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- Time is not absolute, it depends on the speed and gravitational field present. The time measured will be slower when there is a large gravitational field present.
- When the clock is closer to the gravitational source slower the time measured. This effect is called gravitational time dilation.
- Gravitational time dilation is given by,
Here t is the change in time in the gravitationally influenced reference frame, t0 is the change in time in a reference frame an infinite distance from any mass (a "standard" hour), c is the speed of light, G is the gravitational constant, M is the mass of the object being approached, and r the distance from the object being approached
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- James (mass 81.0 kg) and Ramon (mass 57.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. Ramon pulls on the rope to give himself a speed of 1.10 m/s. What is James's speed? It must have the proper dimensions of speed.The mass of an electron is 9.11 x 10 ^-31 kg. The mass of a proton is 1.67 x 10 ^-27 kg. They are about 5.3×10^ −11 m apart in a hydrogen atom. What is the gravitational force between these two particles in the hydrogenatom?A beam of light is moving directly along the spaceship, but through an old-fashioned fiber optic cable. The speed of light in the cable is 0.6 times the speed of light in a vacuum. The spaceship is moving at 0.8 times the speed of light. What speed do you observe from the ground?
- Scientists in the laboratory create a uniform electric field Ē = 1.0 x 10°k [V/m] in a region of space where B = 0. What are the fields in the reference frame of a rocket travelling in the positive x direction at 1.0 × 106 [m/s]?Suppose Google wants to launch a surveillance satellite to invade the privacy of all their users. They need it to revolve around Earth 10.0 times a day for maximum invasive efficiency. a) Draw a free-body diagram b) What should the radius of its orbit be if we neglect the presence of the Moon? c) How fast is it traveling? G = 6.67 * 10 ^-11 N*m^2/kg^2 M earth = 5.97 * 10^24 kgA spaceship travels from the Earth to a star 13 light years away (as measured in the Earth’s frame). An astronaut on the ship says that the trip takes 16 years. What is the speed of the ship relative to the earth in m/s?
- Chapter 37, Problem 015 The center of our Milky Way galaxy is about 24000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 24000 ly (measured in the Galaxy frame) in exactly 27 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number Units (b) Number UnitsWhat is the discrepancy (according to an observer on the surface of the Earth), due to the general relativistic (i.e. gravity-based) time dilation, between the clock on a particular communications satellite and a clock on the surface of the Earth after 1 day. Ignore the sign of the discrepancy. Orbital Radius of satellite = 4.0 x 10 m 6.37 x 106 m %3D Radius of the Earth = Mass of Earth = 5.97 x 1024 kg Gravitational Constant = 6.67 x 10-11m3 kg-1 s-2 Speed of light =3 x 108 m/s %3DConsider an electron orbiting around a proton with an orbital radius of R=8.48⋅10−10R=8.48⋅10-10 m. What is the orbital frequency of the electron motion? Use me=9.11×10−31me=9.11×10-31 kg, e=1.6×10−19e=1.6×10-19 C, and k=9×109k=9×109 Nm2/C2. The frequency, f0 = Units . By how much would this frequency increase (assume the same orbital radius) if an external magnetic field of B = 0.5 T is applied to the system along the the electron axis of rotation? The increase in the frequency , Δf = Units .
- The energy to mové a rocket (mass m) nfinitely far from the Earth (Radius R and mass M) E = jGMma 1 E = x? 2 is What escape velocity at liftoff gives an energy that equals E. RConsider a 5.75 m long sports car going past you at great speed. How fast would it have to be going past you in order for it to appear only 5.25 m long? Give you answer as a ratio of the velocity to the speed of light c. v/c=A star is 12.2 ly (light-years) from Earth. HINT (a) At what constant speed (in m/s) must a spacecraft travel on its journey to the star so that the Earth–star distance measured by an astronaut onboard the spacecraft is 4.36 ly? m/s (b) What is the journey's travel time in years as measured by a person on Earth? NO SCIENTIFIC NOTATION ANSWERS THANK YOU