(a) State Newton's law of gravitation in word form. (b) Use the law to show that that the escape velocity for a planet is given by the expression v= √√28, R. You can assume that the gravitational potential per unit - GM mass U, at the surface of the planet, is given by the expression U = where R M and R are the mass and radius of the planet. (c) Assuming that the Earth is a uniform sphere of radius 6.4 x 106 m and mass 6.0 x 1024 kg, calculate: (1) the gravitational potential at the surface of the Earth and the gravitational potential at a point 6.0 x 105 m above the surface of the Earth. (d) A 5 kg mass is to be delivered to a point in space where the gravitational effect on the mass is negligible. Calculate: (1) the escape velocity for the mass. (iii) the work done in taking the mass to a point 6.0 x 105 m above the surface of the Earth. (iii) the work needed to deliver the mass to the point where the gravitational potential is zero. 3

(a) State Newton's law of gravitation in word form. (b) Use the law to show that that the escape velocity for a planet is given by the expression v= √√28, R. You can assume that the gravitational potential per unit - GM mass U, at the surface of the planet, is given by the expression U = where R M and R are the mass and radius of the planet. (c) Assuming that the Earth is a uniform sphere of radius 6.4 x 106 m and mass 6.0 x 1024 kg, calculate: (1) the gravitational potential at the surface of the Earth and the gravitational potential at a point 6.0 x 105 m above the surface of the Earth. (d) A 5 kg mass is to be delivered to a point in space where the gravitational effect on the mass is negligible. Calculate: (1) the escape velocity for the mass. (iii) the work done in taking the mass to a point 6.0 x 105 m above the surface of the Earth. (iii) the work needed to deliver the mass to the point where the gravitational potential is zero. 3

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)...

See similar textbooks

Similar questions

A solid sphere has a uniformly distributed mass of 1.0 * 104 kg and a radius of 1.0 m.What is the magnitude of the gravitational force due to the sphere on a particle of mass m when the particle is located at a distance of (a) 1.5 m and (b) 0.50 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r < 1.0 m from the center of the sphere.
a) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body of radius R and mass M, using energy conservation. Assume that the planet does not move or spin, so that the total mechanical energy E of a test particle both on the surface and at infinity is equal to zero, and the speed at infinity is zero. Use the formula come up in the last part, Compute this escape speed (in km/s) from Venus, Mars, Jupiter and Neptune. b) Evaluate vIII from the heliocentric orbit of the 4 planets (Venus, Mars, Jupiter and Neptune) mentioned above, assuming circularity of their orbits. Compare the computed speeds with the escape speeds from their surfaces (vII). Notice a big difference in the situation around the inner and the outer planets. What is it due to? A fly-by’s of small bodies near a planet can result in the small particle being accelerated to a final speed close to vII w.r.t. the planet. Draw conclusions as to which planets are able to accelerate small…
A spaceship with m = 1.00 ✕ 104 kg is in a circular orbit around the Earth, h = 800 km above its surface. The ship's captain fires the engines in a direction tangent to the orbit, and the spaceship assumes an elliptical orbit around the Earth with an apogee of d = 3.00 ✕ 104 km, measured from the Earth's center. How much energy (in J) must be used from the fuel to achieve this orbit? (Assume that all the fuel energy goes into increasing the orbital energy and that the perigee distance is equal to the initial radius.)
A space capsule of mass 505 kg is at rest 8.00 x 10' m from the center of the Earth. When it has fallen 5.00 x 10° m closer to the Earth, finu le (a) What is the change in the system's gravitational potential energy? (b) Find the speed of the satellite at that point. m/s
In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?
A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 5 x 1010 m (inside the orbit of Mercury), at which point its speed is 9.6 x 10* m/s. Its farthest distance from the Sun is beyond the orbit of Pluto. What is its speed when it is 6 x 1012 m from the Sun? (This is the approximate distance of Pluto from the Sun.) speed = m/s Additional Materials eBook O Show My Work (Optional)
Plz
The position of four point masses m1=4 kg, M2=2 kg, m3=12 kg,and Mr=4 kg are given by (1,0),(0,2),(1,-1) and (1,3) ,arerespectively. In unit vector notation find the net gravitational force on . Calculate the total potential energy of the system.
An asteroid, whose mass is 3.6 × 10-4 times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 1.7 times the Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth? (a) Number i (b) Number Units Units
Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?
(a) At what height above Earth’s surface is the energy required to lift a satellite to that height equal to the kinetic energy required for the satellite to be in orbit at that height? (b) For greater heights, which is greater, the energy for lifting or the kinetic energy for orbiting?
(a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and place it in a circular low earth orbit—that is, an orbit whose altitude above the earth’s surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE = 6370 km.) Ignore the kinetic energy that the spacecraft has on the ground due to the earth’s rotation. (b) Calculate the minimum amount of additional work required to move the spacecraft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets. (c) Justify the statement “In terms of energy, low earth orbit is halfway to the edge of the universe.”