Problem 2. Relativity the 'pole in barn." (This is a famous paradox and you might find all sorts of variants of online. Read this version carefully and don't get confused with alternate scenarios.) A runner carries a 5-meter-long pole (as measured when the pole is at rest) and runs at an impres- sively high speed of v = c through a 4-meter-long barn (as measured when the barn is at rest). The barn doors are open at both ends, so the runner goes right through. (a) According to the farmer at rest with respect to the barn, will the runner and pole 'fit' inside the barn? Calculate the length-contracted length of the pole to answer the question. (b) According to the runner, will the pole 'fit' in the barn? Calculate the length-contracted length of the barn to answer the question. (c) Suppose the farmer attempts to close the pole inside the barn by closing both doors simul- taneously. Describe what the runner will observe (in terms of when the doors close, and in what order). (d) How long will the runner take to run the length of the barn, according to the farmer? How long will it take according to the runner? (Ignore the pole for this part.)
Problem 2. Relativity the 'pole in barn." (This is a famous paradox and you might find all sorts of variants of online. Read this version carefully and don't get confused with alternate scenarios.) A runner carries a 5-meter-long pole (as measured when the pole is at rest) and runs at an impres- sively high speed of v = c through a 4-meter-long barn (as measured when the barn is at rest). The barn doors are open at both ends, so the runner goes right through. (a) According to the farmer at rest with respect to the barn, will the runner and pole 'fit' inside the barn? Calculate the length-contracted length of the pole to answer the question. (b) According to the runner, will the pole 'fit' in the barn? Calculate the length-contracted length of the barn to answer the question. (c) Suppose the farmer attempts to close the pole inside the barn by closing both doors simul- taneously. Describe what the runner will observe (in terms of when the doors close, and in what order). (d) How long will the runner take to run the length of the barn, according to the farmer? How long will it take according to the runner? (Ignore the pole for this part.)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Problem 2. Relativity the 'pole in barn."
(This is a famous paradox and you might find all sorts of variants of online. Read this version
carefully and don't get confused with alternate scenarios.)
A runner carries a 5-meter-long pole (as measured when the pole is at rest) and runs at an impres-
sively high speed of v = c through a 4-meter-long barn (as measured when the barn is at rest).
The barn doors are open at both ends, so the runner goes right through.
(a) According to the farmer at rest with respect to the barn, will the runner and pole 'fit' inside
the barn? Calculate the length-contracted length of the pole to answer the question.
(b) According to the runner, will the pole 'fit' in the barn? Calculate the length-contracted length
of the barn to answer the question.
(c) Suppose the farmer attempts to close the pole inside the barn by closing both doors simul-
taneously. Describe what the runner will observe (in terms of when the doors close, and in
what order).
(d) How long will the runner take to run the length of the barn, according to the farmer? How
long will it take according to the runner? (Ignore the pole for this part.)
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