hw02.pdf - Physics 5110 Spring 2020 Homework#2 Due in class Friday January 24th 1 Convert the following to units in which c = 1 expressing everything in

hw02.pdf - Physics 5110 Spring 2020 Homework#2 Due in class...

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Physics 5110, Spring 2020 Homework #2 Due in class Friday January 24 th 1. Convert the following to units in which c = 1, expressing everything in terms of m and kg: (a) Power output of 100 W (b) Planck’s constant ¯ h = 1 . 05 × 10 34 J s. (c) Momentum of a car, = 3 × 10 4 kg m/s. 2. Convert the following from c = 1 (or “natural”) units to S.I. units. (a) A pressure of 10 19 kg/m 3 . (b) A time t = 10 18 m. (c) An acceleration of 10 m 1 . 3. Derive relativistic length contraction, using the figure below and the invariance of the “in- terval” Δ s 2 = (Δ t ) 2 - x ) 2 . The figure shows the world lines of the rear and front of a rod of length (at rest) L , moving with speed v in the positive x -direction relative to observer O . The rod is at rest in the O ( x , t ) coordinate system. (a) Start by using the invariance of the interval to find x C in terms of L and v . Remember that t C = vx C . (b) Now, using the fact that line BC has slope x C - x B t C - t B = v solve for X B , the length of the rod as seen by observer O .
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4. Show, by direct substitution, that the
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Unformatted text preview: Lorentz Transformation Equations Δx = γ (Δ x ′ + v Δ t ′ ) Δ t = γ parenleftbiggΔ t ′+ v c 2 Δ x′ parenrightbigg are equivalent to the principle of Invariance of the Interval in Special Relativity: (Δ s )2 = c 2 (Δ t ) 2- (Δ x )2 = c 2 (Δ t′ ) 2-(Δ x ′ ) 2 Assume that the origins of systems O and O ′ coincide at t= t ′= 0.5. Consider the decay, at rest, of the π− meson into a μ −particle (“muon”) and a neutrinoν . The rest mass of the π− is 140 MeV/c 2 , the rest mass of the μ − is 105.7 MeV/c2 ,and we may regard the neutrino as massless. The average proper lifetime of the muon is 2 .20 ×10 − 6 seconds. (a) Calculate the momentum of the μ −and ν . (b) Calculate the kinetic energy of the μ − and ν . (c) Calculate the speed of the muon. (d) How far in the lab, on average, will theμ − travel before decaying?...
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