Verify that the relativistic force law dr dp" = qF",u" (v summation implied), %D where E, E, E. cB. -cB, Fa E, -cB. cB, E. cB, -cB, yields the relativistic Lorentz force equation d(ymv) =q(E+v×B) %3D dt when evaluated on the space components a =1,2,3.
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For i=1,2,3,
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- Your video analysis of the motion of a marble gives it position in frame 23 as (x23, Y23) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, 324) = (0.122 m, 0.112 m). You esti- mate that you can measure the r and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use 8(At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 4. The value of the momentum component p = mv, and its uncertainty, 5. The value of the momentum component py = muy and its uncertainty, and 6. The value of the kinetic energy K = mv² = m(v² + v²) and its uncertainty.Derive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.measured by this observer to be 10 times longer than its lifetime when at rest relative to the observer? 3. The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.9 x 108m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? 4. A computer in a laboratory requires 2.50 us to make a certain calcu- lation, as measured by a scientist in the lab. To someone moving past the lab at a relative speed of 0.995c, how long will the same cal- culation take? 5. The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as V1-v²/c² times the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 95 percent the speed of light? 6. If an electron is speeding down the two-mile-long Stanford Linear Accelerator at 99.98 percent the speed of light,…
- According to the formula for y, what would happen if the motion between the two frames was greater than the speed of light? Oy would be negative. Oy would be imaginary. O y would be one. O Nothing. O y would be infinity. Oy would be zero.dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.An alpha particle has a mass of 6.4E-27kg is propagating at relativistic speeds and has an energy of 6.48GeV (so 6.48E9 eV) What is the speed of the particle, expressed in units of c, c being the speed of light. Keep three significant digits.
- In a parallel universe, the quantity t has the value 3.14049... Express a in that universe to (a) four significant figures: (b) five significant figures:Needs Complete typed solution with 100 % accuracy.Mass of a proton: 1.007825 u; Mass of a neutron: 1.008665 u 1 The lifetime of a free neutron is 887 s. If a neutron moves with a speed 2.9 × 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? What is this an example of? 2. (a) What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7 x 10-3¹ kg? (b) How many MeV's of energy is this? 3. The rest energy of a particular subatomic particle is 1200 MeV. If this particle is traveling at 90% the speed of light, what is its total relativistic energy?
- A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.Does a cylinder surface have "intrinsic' curvature? i.e if you stay on the cylindrical surface and make geometric measurement, will there be devia- tions from euclidean geometry?