Concept explainers
Pinocchio is concerned that Gepetto will see his long hose and realize that he has been lying. So Pinocchio decides to run past Gepetto fast enough that his 10-inch long nose will be seen by Gepetto to be only 2 inches long.
a. How fast must Pinocchio run?
b. When running past Gepetto, will Pinocchio see Gepetto’s nose shortened?
(a)
The speed of person P while running.
Answer to Problem 39A
The running speed of person P is
Explanation of Solution
Given:
The length of nose is
The relativistic length of nose is
Formula used:
The expression for relativistic length contraction is,
Here,
Calculation:
The speed of personcan be calculated as,
Conclusion:
Thus, the running speed of person P is
(b)
To identify:Whether person Pwill see person G nose shortened.
Answer to Problem 39A
Yes, the nose of person G will appear shortened.
Explanation of Solution
Introduction:
If an object is moving at a high speed with respect to an observer, then there is a contraction in the length of the moving object in the direction of motion. The expression for relativistic length contraction is
Here,
Calculation:
The contraction of length of a moving object depends on the time dilation.There will be no relative speed between the people on the spaceship and the things, if they observe from their own reference frame. But there will a relative speed between the person on the spaceship and an observer for different frame of reference.
From the frame of reference of person P, the nose of person G appears to be contracted. So, the nose of person G will be seen shortened to person P.
Conclusion:
Thus, the nose of person G will appear shortened to person P.
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