### Gravitational Force Problem**Background:**A uniform, solid sphere with a mass of 1800.0 kg and a radius of 5.00 m is used in this problem. This scenario involves calculating the gravitational force exerted by the sphere on a point mass.**Part A:**Find the gravitational force this sphere exerts on a 2.00 kg point mass. The point mass is placed at a distance of 5.04 m from the center of the sphere.- **Instructions:** - Express your answer in newtons (N). - Use the input box and the provided tools (variable input, equation editor, etc.) to input your answer. - Submit your answer when ready. - You can request help if needed.**Expression:**\[ F = \_\_\_ \, \text{N} \]**Part B:**Find the gravitational force this sphere exerts on the same 2.00 kg point mass when placed at a distance of 2.35 m from the center of the sphere.- **Instructions:** - Express your answer in newtons (N) again. - Use the input box and the provided tools to input your answer. - Submit your answer when ready. - You can request help if needed.**Expression:**\[ F = \_\_\_ \, \text{N} \]This problem enhances understanding of gravitational forces and how they apply to spherically symmetric mass distributions. For related problem-solving tips and strategies, you can refer to a Video Tutor Solution titled "Journey to the center of the earth."

Given: Uniform mass of solid sphere , M=1800.00 kg Radius of solid sphere , R=5.00 m To determine: (A) The gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 5.04 m to the center of the earth. (B) The gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 2.35 m. (A) The gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 5.04 m to the center of the earth. The gravitational force due to solid sphere of mass M on point mass m separated by distance r is F=GMmr2 Where G is Universal Gravitational constant, G=6.67×10-11 N.m2/kg2 putting m=2.00 kg, M=1800.0 kg and r=5.04 m F=(6.67×10-11N.m2/kg2 )(1800.0 kg)(2.00 kg)(5.04 m)2 F=9.4529×10-11 N(B) The gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 2.35 m The whole mass of sphere beyond r=2.35 m will not contribute any force on point mass. Density= mass/volume mass, M=1800 kg volume of sphere, V=4πR33 Density=1800 kg4πR33 since mass of sphere is uniformly distributed, the mass at radius r>R is M' M'=Density×volume at radius r M'=1800 kg4πR33×4πr33 M'=1800 kg ×r3R3 r=2.35m, R=5.00 m M'=1800 kg ×(2.35 m)3(5.00 m)3 M'=186.88 kg Hence, The gravitational force due to solid sphere of mass M' on point mass m separated by distance r>R is F=GM'mr2 Where G is Universal Gravitational constant, G=6.67×10-11 N.m2/kg2 putting m=2.00 kg, M'=186.88 kg and r=2.35m, R=5.00 m F=(6.67×10-11N.m2/kg2 )(186.88 kg)(2.00 kg)(2.35 m)2 F=4.514×10-9 N

Science

Physics

A uniform, solid, 1800.0 kg sphere has a radius of 5.00 m. Part A For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Journey to the center of the earth. Find the gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 5.04 m Express your answer in newtons. ? F = Submit Request Answer Part Find the gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 2.35 m. Express your answer in newtons. F = N

A uniform, solid, 1800.0 kg sphere has a radius of 5.00 m. Part A For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Journey to the center of the earth. Find the gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 5.04 m Express your answer in newtons. ? F = Submit Request Answer Part Find the gravitational force this sphere exerts on a 2.00 kg point mass placed at the following distances from the center of the sphere 2.35 m. Express your answer in newtons. F = N

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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