Three equal masses, each equal to m, are kept at the vertices of an equilateral triangle of side a. Find the gravitational field and gravitational potential at the centroid of the triangle.
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![Three equal masses, each equal to m, are kept at the
vertices of an equilateral triangle of side a. Find the
gravitational field and gravitational potential at the
centroid of the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ef3fdc1-7235-4109-bde6-df00a4534189%2Feadfd15a-0a92-4d53-9389-561c8e402276%2Fnvpv6k_processed.jpeg&w=3840&q=75)
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- A particle moves in the xy plane from the origin to a point having coordinates x=7 m and y=4 m under the influence of a force given by F= -2y^2i -2xj.The gravitational field of a spherical object at any distance from it points back to the center of the object. That is, in the field simulator it has arrows toward the center of the sphere. Put a test mass in this field and it will fall toward the center with increasing speed following the line of force. Locally, the field is the acceleration of gravity at that point. Now, how would you move a small mass so that you would not have to do work on it during the move? That work would be the change its energy. You would move it radially toward the center. You would move it radially away from the center. You would move it perpendicularly to the line of force, that is, move it in a local plane that is perpendicular to the radius at that point. There is no way to do this. Any displacement direction will take work.A satellite in Earth orbit has a mass of 91 kg and is at an altitude of 2.04 x 10° m. (Assume that U = 0 as r→ o.) (a) What is the potential energy of the satellite-Earth system? (b) What is the magnitude of the gravitational force exerted by the Earth on the satellite? (c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no force enter 0.) N
- A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)A satellite has a mass of 298 kg and is located at 1.97 ✕ 106 m above the surface of Earth. (a) What is the potential energy associated with the satellite at this location? J(b) What is the magnitude of the gravitational force on the satellite? NThe force exerted by an electric charge at the origin on a charged particle at the point (æ, y, z) is F(7) KT where K is constant. (x, y, z) with position vector Assume K = 30. Find the work done as the particle moves along a straight line from (3,0,0) to (3,4,5)
- Problem Thirteen. A potential energy function is given by U(r)=U2 where o = 2.00 m r r and U, = 1.00 J. Find the magnitude of the force at r= 1.00 m. Give an answer in kN. 25.) (A) 280 (В) 106 (С) 420 (D) 470 (E) 530In the figure, a small block of mass m - 0.039 kg can slide along the frictionless loop-the-loop, with loop radius R-18 cm. The block is released from rest at point P, at heighth-6R above the bottom of the loop. How much work does the gravitational force do on the block as the block travels from point P to (a) point Q and (b) the top of the loop? If the gravitational potential energy of the block-Earth system is taken to be zero at the bottom of the loop, what is that potential energy when the block is (c) at point P. (d) at point Q, and (e) at the top of the loop? (a) Number 0.34 (b) Number 0.275 (c) Number 0.41 (d) Number i 0.14 (e) Number i Units Units Units h 2010 Units J R Units Ja) Show that a constant force field does zero work on a particle that moves once uniformly around the circle x2 + y2 = 1 (b) Is this also true for a force field , where is a constant and ?