Calculating Force in System S' Using Lorentz Transformation

In summary, the conversation discusses an object at rest in system S, acted upon by a force with components Fx and Fy. System S' is moving with instantaneous velocity v in the x direction. Using the Lorentz velocity transformation and defining the force as F=d/dt (gamma mv), it is shown that a0 F'x=Fx and b0 F'y=Fy/gamma. The second question addresses whether v/c^2 can be ignored and the conclusion is that it can be seen as zero in this case. The discussion also mentions the relativistic momentum equations for px and py, where u^2 is the particle
  • #1
mntb
19
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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 teh 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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  • #2
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
 

FAQ: Calculating Force in System S' Using Lorentz Transformation

What is Lorentz Transformation and how is it related to calculating force in system S?

Lorentz Transformation is a mathematical equation that describes the relationship between space and time in special relativity. It is used to calculate the effects of time dilation and length contraction on objects moving at high speeds. When applied to calculating force in system S, it helps to account for the changes in mass and velocity of objects as they move through space.

How do you use Lorentz Transformation to calculate force in system S?

To calculate force in system S using Lorentz Transformation, you need to first determine the relative velocity between the observer and the object, as well as the mass of the object. Then, you can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration calculated using Lorentz Transformation.

Is it necessary to use Lorentz Transformation when calculating force in system S?

Yes, Lorentz Transformation is necessary when calculating force in system S because it takes into account the effects of special relativity on the mass and velocity of objects. Without using Lorentz Transformation, the calculated force may not accurately reflect the true effects of the object's motion.

Can Lorentz Transformation be applied to any system or is it only useful for calculating force in system S?

Lorentz Transformation can be applied to any system that involves objects moving at high speeds. It is not limited to calculating force in system S, but can also be used to understand the behavior of particles in particle accelerators and other high-energy systems.

Are there any limitations to using Lorentz Transformation when calculating force in system S?

One limitation of using Lorentz Transformation is that it only applies to systems where objects are moving at constant velocities. It cannot be used to calculate forces in systems with changing velocities or accelerations. Additionally, it assumes that the objects are traveling in a vacuum, so it may not accurately predict forces in systems with air resistance or other external forces.

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