Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?

Question

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. So consider a spacecraft moving at a constant speed to the right, with respect to earth, an observer in the center of the spacecraft notes that two laser beams one green on the left side and the other blue on the right side of the spacecraft hit the extremity of the spacecraft. At the same time, an observer on earth records these same two events according to the observer on earth, which of the two events occurred first. So we're given some multiple choice answers. Let's read them off to see what our final answer might be. A states that the green light hits the spacecraft first B states blue light hits the spacecraft first. C states that the green and blue lights hit the spacecraft at the same time. And D states that it cannot be determined from the given information. OK. So on the right here, we have a quick little diagram, it shows the observer in space when it denotes it as capital O subscript capital S. So the observer in space and then down below is the observer from earth O subscript capital E and the spacecraft is mo the spacecraft is moving to the right at a constant velocity or a constant speed I should say. And on the right is the blue light because the blue light hits the spacecraft on the right side and the green light hits the spacecraft on the left side. OK. So it's set like as stated in the problem itself, the observer in the spacecraft notes that two laser beams one green on the left side and the other blue on the right side of the spacecraft hit the extremity of the spacecraft at the same time. OK. So our main focus is we're trying to find what the observer on earth sees. So capital o subscript capital E so the observer on earth sees, let's make a quick little list. So first off from the observer on earth sees the spacecraft will say s is moving to the right, we'll do a little arrow pointing to the right. And we need to also recall that green light has to travel a greater distance versus blue light. So won't write the note there, the green light travels a greater distance. OK. And then last of all, the spacecraft observer will see the wavefront produced by blue light before it will see the wavefront produced by green light. So essentially, so the space shuttle server will feet like we'll see the wavefront produced by blue light hitting the spacecraft before the green light even reaches the spacecraft. So we'll make a note that that spacecraft observes blue light first, blue light. So with that said, the observer on earth will believe that green light hits the spacecraft first. So O E believes that that green light hits first hits first everybody. Awesome. And that is our final answer, folks. Awesome. So that means that the correct answer is a the green light hits the spacecraft first. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?

Verified Solution

Key Concepts

Relativity of Simultaneity

Reference Frames

Light Travel Time