Two bodies under gravitational attraction with masses of 2kg and 4kg are moving towards each other with velocities 20 m/s and 10 m/s respectively. Calculate the velocity of their centre of mass.
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- A binary star consist of two stars of the same mass m revolving in a circle of radius R about their common centre of mass. Suppose that a meteorite passes through the centre of mass of the binary star in a direction perpendicular to the orbital plane. What is the minimum speed that the meteorite must have at the centre of mass in order for it to escape from the gravitational attraction of the binary star? ANSW: 4Gm R wA meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.We know that the mass of the bagged lunch is m = 1.40 kg and the mass of the astronaut is M = 67.0 kg. Before the collision, the bagged lunch moves with a velocity of vi = 1.60 m/s in the positive x-direction and the astronaut is at rest relative to the space station with velocity Vi = 0. MVi + mvi = MVf + mvf to obtain (67.0 kg)(0 m/s) + (1.40 kg)(1.60 m/s) = (67.0 kg)Vf + (1.40 kg)vf. Because vf = Vf, this further simplifies to (67.0 kg)(0 m/s) + (1.40 kg)(1.60 m/s) = (1.40 kg + 67.0 kg)Vf. What is the velocity of the astronaut after the collision?
- Calculate the increase in velocity of a 4000-kg space probe that expels 3500 kg of its mass at an exhaust velocity of 2.00×103m/s. You may assume the gravitational force is negligible at the probe’s location.A 4,600 kg open train car is rolling on frictionless rails at 21.1 m/s when it starts pouring rain. A while later the car's speed is 19.5 m/s. What mass of water has collected in the car? Provide your answer in appropriate units of meters (m), seconds (s), kilograms (kg), radians (rad) or combinations thereof, such as m/s or m/s^2. Use at least three significant figures in your answer, do not use scientific notation. Using more significant figures will not be considered incorrect; using fewer may lead to errors due to rounding.5) Two neutron stars are separated by a distance of 2.98x10^(10)m. Both have a mass of 3.17x10^(30)kg and a radius of 253000m. They are initially at relative rest. a) What is the speed of both when the distance between them is half the initial value? in m/s b) What is the speed of both when they are about to collide? in m/s
- There is a large crater in Arizona called Meteor Crater. It is estimated that it was formed about 20,000 years ago by a meteorite that had a mass of about 5 x 10^10 kg and was traveling at a speed of 7.5 km/sec. How fast could this meteorite have hit the Earth (whose mass is 6 x 10^24 kg) if we assume a head-on collision?A distant exo-planet has a mass that is 100 times bigger than the Earth's, and orbits at a distance 2 times as far from its star as the Earth does from our Sun. The star has the same mass as our Sun. What is the velocity of the star about the center of mass of the exo-planet/star system? Mass of Earth = 6.0 x 1024 kg. Distance of Earth from Sun = 150 x 109 m. Mass of Sun = 2.0 x 1030 kg.As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted). Find a distance d (in terms of v, c, and the orbital period T) such that α would appear to be simultaneously to the left and right of the center of mass point.
- Two stars in a binary system orbit around their center of mass. The centers of the two stars are 6.96x10¹¹ m apart. The larger of the two stars has a mass of 4.46x10³0 kg, and its center is 1.86x10¹¹ m from the system's center of mass. What is the mass of the smaller star?A space vehicle is traveling at 4450 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 64 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation?Two stars in a binary system orbit around their center of mass. The centers of the two stars are 6.91x1011 m apart. The larger of the two stars has a mass of 4.17x1030 kg, and its center is 2.22x1011 m from the system's center of mass. What is the mass of the smaller star?