Escape velocity and black holes The work required to launchan object from the surface of Earth to outer space is given byW = [F(x) dx, where R = 6370 km is the approximateradius of Earth, F(x) = GMm/x² is the gravitational forcebetween Earth and the object, G is the gravitational con-stant, M is the mass of Earth, m is the mass of the object, andGM = 4 × 1014 m²/s.a. Find the work required to launch an object in terms of m.b. What escape velocity v, is required to give the object a kineticenergy mv? equal to W?c. The French scientist Laplace anticipated the existence ofblack holes in the 18th century with the following argument:If a body has an escape velocity that equals or exceeds thespeed of light, c = 300,000 km/s, then light cannot escapethe body and it cannot be seen. Show that such a body hasa radius R s 2GM/c2. For Earth to be a black hole, whatwould its radius need to be?

Given: The radius (R) of the Earth is 6370 Km. The value of the GM is 4×1014 m3/s2. Introduction:…

Answered: Escape velocity and black holes The…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Diameter 139,820 km · Density 1326 kg/m3 · Gravity 24.79 m/s2 · Mass (1024kg) : 1898 · Escape Velocity (km/s):59.5 The H max= 71.40x10^6m T= 2400 sec or 40 min giving these info please help me solve the issue in the pic
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How to find Kinetic Energy? KE= 1/2mv1 2 m= 60 grams v1= 688.75
1 2. Preparations are under way for a spacecraft visit to the Alpha Centauri star system, 4.30- lightyears away Provisions are placed on board to allow for a trip of 8 years. a. What minimum speed must the spacecraft travel relative to Earth if the provisions are to last?
Washington, D.C., is located at about 750 W longitude and 380 N latitude. San Francisco is near 1270 W longitude and 380 N latitude. Estimate how many minutes later the Sun rises in San Francisco than inWashington, D. C. How far apart would you estimate these cities to be? Assume that the earth’s radius is 6400 km. One day has 1440 minutes and of course the earth rotates 360 degrees around its axis in one day
1. If a subatomic particle moves close to the speed of light. Its decay would occur ___? 2. A space explorer travels between asteroids that are 100 000 m apart. His/her space probe travels with constant speed of 0.8c=2.4x108 m/s. What is the time of the trip between asteroids measured by observer on one of the asteroids? Write your answer rounded to 2 decimal places in ms
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 kg
I Review I Constants I Periodic Table The position of a 55 g oscillating mass is given by T (t) = (1.7 cm) cos 13t, where t is in Part C seconds. Determine the spring constant. Express your answer in newtons per meter. Hνα ΑΣφ ? k = N/m Submit Request Answer Part D Determine the maximum speed. Express your answer in meters per second. Iνα ΑΣφ Umax = m/s Submit Request Answer
QUESTION 3 - The following equation refers to v-pendulum experiment: T4 = (44 L ki g²)(8 m4L/g² )d, where : L: length of the string (2 meters). T: pendulum periodic time d: distance between rods k: pendulum constant g: gravitational acceleration Given that the slope of the graph (T4,d) = -14.2 s4/m, and y-intercept = 13.5 s4, Find the value for g: 9.81 m/s2 O Can't be defined a- 8.51 m/s2 a 10.5 m/s²
A space probe with a diameter of 2.50m is moving past Saturn's moon Enceladus. An observational platform on Enceladus measures the shortest length of the ellipsoidal probe to be 1.25m. How fast is the probe moving relative to the moon? a) .999c b) .995c c) .957c d) .883c e) .866c
The sun generates energy through nuclear fusion, which converts mass intoenergy. If the sun radiates 3.8 × 1026 W of power, calculate the rate at which the sun loses mass (i.e., kg/s). _________×109kg/s ? Compare the energy produced per kg of fuel for the combustion of coal, d-d fusion and d-t fusion.d-d: __________ ×107 MJ/kg?d-t: ___________×108 MJ/kg ? The age of the sun has been estimated at 4.6 billion years. If it has radiatedenergy at the same rate throughout its lifetime, 3.8×1026 W and if its current mass is1.989×1030 kg, what fraction of its original mass has been lost _____________% ?
2. An alternative derivation of the mass-energy formula E, = moc² also given by Einstein, is based on the principle that the location of the center of mass (CM) of an isolated system cannot be changed by any process that occurs inside the system. The Figure below shows a rigid box of length L that rests on a frictionless surface; the mass M of the box is equally divided between its two ends. A burst of electromagnetic radiation of energy E, is emitted by one end of the box. According to classical physics, the radiation has the momentum p = "0%c , and when it is emitted, the box recoils with the speed v z Eo/ so that the total momentum of Mc the system remains zero. After a time t z L/c the radiation reaches the other end of the box and is absorbed there, which brings the box to a stop after having moved the distance S. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. Show that this amount of mass is m, = c2.

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