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Introductory Physics Homework Help
Length Contraction/Relativistic mass question
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[QUOTE="chef99, post: 6005535, member: 639309"] [h2]Homework Statement [/h2] [B]The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of the slower ship is 0.70c, find: a-The speed of spaceship B, relative to an observer on earth[/B] b- [B]The mass of spaceship A, relative to an observer on earth 2. Homework Equations [/B] γ = 1/ √1- v[SUP]2[/SUP] / c[SUP]2[/SUP] m[SUB]m[/SUB] = m[SUB]s[/SUB] / √ 1- v[SUP]2[/SUP] / c[SUP]2[/SUP] [h2]The Attempt at a Solution[/h2][B]a) [/B] Use the Lorentz factor to determine the velocity of ship B γ = proper length B/ contracted length A γ = 120m /42.8m γ = 2.8γ = 1/ √1- v[SUP]2[/SUP] / c[SUP]2[/SUP]rearrange to solve for v. γ[SUP]2[/SUP] = 1/ √1- v[SUP]2[/SUP] / c[SUP]2[/SUP] 1 - v[SUP]2[/SUP] / c[SUP]2[/SUP] = 1/γ[SUP]2[/SUP] v[SUP]2[/SUP] / c[SUP]2[/SUP] = 1 - 1/γ[SUP]2[/SUP] v/c = √1- 1/2.8[SUP]2[/SUP] v/c = √1- 1/7.84 v = 0.934 The speed of spaceship B, relative to an observer on Earth will be 0.934c. b) The mass of spaceship A, relative to an observer on earth. 3mk m[SUB]m[/SUB] = m[SUB]s[/SUB] / √ 1- v[SUP]2[/SUP] / c[SUP]2[/SUP] m[SUB]m[/SUB] = 15000kg / √1- 0.70c[SUP]2[/SUP] / c[SUP]2[/SUP] m[SUB]m[/SUB] = 15000kg / √1- 0.49 m[SUB]m[/SUB] =2100.4 https://www.physicsforums.com/file://localhost/Users/jefferyhewitt/Library/Group%20Containers/UBF8T346G9.Office/msoclip1/01/clip_image016.pngThe mass of spaceship A, relative to an observer on Earth, is 2100kg.The main part I am unsure of is question a, I hadn't specifically been taught about the Lorentz Factor, but this is all I could find that seemed to be able to determine the answer. As such I am not sure if I applied it correctly. If someone could give a few pointers that would be great. [/QUOTE]
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Introductory Physics Homework Help
Length Contraction/Relativistic mass question
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