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- Question : 1-1 - F =
- Question : 1-3 - IN THE REST FRAME: In an elastic collision energy and momentum are conserved. jji=m1vli+m2v2i=(03kg)(5 m/s) + (0.2kg)(-3 m/s) = 0.9 kg m/s Pt=m1vli+m2v2i This equation has two unknowns, therefore, apply the conservation of kinetic energy Ei =E{ =
- Question : 1-5 - This is a case of dilation. T = yT in this problem with the proper time T = T0 in this case T = 2T0, v = \ 1
- Question : 1-7 - The problem is solved by using time dilation. This is also a case of v
- Question : 1-9 - L - ^ ^earth _ ^earth - ^ 2lV2 , L', the proper length so Learth =L = L[l -(0.9)2 ] 1/2 = 0.436L.
- Question : 1-11 - At = yAt' At = At' A
- Question : 1-13 - (b) (a) T=yr'=[l-(0.95)2 ] 1/2(2.2/zs) = 7.05//s Af d 3xl0 3 m ,
- Question : 1-15 - (a) For a receding source we replace v by
- Question : 1-16 - (b) (c) From the relations f =
- Question : 1-17 - (a) Galaxy A is approaching and as a consequence it exhibits blue shifted radiation. From 2- = 0.198. Galaxy 7, 21 u - fi -^source "~o c I2 + A2 "" source T ""obs Example 1.6, p=- = |ource 2
- Question : 1-19 - KjM = -u
- Question : 1-21 - u'x = , . - . , l-uxv/c2 l-(0.50c)(0.80c)/c2 =-0.50c
- Question : 1-23 - (a) Let event 1 have coordinates x^ - yx = Zj = fj = 0 and event 2 have coordinates x2 =100 mm, y2 =z 2 = t2 =0.1n S', x^ = y(x1 -vt1) = Q, y{ =ya =0, zj =zx =0,and ..2 "T1 / 2 and so y = [l -(0.70)2 ]"1/2 = 1.40. In t{ = rh- rn = 0,with ysystemS', x'2 = y(x2-vt2) = l'i0 m, y2 =z 2 =0,and t'2 = 7 h -\-j:\X2 (1.4)(-0.70)(100 m) = -0.33//s. (b) (c) 3.00xl08 m/s Ax' = x 2 -;ti=140m Events are not simultaneous in S', event 2 occurs 0.33 jus earlier than event 1.
- Question : 1-25 - mGM mv 2 We find Carpenter's speed: GM l1 ' 2 R + h. (6.67x10"" X5.98xlOM ) 6.37 xl06 +0.16xl06 1/2 = 7.82 km/s. 2x(R + h) 2^6.53 xlO6 ) , Then the period of one orbit is T = =^ '- =
- Question : 1-27 - For the pion to travel 10 m in time At in our frame, 10 m = vAt = v{yAt') = u(26 x 10"9 s) s) -1/2 (3.85xl08 m/s)" c 2 1.46xlO17 m2 / s 2 = u 2 (l + 1.64) v = 2.37xl08 m/s = 0.789c
- Question : 1-29 - (a) (b) A spaceship, reference frame S', moves at speed v relative to the Earth, whose reference frame is S. The space ship then launches a shuttle craft with velocity v in the forward direction. The pilot of the shuttle craft then fires a probe with velocity v in the forward direction. Use the relativistic compounding of velocities as well as its inverse transformation: u'=- ur-v -, and its inverse u = - ur + v .The above i-Mc 2 )
- Question : 1-31 - In this case, the proper time is T0 (the time measured by the students using a clock at rest relative to them). The dilated time measured by the professor is: At = y T0 where At = T +t. Here T is the time she waits before sending a signal and t is the time required for the signal to reach the students. Thus we have: T +t = yT0. To determine travel time t, realize that the distance the students will have moved beyond the professor before the signal reaches them is: d v d = v(T +t). The time required for the signal to travel this distance is: t =
- Question : 1-33 - (a) We in the spaceship moving past the hermit do not calculate the explosions to be simultaneous. We measure the distance we have traveled from the Sun as L = LpJl-(-) = (6.00 ly)Vl -(0.800)2 = 3.60 ly. We see the Sun flying away from us at 0.800c while the light from the Sun approaches at 1.00c. Thus, the gap between the Sun and its blast wave has opened at 1.80c, and the time we calculate to have elapsed since the Sun exploded is
- Question : 1-35 - In the Earth frame, Speedo's trip lasts for a time At =
- Question : 1-37 - Einstein's reasoning about lightning striking the ends of a train shows that the moving observer sees the event toward which she is moving, event B, as occurring first. We may take the S-frame coordinates of the events as (x = 0, y = 0, z = 0, t = 0)and(x = 100 m, y = 0, z = 0, f = 0). Then the coordinates in S' are given by Equations 1.23 to 1.27. Event A is at (x' = 0, y' = 0,z' = 0,t' = 0). The time of event B is: t' = r\t 1 vn 0.8l 0-^(10 0 m) | = 1.667| 80 m 3x10s m/s = -4.44xl0""7 s. The time elapsing before A occurs is 444 ns.
- Question : 1-39 - (a) For the satellite 2, f = ma '

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