ch37 - 1. From the time dilation equation t = t0 (where t0...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
1. From the time dilation equation t = γ t 0 (where t 0 is the proper time interval, γβ =− 11 2 /, and β = v / c ), we obtain F H G I K J 1 0 2 t t . The proper time interval is measured by a clock at rest relative to the muon. Specifically, t 0 = 2.2000 µ s. We are also told that Earth observers (measuring the decays of moving muons) find t = 16.000 s. Therefore, 2 2.2000 s 1 0.99050. 16.000 s §· = ¨¸ ©¹
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. (a) We find β from γβ =− 11 2 /: () 2 2 1 1 0.14037076. 1.0100000 β γ = (b) Similarly, 2 1 10.000000 0.99498744. = (c) In this case, 2 1 100.00000 0.99995000. = (d) The result is 2 1 1000.0000 0.99999950. =
Background image of page 2
3. We solve the time dilation equation for the time elapsed (as measured by Earth observers): t t = 0 2 1 0 9990 (. ) where t 0 = 120 y. This yields t = 2684 y 3 2.68 10 y. ≈×
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. Due to the time-dilation effect, the time between initial and final ages for the daughter is longer than the four years experienced by her father: t f daughter t i daughter = γ (4.000 y) where γ is Lorentz factor (Eq. 37-8). Letting T denote the age of the father, then the conditions of the problem require T i = t i daughter + 20.00 y and T f = t f daughter – 20.00 y . Since T f T i = 4.000 y, then these three equations combine to give a single condition from which γ can be determined (and consequently v): 44 = γ 4 ¡ γ = 11 ¡ β = 2 30 11 =0.9959.
Background image of page 4
5 . In the laboratory, it travels a distance d = 0.00105 m = vt , where v = 0.992 c and t is the time measured on the laboratory clocks. We can use Eq. 37-7 to relate t to the proper lifetime of the particle t 0 : () 2 2 0 0 2 1 1 0.992 0.992 1/ t vd tt t cc vc §· = ¡ =− = ¨¸ ©¹ which yields t 0 = 4.46 × 10 –13 s = 0.446 ps.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6. From the value of t in the graph when β = 0, we infer than t o in Eq. 37-9 is 8.0 s. Thus, that equation (which describes the curve in Fig. 37-23) becomes t = t o 1 - ( v / c ) 2 = 8.0 s 1 − β 2 If we set β = 0.98 in this expression, we obtain approximately 40 s for t .
Background image of page 6
7. (a) The round-trip (discounting the time needed to “turn around”) should be one year according to the clock you are carrying (this is your proper time interval t 0 ) and 1000 years according to the clocks on Earth which measure t . We solve Eq. 37-7 for β : 2 2 0 1y 1 1 0.99999950. 1000y t t §· =− = ¨¸ ©¹ (b) The equations do not show a dependence on acceleration (or on the direction of the velocity vector), which suggests that a circular journey (with its constant magnitude centripetal acceleration) would give the same result (if the speed is the same) as the one described in the problem. A more careful argument can be given to support this, but it should be admitted that this is a fairly subtle question which has occasionally precipitated debates among professional physicists.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8. The contracted length of the tube would be LL =− = = 0 22 1 300 1 0 999987 0 0153 β .. . mm . b g
Background image of page 8
9. (a) The rest length L 0 = 130 m of the spaceship and its length L as measured by the timing station are related by Eq. 37-13. Therefore, L =− = 130 1 0 740 87 4 2 mm .
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This homework help was uploaded on 10/01/2007 for the course PHYS 2213 taught by Professor Perelstein,m during the Fall '07 term at Cornell University (Engineering School).

Page1 / 95

ch37 - 1. From the time dilation equation t = t0 (where t0...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online