v/c^2 as zero, concluding that under this assumption, F'y simplifies to Fy/gamma. The discussion emphasizes the relationship between relativistic momentum and force components in different inertial frames.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with relativistic momentum
  • Basic calculus for force derivation
  • Knowledge of the Lorentz factor (gamma)
NEXT STEPS
  • Study the derivation of the Lorentz factor (gamma) in detail
  • Learn about relativistic dynamics and its implications on force
  • Explore the concept of relativistic momentum in various inertial frames
  • Investigate the conditions under which v/c^2 can be approximated as zero
USEFUL FOR

Physics students, educators, and professionals in fields involving relativistic mechanics, particularly those focused on force calculations in different inertial frames.

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Consider an object of mass m at rest in S acted upon by a force F with components Fx and Fy. Sys tem S' moves with instantaneousvelocity v in the x direction. Defining the force with F=d/dt (gamma mv), and using the Lorentz velocity transformation, show that a0 F'x=Fx,b0 F'y=Fy/gamma
I show my work and problem in word doc: problem with calculus, cause it couldn't show up properly here
second question, is it okay to see v/c^2 as zero in this case, then F'y would be equal to Fy/gamma, I mean to ignore v/c^2?
 

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For relativtistic momentum px = gamma(u)*m*ux and py = gamma(u)*m*uy where u^2 = ux^2 + uy^2 is the particle speed in S
 

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