(a)
Does the muon reach Earth's surface within one half-life if Muons have a proper half-life of
Answer to Problem 77QAP
The muon does not make it to Earth
Explanation of Solution
Calculation:
Muons have a proper lifetime of
Length contraction in the muon's reference frame:
Distance traveled by the muon in the muon's reference frame:
Because 444.6 m <937 m, the muon does not make it to Earth.
Time dilation in Earth's reference frame:
Distance traveled in Earth's reference frame:
Because 1425 m <3000 m, the muon does not make it to Earth.
Conclusion:
The muon does not make it to Earth
(b)
The minimum speed of the muon so that it just barely reaches Earth's surface after one half-life?
Answer to Problem 77QAP
The minimum speed = 0.988c
Explanation of Solution
Calculation:
The minimum speed = 0.988c
Want to see more full solutions like this?
Chapter 25 Solutions
COLLEGE PHYSICS
- Two spaceships, each 100 m long when measured at rest, travel towardeach other with speeds of 0.85c relative to Earth. • How long is each ship as measured by someone on Earth?• How fast is each ship traveling as measured by an observer on the other?• How long is one ship when measured by an observer on the other?• At time t0 on Earth, the fronts of the ships are together as they just begin to pass each other. At what time on Earth are their ends together?arrow_forwardA charge particle moves along a straight line in an uniform electric field E with speed v. • If the motion and the electric field are in the x direction by Considering relativistic form of newton's second law show that the magnitude of the acceleration of charge q a = dt dv qE (1- m Discuss the significance of the dependence of the acceleration on the speed. If the particle starts from the rest x = 0 at t = 0 find the speed of the particle and its position after a time t has elapsed. • Comment of the limiting values of v and x as t –→∞arrow_forwardspecial relativity • A) Find the value of y for the following situation. An astronaut measures the length of her spaceship to be 25.0 m, while an Earth- bound observer measures it to be 100 m. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent? • Solution (a) y = 0.250. (b)It is unreasonable because the value of y is less than one. This opposed the idea of length contraction. © It will give imaginary value. The observer must measure the ship 25m, while the astronaut measures her ship 100m.arrow_forward
- 3. • A futuristic spaceship flies past Pluto with a speed of 0.964c relative to the surface of the planet. When the spaceship is directly overhead at an altitude of 1500 km, a very bright sig- nal light on the surface of Pluto blinks on and then off. An observer on Pluto measures the signal light to be on for 80.0 us. What is the duration of the light pulse as measured by the pilot of the spaceship?arrow_forwardWe cannot move a finger without disturbing all stars. Explain.arrow_forward4 In projection television sets electrons are accelerated through a potential difference of 50kV. • Calculate the speed of the electrons using the relativistic form of kinetic energy assuming the electrons start from rest. (Rest energy of electron is 0. 511MEV) • Calculate the speed of the electrons using the classical form of kinetic energy. o Determine the difference percentage and is this difference in speed significant in the design of this TV set? The free neutron is known to decay into a proton an electron and an antineutrino (of zeroarrow_forward
- 5) At the Fermilab accelerator, protons of momentum 5.3 × 10-16 kg.m/s are held in a circular orbit of diameter 2 km by a vertial B. Find the magnitude of the B required for this task.arrow_forwardUnreasonable ResultsA spaceship is heading directly toward the Earth at a velocity of 0.800c . The astronaut on board claims that he can send a canister toward the Earth at 1.20c relative to the Earth. (a) Calculate the velocity the canister must have relative to the spaceship. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forward•34 The speeds of 22 particles are as follows (N, represents the number of particles that have speed v,): 2 4 6 4.0 v, (cm/s) 1.0 2.0 3.0 2 N, 5.0 What are (a) vavg. (b) Vrms, and (c) vp?arrow_forward
- A3] The muon is a subatomic particle with a rest mass of 106 MeV/c2. At rest the average muon lifetime is 2.2 us. A beam of muons is produced in a laboratory in which the muons move at 0.8 c with respect to the laboratory. a) Specify whether the muon lifetime in the laboratory frame is longer or shorter than the lifetime for muons at rest. b) What is the average lifetime observed in the laboratory for muons in the beam? c) What is the total energy of each of the muons in the muon rest frame? d) What is the total energy of each of the muons in the laboratory frame? e) What is the kinetic energy of each of the muons in the laboratory frame? f) In the muon rest frame what is the distance between the point at which the muons are produced and the average decay point.arrow_forwardLength Contraction• Describe proper length.• Calculate length contraction.• Explain why we don’t notice these effects at everyday scales.arrow_forwardPart A What is the velocity, as a fraction of c, of a proton with 600 GeV total energy? Hint: This problem uses relativity. •C Submit Previous Answers Request Answer Incorrect: Try Again: 3 attemnts remainingarrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegeUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax