410ahw8soln - HW#8—Solutions —Phys410—Fall 2011 Prof Ted Jacobson Room 4115(301)405-6020 www.physics.umd.edu/grt/taj/410a [email protected]

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Unformatted text preview: HW#8—Solutions —Phys410—Fall 2011 Prof. Ted Jacobson Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/410a/ [email protected] 15.12 ( Lorentz contraction ) Answer only (b) How long is the pipe as “seen” (better word would be “reckoned”, or even “defined”) by the pions, and how long does it take to pass the pions? Pions travel time to go a distance d at speed v is Δ t = d/v in the earth frame, and the proper time is Δ τ = Δ t/γ . In the pions frame, the pipe is moving at speed v = 0 . 8c for a time Δ τ , so between the time the front and back of the pipe pass a pion the pipe travels a distance d = v Δ τ = d/γ . This is the “Lorentz contracted” length of the pipe as defined in the pion frame. Numerically, γ = [1- (0 . 8) 2 ]- 1 / 2 = 5 / 3, so d = (3 / 5)36 = 21 . 6 meters, and Δ τ = d /v = 90 ns. 15.56 ( rest energy in chemical reaction ) (a) ∑ ( m i + T i ) = ∑ ( m f + T f ) = ⇒ ∑ m i- ∑ m f = T f- T i = 5 eV. (b) M tot , i = ∑ m i ≈ 36amu ≈ 36 × 931 . 5MeV = 33 . 5 GeV, so Δ M/M ≈ 1 . 5 × 10- 10 . (c) Δ M ≈ 1 . 5 × 10- 9 g. 15.57 ( rest energy in nuclear reaction ) The rest mass decrease is 0.0087 amu so the kinetic energy is (0 . 0087)(931 . 5) = 8 . 1 MeV, and (0 . 0087)(1 . 66 × 10- 27 kg)(3 × 10 8 m / s) 2 = 1 . 3 × 10- 12 J. 15.58 ( rest energy vs. kinetic energy ) (a) ( γ- 1) mc 2 = T = mc 2 = ⇒ γ = 2 = ⇒ v/c = √ 3 / 2....
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This note was uploaded on 12/29/2011 for the course PHYSICS 410 taught by Professor Jacobson during the Fall '11 term at Maryland.

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410ahw8soln - HW#8—Solutions —Phys410—Fall 2011 Prof Ted Jacobson Room 4115(301)405-6020 www.physics.umd.edu/grt/taj/410a [email protected]

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