Muons are elementary particles that are formed high in the atmosphere by the interactions of cosmic rays with atomic nuclei up there. Muons are radioactive and have average lifetimes of about two-millionths of a second. Even though they travel at almost the speed of light, very few should be detected at sea level after traveling through the atmosphere—at least according to classical physics. Laboratory measurements, however, show that muons in great number do reach Earth’s surface. What is the explanation?

Q: Suppose that Penny's spaceship zooms past Jane at a speed of 2.236 x 108 m/s. What does Jane observe…

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Q: What effect do mass and velocity have on the momentum of objects moving at relativistic speeds?

A: Relativistic momentum is given by: p=γmuwhere, γ=lorrentz factor                =11-v2c2m= mass of…

Q: What is the speed of a pion if its average lifetime ismeasured to be 4.40 x10 -8 s At rest, its…

A: Given: The average lifetime of the pion is ∆t=4.40×10-8 s. The average lifetime of the pion at…

Q: A spacecraft receding from the earth emits radio waves at a constant frequency of 10^9 Hz. If the…

A: Let the difference between the classical and relativistic frequency of the radio wave be 1 Hz. For…

Q: What is the speed of a particle whose kinetic energy is equal to (a) its rest energy and (b) five…

A: (a) The expression of kinetic energy is given by, Ek=mc211-v2c2-1...…(1) Here, m is the mass of the…

Q: A new particle, the aarnion, has just been discovered! Careful measurements show that the aarnion…

A: GivenThe aarnion has an average lifetime (at rest), τ= 87 nsDistance tavelled by aarnion, d=24 m

Q: In the muon decay experiment discussed in Section 2.9 as a verification of time dilation, the muons…

A: Time dilation: When the observer is moving wrt to the event happening then both the frame of…

Q: At what speed do the classical and relativistic values of a particle’s momentum differ by 10.0%?

A: Let the mass of the particle be defined as m. Let the speed of the particle be defined as u.The…

Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

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Q: Particles called π -mesons are produced by accelerator beams. If these particles travel at 2.70×108…

A: Given:  velocity, v = 2.7 x 108 m/s t = 2.6 x 10-8 s

Q: Take the ratio of relativistic rest energy, E = γmc 2, to relativistic momentum, p = γmu , and show…

A: The relativistic rest energy is, E=γmc2p=γmc andEp=γmc2γmc=c

Q: How fast will a space ship be moving, if the observer on earth notices that the time on the…

A: The equation for the time dilation is given by

Q: How fast must a meter stick be moving if its length is observed to shrink to half a meter by an…

A: l=l01-v2c2

Q: ay from Earth? (b)To what frequency must Earth receivers be tuned to receive the report when the…

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Q: Show that for any object moving at less than one-tenth the speed of light, the relativistic kinetic…

A: The relativistic kinetic energy of a particle, with mass relativistic mass m and rest mass m0,…

Q: If a high-speed spaceship appears shrunken to half its normal length, how does its momentum compare…

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Q: How fast must an object travel for its total energy to be 50% more than its rest energy?

A: Given Data:- Total energy of the object is 50%  more than its rest energy. Required:- Speed of the…

Q: Frame S' has a speed v = 0.6c relative to S in x direction which is parallel to x'. The clocks on S…

A: Given : Speed of S' with respect to S, v = 0.6c The clocks on S and S' are adjusted so that t= t'= 0…

Q: A new particle, the joelon, has just been discovered! Careful measurements show that the joelon has…

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Q: A spacecraft receding from the earth emits radio waves at a constant frequency of 109 Hz. If the…

A: Given data: Frequency f = 109 Hz

Q: An electron, which has a mass of 9.11 × 10-31 kg, moves with a speed of 0.750c. Find the magnitude…

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Q: If relativistic effects are to be less than 3%, then γ must be less than 1.03. At what relative…

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Q: Starting with the definitions of relativistic energy and momentum, show that E2 = p2c2 + m2c4

A: The relativistic energy is

Q: What is the momentum in MeV/c of an electron with a kinetic energy of 2.00 MeV?

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Q: In a lab, two electrons A and B are emitted in opposite directions with velocities +0.6c and -0.7c,…

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Q: A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a…

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Q: A tuning fork has a frequency of 800 Hz and hence a period of 1.25 × 10 −3 s. If the tuning fork is…

A: The given values are, f=800 HzT=1.25×10-3 sv=0.690c

Q: What is the speed of a particle whose momentum is mc?

A: We know that, relativistic momentum is, p=γmv   It is given that, the particle's relativistic…

Q: At what speed is a particle’s momentum twice its Newtonian value?

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Q: If relativistic effects are to be less than 3%, then y must be less that 1.03. At what relative…

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Q: A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a…

A: Since there are multiple sub parts posted, we will answer the first three sub parts. a) The equation…

Q: At what speed (in m/s) is the magnitude of a particle's relativistic momentum 20.8% larger than its…

A: Relativistic momentum p is classical momentum multiplied by the relativistic factor γ. p = γmu where…

Q: An elementary particle of mass 9.5 x 10-27 kg is moving at speed 9 x 107 m/s. (A) Its relativistic…

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Q: Pls help ASAP

A: speed (v) = 2.7×108 msLifetime at rest (To) = 2.60×10-8 seconds

Q: Suppose a spacecraft of mass 17000 kg is accelerated to 0.200 c. How much kinetic energy would it…

A: Given:- Mass(m)=17000 kg Velocity (V)=0.20 c Now, The relativistic kinetic energy of the particle.…

Q: Is the relativistic Doppler effect valid only for light waves? Can you think of another situation in…

A: The relativistic Doppler effect of light is the variation in the frequency of a light wave when the…

Q: A golf ball travels with a speed of 90.0 m/s. By what fraction does its relativistic momentum…

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Q: The proper mean lifetime of a muon is 2.2 × 10–6 s. A beam of muons is moving with speed 0.6c…

A: Proper lifetime = 2.2 *10-6SecUsing relativistic formula for time t = to/1 - (v/c)2t = 2.2 *10-6…

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.