Concept explainers
The proof of
Answer to Problem 40PQ
The proof of
Explanation of Solution
Write the Lorentz’s transformation equations.
Here,
Differentiate above Lorentz’s equations to find
Case 1:
Write the equation for the velocity of the particle in the unprimed frame.
Substitute equation (IV) and equation (V) in above equation to find
Write the equation for the velocity of the particle in primed frame along
Write the equation for the velocity of the particle in primed frame along
Substitute equation (IX) and (X) in equation (VIII) to find
Case 2:
Write the equation for the velocity of the particle in the primed frame.
Substitute
Write the equation for the velocity of the particle in unprimed frame along
Write the equation for the velocity of the particle in unprimed frame along
Substitute equation (IX) and (X) in equation (VIII) to find
Conclusion:
Therefore, the transformation of a velocity component perpendicular to
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Chapter 39 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- Owen and Dina are at rest in frame S. which is moving at 0.600c with respect to frame S. They play a game of catch while Ed. at rest in frame S, watches the action (Fig. P39.91). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S') is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina?arrow_forwardAn observer in frame S sees lightning simultaneously strike two points 100 m apart. The first strike occurs at x1 = y1 = z1 = t1 = 0 and the second at x2 = 100 m, y2 = z2 = t2 = 0. (a) What are the coordinates of these two events in a frame S moving in the standard configuration at 0.70c relative to S? (b) How far apart are the events in S? (c) Are the events simultaneous in S? If not, what is the difference in time between the events, and which event occurs first?arrow_forwardConsider an electron moving with speed 0.980c. a. What is the rest mass energy of this electron? b. What is the total energyof this electron? c. What is the kinetic energy of this electron?arrow_forward
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