Assume that your heart normally beats once every second, and that you are in a spaceship that moves past Earth at 0.6c.
a. What time do you measure between your own heartbeats?
b. Show that your heartbeats are measured by someone on Earth to be 1.25 s apart.
c. As you and the spaceship whiz past Earth, you make similar measurements on Earthlings who measure their own heart-beats to be 1 s apart. How much time do you measure between their heartbeats?
(a)
The time measured by a person’s own heartbeat.
Answer to Problem 34A
The time measured by a person’s own heartbeat is once every second.
Explanation of Solution
Given:
The speed of spaceship is
Calculation:
To propel the spaceships to relativistic speeds, the amounts of energy requiredare billions of times the energy that is used to put the space shuttles into orbit.
Given that the persons heart normally beats once every second. So, the time measured by a person’s own heartbeat is once every second since the body is at rest with respect to reference frame.
Conclusion:
Thus, the time measured by a person’s own heartbeat is once every second.
(b)
the time period of heartbeats by someone on Earth to be
Answer to Problem 34A
The time period of heartbeats by someone on Earth is
Explanation of Solution
Given info:
The speed of spaceship is
Formula used:
Show the expression for relative time in a frame of reference as follows:
Here,
Calculation:
Refer to part (a).
The time measured by a person’s own heartbeat is once every second. That is, the time of heartbeats is
Find the time period of heartbeats by someone on Earth as follows:
Hence, the time period of heartbeats by someone on Earth is
Conclusion:
Thus, the time period of heartbeats by someone on Earth is
(c)
the time period of heartbeats by someone on Earth.
Answer to Problem 34A
The time period of heartbeats by someone on Earth is
Explanation of Solution
Given info:
The time of heartbeats is
The speed of spaceship is
Formula used:
Show the expression for relative time in a frame of reference as follows:
Here,
Calculation:
Find the time period of heartbeats by someone on Earth as follows:
Hence, the time period of heartbeats by someone on Earth is
Conclusion:
Thus, the time period of heartbeats by someone on Earth is
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