4. [#224] Artificial gravity a of Science fiction writers imagine a ship in deep space, accelerating at a constant 9.8 m.s 2, which gives the travellers a sensation similar to the weight they feel on the Earth, where falling objects accelerate at g = 9.8 m.s ?. Starting from rest (and ignoring effects due to special relativity), how long does it take such a ship to accelerate to 0.1 times the speed of light c (recalling that c= 3.0*10 m.s ), and how far does it travel during that time? (Note: 0.1 has only 1 sig fig!) Answer: The ship travels for and travels a distance of 4 days, 5 x 10* km 40 days, 5 x 104 km 40 days, 5 x 1010 km O 4 days, 5 x 104 km

B8] This question concerns two inertial frames S and S' with origins coinciding at t = t' = 0, and a set of events taking place along the x-axis, which defines the direction of relative motion. -8 a) The coordinates of event A in frame S are x = 12 m and t = 8x10 s. If the coordinates of this event in frame S' are x' = -3 m and t' = 7 x 10- s, show that the y factor for transformations between S and S' is 5/4. b) Events B and C take place in S' at a time t' = 6 × 10-* s at x' = 1 m and x' = 2 m respectively. What is their spatial separation in frame S? %3D -8- c) Event D takes place in S' at t' = 3 x 10 s and x' = 1 m. What is the time difference between events B and D in S? d) Is it possible for events A and D to take place at the same time in the frame of an observer moving along the x-axis?

24. A person in a spaceship passing Earth observes her own heart rate to be 75 beats / minute and her spaceship to be 60 m long. A person on Earth observes the spaceship person's heart rate to be 45 beats / minute and her spaceship to be long. A.36 m B. 48 m C. 60 m D. 75 m E. 100 m

6. One of the potentially confusing things about special relativity is that it shows us that the time measured between two events depends upon your inertial frame of reference. In particular, two events that appear to be simultaneous in one inertial frame may be measured to occur at different times in a different inertial frame. Even more interesting is that Event 1 might occur either before or after (or at the same time as) Event 2, depending upon your reference frame! The proper interpretation of these facts is to say that nothing in physics forces two simultaneous events in one frame to be simultaneous in any other frame. However, what about the order of events when Event 1 CAUSES Event 2? For example, let's consider two events from a game of pool: 1) A cue ball, traveling at 10 m/s, hits the eight ball (of mass equal to the cue ball). An elastic collision transfers all the linear momentum of the cue ball to the eight ball. 2) 0.1 seconds later, the eight ball sinks in a corner…

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9. An astronomer on earth observes two spacecraft moving away from each other along an axis that passes through the earth. The astronomer measures the speed of each spacecraft to be 0.875c relative to the earth. At what speed are the spacecrafts moving apart relative to each other? a) 0.496c b) 0.467c c) 1.750c d) 0.143c e) 0.991c 10. How far apart must two objects on the moon be to be resolved by a telescope which has a 7.80-m diameter mirror? The wavelength of the light used is A610 nm, and the distance to the moon to be 3.80 x 105 km. a) 24.4 m b) 29.7 m c) 36.3 m d) 72.5 m e) 12.2 m 11. A converging lens with a focal length of (f₁ = 32.0 cm) is placed 42.0 cm to the left of a diverging lens with a focal length of (f2 = -25.5 cm). An object is placed 40.0 cm to the left of the converging lens. What is the location of the image produced by the combination of lenses? a) 32.5 cm to the right of the diverging lens b) 32.5 cm to the left of the diverging lens c) 160 cm to the left of the…