Answers to Selected Problems - West Valley College

Problem Sets Physics 4D
A very fast pole vaulter lives in the country. One day, while practicing, he notices a 10 m long barn with
the doors open at both ends. He decides to run through the barn a 0.866 c while carrying his 16 m long
pole. The farmer, who sees him coming, says, “Aha! This guy’s pole is length contracted. There will be
a short interval of time when the pole is entirely inside the barn. If I’m quick, I can simultaneously close
both barn doors while the pole vaulter and his pole are inside.” The pole vaulter, who sees the farmer
beside the barn, thinks to himself, “That farmer is crazy. The barn is length contracted shorter than my
pole. My 16 m long pole cannot fit into that short barn. If the farmer closes both doors just as the tip of
my pole reaches the back door, the front door will break off the end of my pole.”
So, the farmer bets the pole vaulter that he can close both doors while the pole is in the barn. As the
conditions of the bet, the farmer and vaulter agree that:
When the farmer sees the front of the pole reach the back door, the farmer will open the back door.
When the farmer sees the rear of the pole pass through the front door, the farmer will close both
doors.
Can the farmer close the doors without breaking the pole?
Show that, when properly analyzed, the farmer and the pole vaulter agree on the outcome. Your analysis
should contain both quantitative calculations and a written explanation.
Furthermore, this analysis must contain a thorough discussion of each event (the closing of the front door,
the closing of the rear door, and the opening of the rear door). For example: Were the events
simultaneous to each observer? If not, when and where did each event occur? How are these events
represented by a spacetime diagram?
Answer(s)
In the farmer’s reference frame:
1) At t = 0 s, both doors are closed
2) At t = +7.7 ns the back door is opened
In the pole vaulter’s reference frame:
1) At t = -57 ns the back door is cloded
2) At t = 0 42 ns the back door is opened
3) At t = 0 s the front door is closed.
Since, in the pole vaulter’s reference frame, the back door is closed, then opened, followed by the fro
door being opened, there is no paradox because there is no time at which the doors are closed at the
same time.
There is no paradox in the farmer’s reference frame, because there is a time at which the pole completely
fits within the barn, so . . . they BOTH WIN the bet!!
Melvin J. Vaughn Page 6 of 61 West Valley College