One of the classic paradoxes of special relativity is the pole/barn paradox. The setup: a person carrying a 20.0 m pole runs at relativistic speeds at a 15.0 m long barn (with doors open on both ends). According to the observer on the ground frame of reference, which we'll call S (like the textbook does), if the person runs sufficiently fast enough, the pole will contract (in length, according to the Lorentzian transformations, so that it will be short enough to fit inside the barn. To give a contrast, the door opening width in the barn (measured perpendicular to the runner's motion) is 5.00 m. However, from the person carrying the pole frame of reference (which we will call S'), it is the barn that contracts in length, with the pole staying 20.0 m long, and the pole will never fit inside the barn. Which scenario is correct? How can the paradox be resolved? 1. Let the pole speed be 0.662c. Use the Lorentz transformation equations to calculate the following quantities (then fill in the table): S' Frame of reference Length of pole Length of barn Width of barn door opening S 2. a. Does the pole fit in the barn in frame S? b. Does the pole fit in the barn in frame S'?
One of the classic paradoxes of special relativity is the pole/barn paradox. The setup: a person carrying a 20.0 m pole runs at relativistic speeds at a 15.0 m long barn (with doors open on both ends). According to the observer on the ground frame of reference, which we'll call S (like the textbook does), if the person runs sufficiently fast enough, the pole will contract (in length, according to the Lorentzian transformations, so that it will be short enough to fit inside the barn. To give a contrast, the door opening width in the barn (measured perpendicular to the runner's motion) is 5.00 m. However, from the person carrying the pole frame of reference (which we will call S'), it is the barn that contracts in length, with the pole staying 20.0 m long, and the pole will never fit inside the barn. Which scenario is correct? How can the paradox be resolved? 1. Let the pole speed be 0.662c. Use the Lorentz transformation equations to calculate the following quantities (then fill in the table): S' Frame of reference Length of pole Length of barn Width of barn door opening S 2. a. Does the pole fit in the barn in frame S? b. Does the pole fit in the barn in frame S'?
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Transcribed Image Text:One of the classic paradoxes of special relativity is the pole/barn paradox.
The setup: a person carrying a 20.0 m pole runs at relativistic speeds at a 15.0 m long barn
(with doors open on both ends). According to the observer on the ground frame of
reference, which we'll call S (like the textbook does), if the person runs sufficiently fast
enough, the pole will contract (in length, according to the Lorentzian transformations, so
that it will be short enough to fit inside the barn. To give a contrast, the door opening
width in the barn (measured perpendicular to the runner's motion) is 5.00 m.
However, from the person carrying the pole frame of reference (which we will call S'), it is
the barn that contracts in length, with the pole staying 20.0 m long, and the pole will never
fit inside the barn.
Which scenario is correct? How can the paradox be resolved?
1. Let the pole speed be 0.662c. Use the Lorentz transformation equations to calculate
the following quantities (then fill in the table):
Frame of
reference
Length of pole
Length of barn
Width of barn
door opening
S
S'
2. a. Does the pole fit in the barn in frame S?
b. Does the pole fit in the barn in frame S'?
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