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Chapter 26 - CHAPTER 26 Quick Quizzes 1(b Assuming that...

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C HAPTER 26 Quick Quizzes 1. (b). Assuming that your on-duty time was kept on Earth, you will be pleasantly surprised with a large paycheck. Less time will have passed for you in your frame of reference than for your employer back on Earth. 2. The answers to both of these questions is no . Both your clothing and your sleeping cabin are at rest in your reference frame, thus, they will have their proper length. There will be no change in measured lengths of objects within your spacecraft. Another observer, on a spacecraft traveling at a high speed relative to yours, will measure you as thinner (if your body is oriented in a direction perpendicular to the direction of motion relative to him) or will claim that you are able to fit into a shorter sleeping cabin (if your body is oriented in a direction parallel to your direction of travel relative to the other observer). 3. (a), (e). The outgoing rocket will appear to have a shorter length and a slower clock. The answers are the same for the incoming rocket. Length contraction and time dilation depend only on the magnitude of the relative velocity, not on the direction. 4. (a) False (b) False (c) True (d) False A reflected photon does exert a force on the surface. Although a photon has zero mass, a photon does carry momentum. When it reflects from a surface, there is a change in the momentum, just like the change in momentum of a ball bouncing off a wall. According to the momentum interpretation of Newton’s second law, a change in momentum results in a force on the surface. This concept is used in theoretical studies of space sailing. These studies propose building nonpowered spacecraft with huge reflective sails oriented perpendicularly to the rays from the Sun. The large number of photons from the Sun reflecting from the surface of the sail will exert a force which, although small, will provide a continuous acceleration. This would allow the spacecraft to travel to other planets without fuel. 5. (a). The downstairs clock runs more slowly because it is closer to the Earth and hence experiences a stronger gravitational field than the upstairs clock does. 327
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C H A P T E R 2 6 Problem Solutions 26.1 (a) As the plane flies from O to B along path I, ground air wind = + v v v gives m m 100 20.0 120 s s ground v = + = m s , and 3 200 10 m 120 m s O B ground L t v × = = = 3 1.67 10 s × v ground v wind v air For the plane following path II from O to A , ground air wind = + v v v with perpendicular to each other. The Pythagorean theorem then yields and ground wind v v 2 2 2 2 m m 100 20.0 98.0 s s ground air wind v v v = = = m s , and 3 200 10 m 98.0 m s O A ground L t v × = = = 3 2.04 10 s × v ground v wind v air (b) For the return flight along path I, ground air wind = + v v v gives m m 100 20.0 80.0 s s ground v = = m s , so 3 200 10 m 80.0 m s BO ground L t v × = = = 3 2.50 10 s × v ground v wind v air As the plane flies from A to O along path II, are again perpendicular to each other. The Pythagorean theorem gives and ground wind v v 2 2 m 98.0 s ground air wind v v v = = , and AO ground L t v = = 3 2.04 10 s × v ground v wind
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