### Understanding Gravitational ForceThe gravitational force ($ F_g $) between two masses is described by the equation:\[ F_g = \frac{G m_1 m_2}{r^2} \]Where:- $ G $ is the gravitational constant,- $ m_1 $ and $ m_2 $ are the masses,- $ r $ is the distance separating the two masses.Let's analyze how changes in the variables affect the force of attraction $ F $:#### A) If $ m_1 $ increases by 9, how does $ F $ change?If $ m_1 $ is increased by a factor of 9, the new mass $ m_1' $ = 9 $ m_1 $. The gravitational force will change as follows:\[ F_g' = \frac{G \cdot (9m_1) \cdot m_2}{r^2} = 9 \cdot \frac{G m_1 m_2}{r^2} \]Hence, $ F $ increases by a factor of 9.#### B) If $ r $ is halved ($\frac{1}{2}$), how would $ F $ change?If the distance $ r $ is halved, the new distance $ r' $ = $ \frac{r}{2} $. The new gravitational force will be:\[ F_g' = \frac{G m_1 m_2}{(\frac{r}{2})^2} = \frac{G m_1 m_2}{\frac{r^2}{4}} = 4 \cdot \frac{G m_1 m_2}{r^2} \]Thus, $ F $ increases by a factor of 4.#### C) If $ r $ is not changed but both masses increase by a factor of 7, how would $ F $ change?If both $ m_1 $ and $ m_2 $ increase by a factor of 7, the new masses are $ m_1' $ = 7 $ m_1 $ and $ m_2' $ = 7 $ m_2 $. The new gravitational force will be:\[ F_g' = \frac{G \cdot (7m_1

Name: ### Understanding Gravitational ForceThe gravitational force ($ F_g
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: ### Understanding Gravitational ForceThe gravitational force (\( F_g $) between two masses is described by the equation:\[ F_g = \frac{G m_1 m_2}{r^2} \]Where:- $ G $ is the gravitational constant,- $ m_1 $ and $ m_2 $ are the masses,- \( r \

Answered: Image /qna-images/answer/a6472281-05bd-4798-8ddc-6afa48162e76.jpg

Science

Physics

F = 8 Gm₁m₂ 2 r Two masses, m₁ and m₂ are separated by a distance, r. The force of attraction between the two masses is F. A) If m₁ increases by 9, how does F change? B) If r is halved (1/2), how would F change? C) If r is not changed but both masses increase by a factor 7, how would F change? D) If all variables (r, m₁ and m₂) increase by 4, how would F change?

F = 8 Gm₁m₂ 2 r Two masses, m₁ and m₂ are separated by a distance, r. The force of attraction between the two masses is F. A) If m₁ increases by 9, how does F change? B) If r is halved (1/2), how would F change? C) If r is not changed but both masses increase by a factor 7, how would F change? D) If all variables (r, m₁ and m₂) increase by 4, how would F change?

