A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.4 x 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.4 x 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter1: Relativity I

Section: Chapter Questions

Problem 34P: Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and...

See similar textbooks

Related questions

Q: Earth's neighboring galaxy, the Andromeda Galaxy, is a distance of 2 taken to be 75.0 years, a…

A: Givento=2.54×107 light yeart=75 years

Q: A high speed particle enters a medium and travels 7.8 mm before it decays. If the particle was…

Q: Two particles in a high-energy accelerator experiment approach each other head-on with a relative…

A: The formula to find the magnitude of velocity of particles relative to each other is v'=v-u1-uvc2…

Q: Two particles in a high-energy accelerator experiment are approaching each other head-on, each with…

A: The initial speed of the first particle, u=0.938 c The initial speed of the second particle,…

Q: A particle has a lifetime, as measured in its own reference frame, of 0.42 µs. It propagates at a…

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Given that speed of pion and also given the lifetime of pion.Then We have to determine the value of…

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Given data as per question speed = 0.990c t = 3.5* 108

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Given Data:The speed of the particle Lifetime of pion To Determine:(a). The lifetime of the pion…

Q: An observer on the earth sees a spaceship approaching at 0.52c. The ship then launches an…

Q: An alien spaceship has a mass ofm= 3.2×109kg, and according to the crew, onboard the bow-to-stern…

A: mass of spaceship (m) = 3.2×109 kg Length measured onboard (Lo) = 680 m Length measured by…

Q: A spaceship goes past a planet at a speed of 0.80c relative to the planet. An observer on the planet…

Q: A subatomic particle moves through the laboratory at 0.90c. Laboratory experimenters measure its…

A: The given values are, v=0.90ct=2.3 ps=2.3×10-12 s

Q: Two particles are created in a high-energy accelerator and move off in opposite directions. The…

A: Given data: The speed of the particle measured in the laboratory is v=0.65c. The relative speed is…

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Speed (v) = 0.990c Where, c = 3 × 108 m/s t = 2.6 × 10-8 s

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Given Data: Speed of the particle (v) = 0.986c.Lifetime of pion (T) = 2.8×10-8 s. To Determine: (a).…

Q: A muon is created 60.0 kmkm above the surface of the earth (as measured in the earth's frame). The…

A: Dear student, this question contains more than three sub-parts. As per guide lines we will answer…

Q: A particle whizzes through your lab at a speed of 0.74c. Your detectors determine that its lifetime…

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Speed (v) = 0.990cWhere, c = 3 × 108 m/st = 2.8 × 10-8 s

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: Given Data:Speed of the particle Lifetime of pion To Determine:(a). The lifetime of the pion…

Q: A garage is a box 3m wide (x-direction) by 2m high (y-direction) and 8m deep (z-direction). You…

Q: A high speed particle enters a medium and travels 7.1 mm before it decays. If the particle was…

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: a) Write the expression for the time dilation and substitute the corresponding values to calculate…

Q: J Astronomer David observes that a distant quasar is receding from the Earth at a speed of He also…

Q: Mavis boards a spaceship and then zips past Stanley on earth at a relative speed of 0.600c. At the…

A: Given: To find the Mavis's time read and blink duration is given as,

Q: A particle known as a pion lives for a short time before breaking apart into other particles.…

A: According to the theory of relativity, the time dilates for a body moving with speed comparable to…

Concept explainers

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of
0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.4 x 10-8 s. (a) What is the lifetime
according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the
laboratory move before the pion breaks apart?
(a) Number
MI
(b) Number i
Units
Units

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction.

VIEW

Step 2: Find the time in pion's frame

VIEW

Step 3: The distance the laboratory moves

VIEW

Solution

VIEW

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34
An observer in frame S sees lightning simultaneously strike two points 100 m apart. The first strike occurs at x1 = y1 = z1 = t1 = 0 and the second at x2 = 100 m, y2 = z2 = t2 = 0. (a) What are the coordinates of these two events in a frame S moving in the standard configuration at 0.70c relative to S? (b) How far apart are the events in S? (c) Are the events simultaneous in S? If not, what is the difference in time between the events, and which event occurs first?
Owen and Dina are at rest in frame S, which is moving at 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P9.63). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina? Figure P9.63
Suppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
Owen and Dina are at rest in frame S. which is moving at 0.600c with respect to frame S. They play a game of catch while Ed. at rest in frame S, watches the action (Fig. P39.91). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S') is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina?
Consider an electron moving with speed 0.980c. a. What is the rest mass energy of this electron? b. What is the total energyof this electron? c. What is the kinetic energy of this electron?
A spacecraft moves at a speed of 0.900c. If its length is L as measured by an observer on the spacecraft, what is the length measured by a ground observer?
Joe and Moe are twins. In the laboratory frame at location S1 (2.00 km, 0.200 km, 0.150 km). Joe shoots a picture for aduration of t= 12.0 s. For the same duration as measured inthe laboratory frame, at location S2 (1.00 km, 0.200 km,0.300 km), Moe also shoots a picture. Both Joe and Moe begintaking their pictures at t = 0 in the laboratory frame. Determine the duration of each event as measured by an observer ina frame moving at a speed of 2.00 108 m/s along the x axisin the positive x direction. Assume that at t = t = 0, the origins of the two frames coincide.
(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly away is receding from us at 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
Calculate the momentum of a proton moving with a speed of (a) 0.010c, (b) 0.50c, (c) 0.90c. (d) Convert the answers of (a)(c) to MeV/c.
(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0109ly ly away is receding from us at 0. 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
Owen and Dina are at rest in frame S, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving? Figure. P26.45