How much work is required to lift a 800-kg satellite to an altitude of 3 · 106 m above the surface of the Earth? The gravitational force is F = GMm/r², where M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the Earth's center. The radius of the Earth is 6.4 · 106 m, its mass is 6 · 1024 kg, and in these units the gravitational constant, G, is 6.67. 10-¹¹. Work =
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- The mass of an object is an unchanging property of an object. It is a fundamental measure of the amount of matter (stuff) present in the object. The SI unit of mass is kilogram (kgkg). [1 kgkg=2.2 lblb on Earth] Whereas, the weight is the force, the pull of gravity, acting on the object by the nearest most massive body such as Earth. The more massive the body, the greater is its force of gravitation. The mass of an object remains the same no matter where it is located whereas the weight depends entirely upon its location since the value of gravity varies from place to place. The relative gravity at different celestial location compared to Earth are listed below: Location Relative Gravity Earth 1.00 Outer space 0 Earth's moon 0.17 Mars 0.38 Jupiter 2.36 Saturn 0.92 Part A Consider an object of mass 45 kgkg. Rank the weight of this object at the following locations. Rank from heaviest to lightest. To rank items as equivalent, overlap them. Part B What would be…A planet of mass 7.00×1024 kg is at location (-3.75×10¹¹, 6.25×10¹¹, 0) m. A star of mass 8.00×1030 kg is at location (5.00×10¹¹, -4.25×10¹¹, 0) m. What is the force exerted on the planet by the star? (It will probably be helpful to draw a diagram, including the relevant vectors.) on planet =An object of mass m is dropped from height h above a planet of mass M and radius R. Find an expression for the object's speed as it hits the ground. Express your answer in terms of the variables m, M, h, R, and gravitational constant G.
- In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?The magnitude F (in newtons) of a force F and the magnitude G (in newtons) of a force G satisfy the vector equation 2Fi-3Fj+2Gi+2Gj-3i=0 where i and j are the Cartesian unit vectors. What is the value of F? 9 10 3 O 5/60/5 10 06The Moon has a mass 7.35 x 1022 kg of and a radius of 1740 km. Air resistance can be neglected on the Moon. G = 6.67 x 10-11 m3 kg-1 s-2 is the universal gravitational constant. (a) If a ball is launched upwards from the surface of the moon with an initial speed of 1.15 km/s, what height maximum height above the surface of the moon will it reach? Give your answer in kilometers. (b) What is the escape speed of the moon? Give your answer in km/s.
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- A new planet named Vulcan has been discovered. Vulcan is a rather large planet with a radius twice that of Earth and a mass three times that of Earth. An astronaut has a mass of 60.0 kg and weighs about 132 lbs. on Earth. If the astronaut is on the planet Vulcan, what is her weight? The following numerical values may be helpful in this question. G = 6.67 ∙10-11 N∙m2/ kg2 Earth’s mass = 5.98 · 1024 kilograms g = 9.80 m/sec2 1 kilometer = 1000 metersThe gravitational acceleration constant gx on Planet X can be approximated by determining the acceleration of an object assuming Newton's Law of Universal Gravitation. If gx = 3.8 m/s^2 , G = 6.7 x 10^-11 Nm^2/kg^2, and Planet X's radius is 4000 km, what is the approximate mass of planet X? Give answer in kg.A sphere of copper has a radius of 50.0 cm and a mass of 4690 kg. A sphere of unknown metal has a radius of 30.0 cm. The surfaces of the spheres are 20.0 cm apart. The force of gravitational attraction between the two spheres is 0.372 mN. What is the mass of the unknown metal?