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Unformatted text preview: Homework 12 Chapter 29 SOLUTIONS QUESTION 1 How fast does a 220m spaceship move relative to an observer who measures the ship's length to be 150 m? SOLUTIONS Frames: Ship (S') and Observer (S) Proper Length measured in S': L ' = L = 220 m In frame S: L = 150 m = L / L = L 1 v 2 c 2 1 v 2 c 2 = L L 2 v c = 1 L 2 L 2 = 1 150 m 2 220 m 2 = 0.73 v = 0.73 c QUESTION 2 Find the work that must be done to accelerate a proton from rest to a speed of 0.9 c. SOLUTION Use the Work Kinetic Energy Theorem: W = K And the relativistic definition of Energy: E = m c 2 = K m c 2 E = E f E i = m c 2 K f m c 2 K i = K Then using the work K.E. theorem W = K = E = f m c 2 i m c 2 = f 1 m c 2 where i = 1 because v i = 0, and f = 1 1 v f 2 / c 2 = 1 1 0.9 2 = 2.294 so: W = (2.294 1) (1.673 x 1027 kg) (3.0 x 10 8 m/s) 2 W = 1.95 x 1010 J QUESTION 3 A proton moves with a speed of 0.99c, what is its (a) total energy, (b) rest energy, and (c) kinetic energy? (The mass of proton is 1.672 x 1027 kg.) SOLUTIONS (a) E = m o c 2 = 1 1 v 2 / c 2 = 1 1 0.99 2 = 7.0888 E = (7.0888) (1.672 x 1027 kg) (3.0 x 10 8 m/s) 2 E = 1.07 x 109 J (b) Rest Energy = m o c 2 = (1.672 x 1027 kg) (3.0 x 10 8 m/s) 2 E o = 1.50 x 1010 J (c) K = E m o c 2 = (1.07 x 109 J) (1.50 x 1010 J) K = 9.16 x 1010 J QUESTION 4 Electrons are accelerated from rest through a potential difference of 256 kV. What is the final speed predicted by (a) classical mechanics, (b) relativity.final speed predicted by (a) classical mechanics, (b) relativity....
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This note was uploaded on 07/02/2011 for the course PHYS 202 taught by Professor Warren during the Spring '09 term at Indiana.
 Spring '09
 WARREN
 Physics, Work

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