i need the answer quickly 116 Mechanics-l1Example 3 Three particles each of mass m are located at the vertices of anequilateral triangle of side a. Ar what speed must they move if they all revolveunder the influence of their gravitational force of attraction in a circular orbitcircumscribing the triangle while still preserving the equilateral triangle ?mFig. 10.39

This question is based on gravitational force.

Answered: 116 Mechanics-II Example 3 Three…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 53PQ: Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 ...

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A spaceship at rest relative to a nearby star in interplanetary space has a total mass of 2.50 104 kg. Its engines fire at t = 0, steadily burning fuel at. 76.7 kg/s with an exhaust speed of 4.25 103 m/s. Calculate the spaceships (a) acceleration at t = 0, (b) mass at t = 125 s, (c) acceleration at t = 125 s, and (d) speed at t = 125 s, relative to the same nearby star.
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
An average-sized asteroid located 5.0107km from Earth with mass 2.01013kg is detected headed directly toward Earth with speed of 2.0km/s . What will its speed be just before it hits our atmosphere? (You may ignore the size of the asteroid.)
If a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.
When a star dies, much of its mass may collapse into a single point known as a black hole. The gravitational force of a black hole on surrounding astronomical objects can be very great. Astronomers estimate the strength of this force by observing the orbits of such objects around a black hole. What is the gravitational force exerted by a black hole on a 1-solar-mass star whose orbit has a 1.4 1010 m radius and a period of 5.6 days?
Two identical particles, each of mass 1 000 kg, are coasting in free space along the same path, one in front of the other by 20.0 m. At the instant their separation distance has this value, each particle has precisely the same velocity of 800 m/s. What are their precise velocities when they are 2.00 m apart? Figure P13 74
A satellite of mass 16.7 kg in geosynchronous orbit at an altitude of 3.58 104 km above the Earths surface remains above the same spot on the Earth. Assume its orbit is circular. Find the magnitude of the gravitational force exerted by the Earth on the satellite. Hint: The answer is not 163 N.
A single-stage rocket of mass 308 metric tons (not including fuel) carries a payload of 3150 kg to low-Earth orbit. The exhaust speed of the rockets cryogenic propellant is 3.20 103 m/s. a. If the speed of the rocket as it enters orbit is 8.00 km/s, what is the mass of propellant used during the rockets burn? b. The rocket is redesigned to boost its exhaust speed by a factor of two. What is the mass of propellant used in the redesigned rocket to carry the same payload to low-Earth orbit? c. Because the exhaust speed of the redesigned rocket is increased by a factor of two, why is the fuel consumption of the redesigned rocket not exactly half that of the original rocket?
Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?
To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at g. Why will they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?
An astronaut out on a spacewalk to construct a new section of the International Space Station walks with a constant velocity of 2.00 m/s on a flat sheet of metal placed on a flat, frictionless, horizontal honeycomb surface linking the two parts of the station. The mass of the astronaut is 75.0 kg, and the mass of the sheet of metal is 245 kg. a. What is the velocity of the metal sheet relative to the honeycomb surface? b. What is the speed of the astronaut relative to the honeycomb surface?
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses (m1m2) . While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)

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