Chapter 12: Q21P (page 529)

The coordinates of event Aare $(x_{A}, 0, 0), t_{A,}$ and the coordinates of event B are $(x_{B}, 0, 0), t_{A}$ . Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.

Short Answer

Expert verified

The velocity of the system is $v = (\frac{t_{B} - t_{A}}{x_{B} - x_{A}}) c^{2}$ .

Step by step solution

Expression for the Lorentz transformation equation:

Write the expression for the Lorentz transformation equation.

$t = Y (t - \frac{v}{c^{2}} x)$ …… (1)

Here, v is the velocity of the system, x is the displacement, and c is the speed of light.

Determine the velocity of the system:

Write equation (1) in terms of $∆$ .

$∆ t = γ (∆ t - \frac{v}{c^{2}} ∆ x)$

Here, $∆ t = 0$

Hence, the equation becomes,

$γ (∆ t - \frac{v}{c^{2}} ∆ x) = 0 ∆ t - \frac{v}{c^{2}} ∆ x = 0 ∆ t - \frac{v}{c^{2}} ∆ x v = \frac{c^{2} ∆ t}{∆ x}$

As the coordinates of event A and B are given as $(x_{A}, 0, 0), t_{A}$ and $(x_{B}, 0, 0), t_{B}$ respectively, the velocity of the system will be,

$v = \frac{c^{2} (t_{B} - t_{A})}{(x_{B} - x_{A})} v = (\frac{t_{B} - t_{A}}{x_{B} - x_{A}}) c^{2}$

Therefore, the velocity of the system is $v = (\frac{t_{B} - t_{A}}{x_{B} - x_{A}}) c^{2}$ .

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The coordinates of event Aare $(x_{A}, 0, 0), t_{A,}$ and the coordinates of event B are $(x_{B}, 0, 0), t_{A}$ . Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.

Short Answer

Step by step solution

Expression for the Lorentz transformation equation:

Determine the velocity of the system:

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The coordinates of event Aare (xA,0,0),tA, and the coordinates of event B are(xB,0,0),tA. Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.

Short Answer

Step by step solution

Expression for the Lorentz transformation equation:

Determine the velocity of the system:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Circular Motion and Gravitation

Kinematics Physics

Translational Dynamics

Conservation of Energy and Momentum

Particle Model of Matter

Study anywhere. Anytime. Across all devices.

The coordinates of event Aare $(x_{A}, 0, 0), t_{A,}$ and the coordinates of event B are $(x_{B}, 0, 0), t_{A}$ . Assuming the displacement between them is spacelike, find the velocity of the system in which they are simultaneous.