Determine the escape velocity (minimum speed of an object/body) for planet earth.Start from the definition of Gravitational forceGM mF =and Workw= S Fdzwhere G is the universal gravitational constant, Me is the mass of earth, m is the mass of the object/body, and z is the distancebetween Earth and object/body (the same as the radius of earth).

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Answered: an öbject/bödy) för planet éarth. the…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 51P

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Question 3 a. A space craft achieved a maximum speed of 125,000 km/h on its way to photograph Mars. Beyond what distance from the Sun is this speed sufficient to escape the solar system? b. Consider a large massive spherical shell object. With all of its mass M is distributed at its radius R (shown in the figure). Draw a schematic granh of gravitational force and corresponding Page 1 of 2 gravitational potential energy experienced by another object m at a distance r, where the distance varies as, r → 0 to r 0o. Figure 2: Question 3(b) Two masses system
GMmr. Find work done by a rocket escaping the gravity field of a planet by integrating a. Show steps using a limit for the improper integral and set the result equal to kinetic energy of escape velocity mus to find a formula for escape velocity. b. Given G= G = 6.67 x10,M= 5.97 x 10* and r, = 6,680,000 compute escape velocity at an altitude of 300 km about the surface of the Earth. Write answer in meters/sec and miles/hour.
The following question is referring to the application gravitational potential energy in physics problems and calculation of quantities related to planetary or satellite motion. Solve for the unknown quantities and round-off your final answers in the nearest hundredths. A10,000-kilogram satellite is pulled toward Planet A, with a radius of 65,000 kilometers and a mass of 6.7 x 1033. When the satellite is 2,000 kilometers from the planet’s surface, what is the satellite’s acceleration (providing that its engines are turned off)?
A satellite of mass 500 kg us in an approximately cultist orbit around Earth with a period of 1.5 hours. What is its height h above the Earth’s surface and what is the gravitational potential energy?
The relationship between work done by a force resultant and change in particle kinetic energy can be derived from Newton's second law expression Fr = where ma, by dotting both sides of the equation by v. V, is the velocity of the particle or body mass-center. O True O False
In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work W applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 993 kg and 243 km. Earth's mass and radius are 5.98 × 1024 kg and 6370 km.
calculate the energy required to send a 1 kg object from the surface of Earth to the satellite located 42.16*10^6m from the center of the Earth. Assume the location from which the object is being launched is 6.37*10^6m from the center. a. Use the object's weight at the surface of the earth (g=9.8) to find Newton's proportional constant k for this object. b. Write a definite integral that calculates the energy required to send the object to orbit, then use the Fundamental theorem of calculus to calculate the energy. c. Write t he formula for a Reimann sum that is guaranteed to estimate the energy required to send the object to orbit, accurate with 10^5 J. d. calculate the fraction of the object's total distance traveled at which half of the total required energy is expended.
Questions 3 and 4 below refer to the universal gravitational potential energy function U(r) for a planet with mass M and radius R, which is shown in the figure below. R 3. If a projectile is launched from the surface of the planet with a speed equal to the planets escape speed, how much mechanical energy does it have when it reaches a distance r = ∞ ? (n I I I Distance from center of planet, r 4. If an astronaut who is orbiting the planet at a radius of 3R wants to move their orbit to a radius of 2R, what direction should they fire their thrusters? (and how is your answer supported by the given graph of U(r) ?)
GPE-1 The planet Mars has a mass of 6.39×1023 kilograms (kg) and a radius of 3390 kilometers (km). A satellite is in orbit around Mars, at a height of 4250 km above the surface. You are on the surface of Mars, and you want to deliver a package to the satellite. What is the minimum initial speed (v) the package needs to be launched upwards in order to make it to the satellite? Assume that mechanical energy is conserved. Give your answer in units of km/s. The universal gravitational constant is 6.67×10-11 N m²/kg². GPE-2 Calculate the escape velocity of Mars using the data above. GPE-3 Consider a 1550 kg satellite in circular orbit around Mars with an altitude of 105 km. You want to move the satellite to a circular orbit with an altitude of 905 km. How much work must be done on the satellite (in units of Joules) in order to achieve this? 4250 km V = ?

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