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The percentage contraction of a rod moving with a velocity 0.8 c in a direction inclined at 60° to its own length ______% (up to one decimal place)
Correct answer is '8.3'. Can you explain this answer?
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The percentage contraction of a rod moving with a velocity 0.8 c in a ...
Let the proper length be L0. The proper length component of rod perpendicular to the velocity v0 = L0 cos 60°.
There is no length contrction along the direction perpendicular to velocity.
The length of the perpendicular component to the velocity in lab frame is
Total lensth of rod in Lab frame.
Percentage contraction =
There is no length contrction along the direction perpendicular to velocity.
The length of the perpendicular component to the velocity in lab frame is
Total lensth of rod in Lab frame.
Percentage contraction =
Most Upvoted Answer
The percentage contraction of a rod moving with a velocity 0.8 c in a ...
Degrees to its length is given by the formula:
% contraction = sqrt(1 - v^2/c^2) * 100
where v is the velocity of the rod and c is the speed of light. In this case, v = 0.8c, so:
% contraction = sqrt(1 - (0.8c)^2/c^2) * 100
% contraction = sqrt(1 - 0.64) * 100
% contraction = 45.56%
Therefore, the rod will contract by approximately 45.56% when moving with a velocity of 0.8c in a direction inclined at 60 degrees to its length.
% contraction = sqrt(1 - v^2/c^2) * 100
where v is the velocity of the rod and c is the speed of light. In this case, v = 0.8c, so:
% contraction = sqrt(1 - (0.8c)^2/c^2) * 100
% contraction = sqrt(1 - 0.64) * 100
% contraction = 45.56%
Therefore, the rod will contract by approximately 45.56% when moving with a velocity of 0.8c in a direction inclined at 60 degrees to its length.
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The percentage contraction of a rod moving with a velocity 0.8 c in a ...
Not to do complex
just take the velocity of the moving frame in the direction of the rod length.
set a frame to the moving rod namely S' which moves with a velocity of 0.8c with respect to the rest frame at an angle of 60 degree with its own length.
set an observer to the rest frame .
the rod is placed in that frame along the x- axis so we have to calculate only the velocity in the x-direction on that moving frame and i.e.,
0.8c × cos 60 = 0.4c
now the ratio of the length appeared in S frame to its original length is given by
√(1-{(0.4c)²/c2} =. √21/5 = 0.9165
now,
the contraction in length is given by
1- 0.9165 = 0.08348
in percentage
8.35% .
just take the velocity of the moving frame in the direction of the rod length.
set a frame to the moving rod namely S' which moves with a velocity of 0.8c with respect to the rest frame at an angle of 60 degree with its own length.
set an observer to the rest frame .
the rod is placed in that frame along the x- axis so we have to calculate only the velocity in the x-direction on that moving frame and i.e.,
0.8c × cos 60 = 0.4c
now the ratio of the length appeared in S frame to its original length is given by
√(1-{(0.4c)²/c2} =. √21/5 = 0.9165
now,
the contraction in length is given by
1- 0.9165 = 0.08348
in percentage
8.35% .
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The percentage contraction of a rod moving with a velocity 0.8 c in a direction inclined at 60° to its own length ______% (up to one decimal place)Correct answer is '8.3'. Can you explain this answer?
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