The nonrelativistic expression for the momentum of a particle,p = mv, can be used if v <<c. For what speed does the use of this formula give an error in the momentum of (a) 1.00% and (b) 10.0%? (a) Show that a potential difference of 1.02 × 106 V would be sufficient to give an electron a speed equal to twice the speed of light if Newtonian mechanics remained valid at high speeds. (b) What speed would an electron actually acquire in falling through a potential difference equal to 1.02 × 106 V?

Q: 1. A rocket ship has a mass of 1.50 x 105 kg. Its relativistic momentum is 3.00 x 1012 How fast is…

A: Given data: Rest mass of rocket ship is, mo=1.50×105 kg. Relativistic momentum of rocket ship is,…

Q: A particle travels at 1.90 x 108 m/s and lives 2.10 x 10-8 s when at rest relative to an observer.…

A: The decay time in the rest frame is, The particle’s velocity is,

Q: Calculate the relativistic momentum of a particle of mass 1.76x10 kinetic energy is equal to three…

A: Given,

Q: If a spaceship, approaching the Earth at 0.190c, sends a message capsule toward the Earth at 0.390c…

A:

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

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Q: A supertrain of proper length 94 m travels at a speed of 0.93c as it passes through a tunnel having…

A: The Lorentz transformation is the contraction of length l of any object with respect to the moving…

Q: It is said that Einstein, in his teenage years, asked the question, “What would I see in a mirror if…

A: The theory of relativity says that all experiments will give the same results in all inertial frames…

Q: Calculate the interval ∆s2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

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Q: An inertial observer finds that the relativistic momentum of a particle is 1.55 times larger than…

A:

Q: what will be the velocity of light as seen by an observer at rest?

A: according to Galileo's classical view of relativity light is treated as all other things.

Q: ?⃗ =?⃗ +?⃗ ?v→=w→+v→F

A: As dog moving forward with velocity of 2 m/s forward and also spider moving in same direction with…

Q: Compute the kinetic energy of a proton (mass 1.67 * 10-27 kg) using both the nonrelativistic and…

A: Given data The mass of the proton is m=1.67×10-27 kg The first speed of proton is v1=8.00×107 m/s…

Q: A rod is to move at constant speed v along the x axis of reference frame S, with the rod's length…

A: La = 1.5 m v = 0.94 c L at β having value 0 = 45×La= 0.8×1.5 m = 1.2 m

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: At what speed is the magnitude of the relativistic momentum of a particle five times the magnitude…

A: We know that the momentum of a particle of mass m moving with velocity v is given by  p = mv…

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: An electron with an inertial energy of 0.511MeV is moving with a velocity v = 0.6c relative to an…

A: Given, Internal energy = 0.511 MeV Velocity v = 0.6c

Q: A particle has a rest mass of 7.15×10−27 kg and a momentum of 5.75×10−18 kg·m/s. Determine the total…

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Q: A rocket cruises past a laboratory at 0.400 x 10° m/s in the positive I-direction just as a proton…

A:

Q: Suppose there is someone in a spaceship ̄O moving at some velocityνrelative to anobserver O. The…

A: Given,Spaceship O¯ which is moving at some velocity, v relative to an observer OThe time interval…

Q: The neutron has a mass of 1.67 ✕ 10−27 kg. Consider a neutron moving with a speed of 0.910c. (Enter…

A: Given:- The proton has a mass m = 1.67 ✕ 10−27 kg a proton moving with a speed of 0.910c

Q: If a m = 81.1 kg person were traveling at v = 0.980c, where c is the speed of light, what would be…

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Q: The origins of two frames coincide at t = t' = 0 and the relative speed is 0.956c. Two…

A: If the relative speed between S and S' frame is v then the Lorentz transformation gives the…

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: If an object at rest in a given frame has no potential energy, then it has a)a rest energy of mc2…

A: Potential energy is the energy of an object due to its position with respect to other objects,…

Q: The origins of the two frames coincide at t = t’ = 0 and the relative speed is 0.990 c. Two…

A:

Q: Determine the total relativistic energy E of the particle.   Find the ratio of the particle's…

A: Given:- mo=7.15×10^−27 kg p= 5.56×10^−18 kg·m/s We know that the relation between relativistic…

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: A moving spaceship is measured by a stationary observer to have a length that is four-fifths of its…

A: Given, A moving spaceship is measured by a stationary observer to have a length that is four-fifths…

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

A:

Q: The formula for length contraction gives the length of an interval on a ruler moving with velocity v…

A: Given: The formula for length contraction gives the length of an interval on a ruler moving with…

Q: At what speed, in m/s,  would a moving clock lose 1.1 ns in 1.0 day according to experimenters on…

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Q: At the instant that a clock standing next to you reads t = 1.0 μs, you look at a second clock, 300 m…

A: The expression for find time taken by the light to reach the given distance is t=dv

Q: At what speed does the classical momentum, p=mv, give an error, when compared with the relativistic…

A:

Q: Ignoring relativistic effects, what is the speed of an electron (m=9.11x10-31 kg) that has been…

A: Given Mass of the electron, m=9.11×10-31kg Potential difference, E=80.0kV Kinetic energy:  is a form…

Q: Two identical particles P and Q of rest mass m,, are moving with velocities 5c 2c and 19 in…

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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: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: a) The equation to determine the life time of the moving muon is,

Q: kinetic energy for an electron

A:

Q: A particle has a rest energy of 4.31×10−13 J and a total energy of 8.33×10−13 J. Calculate the…

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

A:

Q: The positive muon (?+), an unstable particle, lives on average 2.20?10−16 ? (measured in its own…

A: Given: A positivive mu+ Time ∆to = 2.20 × 10-16 s u = 0.900c To determine: Average lifetime and…

Q: Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0, t1 = 1…

A: Einstein with his special theory of relativity brought in an entirely new understanding of the world…

Q: A projectile was launched from a certain location on earth and landed a certain distance away. An…

A:

Q: Show that the energy–momentum relationship as shown, E2 = p2c2 +(mc2)2, follows from the expressions…

A: The given expression is,  E = γmc2taking the square, E2 = γmc22 E2 = γ2m2c4

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.