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

Please answer the question and subquestions entirely. This is one single question. According to the official guideline, I can ask two subquestions! Thank you! 1) Two point masses are placed 10.0 cm apart and attract each other with a force of 10.0 N. Find the force of gravitational attraction between the masses when they are placed 5.00 cm apart. 3.00 N 4.50 N 20.0 N 40.0 N a) The radius of the orbit of a certain asteroid is four astronomical units. What is the period (in years) of this asteroid? 2 years 4 years 6 years 8 years b) A satellite is orbiting the earth at an altitude where the acceleration due to gravity is 8.70 m/s 2. What is its speed? 2.65 x 103 m/s 7.45 x 103 m/s 7.68 x 103 m/s 7.91 x 103 m/s
A satellite of mass 200 kg is launched from a site on Earth’s equator into an orbit 200 km above the surface of Earth. a. What is the satellite’s speed before it’s launched (in m/s)? (Hopefully, it’s moving along with the surface of the Earth as the Earth rotates.) b. What is the satellite’s speed in its orbit (in m/s)? (Remember there is only onespeed a satellite can have in order to maintain a stable circular orbit with agiven radius.) c. Assuming a circular orbit, what is the orbital period of this satellite? (In other words, how long (in hours) does it take for the satellite to complete one orbit?) d. What is the minimum energy (work) necessary to place the satellite in orbit,assuming no air friction? (Remember, work is the amount of energy added tothe system, and the total energy of the system is a combination of kinetic andgravitational potential energies.)
Problems: 1. A stone is thrown near the surface of a planet and its horizontal and vertical position as a function of time are given as x(t) = 5 + 8t (horizontal) y(t) = 3+ 12t – 8t2 (vertical) where x and y are given in meters and t is in seconds. a) planet in units of mis. by c) d) is 9m. Calculate the magnitude of surface gravitational acceleration of this Calculate the time when the stone is at its maximum height. Calculate the velocity vector at t=1.125s. Calculate the velocity vector when horizontal position of the stone
Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r₁, and planet 2 has r₂ = 4r₁ Planet 1 orbits with period T₁ Planet 2 orbits with period A. T₂ = -1/T₁ B. T₂=2T₁ C. T₂ = 4T₁ D. T₂=8T₁
2. a. Consider two planets orbiting a distant star. Planet A is further from the star. A is orbiting at a speed of 14625 m/s and has an orbital period of 12.45 years. What is the radius of A's orbit? Hint: remember to convert the period into seconds. 4.57E11 Previous submissions: 457000000000 b. What is the mass of the star? 1.465E30 Previous submissions: 1.465e30 kg c. Planet B is closer in. B has a larger velocity of 38500 m/s. What is the radius of B's orbit? 6.598E10 Previous submissions: m 65980000000 m m kg m incorrect incorrect V incorrect
M. 00 F. %24 D. %23 HP TrueVision HD Pavi Se th Site w Technical A AN Careers Mail - boss Texas Work MOe Homework A College X C O 8 https://www.webassign.net/web/Student/Assignment-Responses/last?dep3D28680740 不。 CTN LIAL The International Space Station has a mass of 4.19 x 105 kg and orbits at a radius of 6.79 x 106 m from the center of Earth. Find the gravitational force exerted by Earth on the space station, the space station's gravitational potential energy, and the weight of a 71.4 kg astronaut living inside the station. HINT (a) the gravitational force (in N) exerted by Earth on the space station (Enter the magnitude.) N (b) the space station's gravitational potential energy (in J) (c) the weight (in N) of an 71.4 kg astronaut living inside the station Need Help? Watch It Read It MY NOTES ASK YOUR TEACHER PREVIOUS ANSWERS SERCP11 7.5.P.039. 8. [2/2 Points] DETAILS dp AMIN g ong Pva ladurial A 732006020610 ADVANCED AUD insert Oly f5 114 米 $ ヤ % 6 #3 9. %3D K. pa B. 目
Two objects, m1 and m2 are gravitationally attracted to one another. However, m1 is 500 times more massive than m2. Which mass experiences the greater gravitational attractive pull force? A) mass m1 experiences a greater attractive force from m2 B) mass m2 experiences a greater attractive force from m1 C) both masses experience equal but opposite attractive forces D) the problem statement does not provide enough information to be solved
CM-2 A water molecule consists of an oxygen atom with y a mass of 16.0u (u is one atomic mass unit) and two hydrogen atoms, each with a mass of 1.00u. The distance of each hydrogen atom from the center of the oxygen atom is 0.100nm (n=10"). The angle between the hydrogen atoms is 106°. Suppose that a coordinate system is used such that the x axis splits the angle between the two hydrogen atoms as shown to the right. a) Find the y coordinate of the center of mass of the water molecule. b) Find the x coordinate in nm of the center of mass of the water molecule. 0.100nm, 53.0° 53.0° 0.100nm 梦 0 hp
= 400 kg with their centers 8 meters apart. If you In the simulation, start with mị = 200 kg and m2 want to increase in the gravitational force between the two masses by the greatest amount, should you double the mass of m2 or should you halve the distance between the masses? In one or two sentences, explain which option would create the greater increase in the gravitational force and why.
D Gm₁m₂ Fg KE = mv², Ug = - 2πr , ac = =²₁, v = ²7₁ T Gm₁m₂ GM g = G, Vesc = 2GM R , E = KE + Ug, G = 6.674 x 10-¹1 Nm²/kg² Problem 1: You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its radius to be 9 x 106 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2 x 10¹¹ m from its star with a period of 402 days (3.473 x 107 sec). Once on the surface you find that the free-fall acceleration is 12.2 m/sec². a) What is the mass of the planet? Answer: 1.5 x 1025 kg. b) What is the mass of the star? Answer: 5.2 x 1030 kg.
Planet X with a radius of 4.0 Rearth⊕ is found orbiting a star of mass 0.80M⊙ . The eccentricity of its orbit is 0.05, and at its farthest approach to the star, it is 0.63 AU away, while at its closest approach to the star, it is 0.57 AU away. a. How long does it take Planet X to make a complete orbit around its star in years? b.The semi major axis of the planet is changed such that its closest approach to the star is now 2.9 AU. Would the gravitational force exerted by the star on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? c. The mass of the star was increased to 2.4M⊙ . Would the gravitational force exerted by it on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? d. What must the mass of Planet X be in Mearth⊕ such that an astronaut on its surface would have the same weight as…
The Earth is about 81 times more massive than the Moon.The Earth and the Moon apply gravitational forces to each other. The magnitude of the gravitational force acting on the Earth is the gravitational force acting on the Moon.a greater thanb) equal toc) less thand) not enough information to tell