### Problem Statement:A spaceship of mass \( m \) is located directly in the middle of the two planets shown below. What is the \( x \)-component of the net gravitational force the spaceship experiences due to the two planets?### Diagram:There is an illustration provided depicting two planets and a spaceship placed directly in the middle. The details of the diagram are as follows:- On the left side, there is a blue-colored planet with mass \( 1.5M \).- On the right side, there is a yellow-colored planet with mass \( 2M \).- The distance between the two planets is labeled as \( 6L \).- The spaceship is positioned exactly in the middle between the two planets.- An arrow labeled \( +x \) points towards the right.### Answer Choices:A list of multiple-choice answers is provided to determine the \( x \)-component of the net gravitational force on the spaceship:- \( \frac{7GMm}{18L^2} \)- \( \frac{GMm}{6L} \)- \( \frac{7GMm}{6L} \)- \( -\frac{GMm}{18L^2} \)- \( \frac{GMm}{18L^2} \)- \( -\frac{7GMm}{18L^2} \)### Explanation of the Diagram:The diagram helps visualize the positions and masses of the planets relative to the spaceship. The forces due to gravitational attraction exerted by each planet on the spaceship need to be calculated to find the net \( x \)-component of the gravitational force acting on the spaceship.

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A spaceship of mass m is located directly in the middle of the two planets shown below. What is the x component of the net gravitational force the spaceship experiences due to the two planets? 1.5M 7GMm 181² GMm 6L 7GMm 6L GMm 6L +x 2M

A spaceship of mass m is located directly in the middle of the two planets shown below. What is the x component of the net gravitational force the spaceship experiences due to the two planets? 1.5M 7GMm 181² GMm 6L 7GMm 6L GMm 6L +x 2M

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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Concept explainers

Gravitational force

In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.

Acceleration Due to Gravity

In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.

Question

### Problem Statement:

A spaceship of mass \( m \) is located directly in the middle of the two planets shown below. What is the \( x \)-component of the net gravitational force the spaceship experiences due to the two planets?

### Diagram:

There is an illustration provided depicting two planets and a spaceship placed directly in the middle. The details of the diagram are as follows:

- On the left side, there is a blue-colored planet with mass \( 1.5M \).
- On the right side, there is a yellow-colored planet with mass \( 2M \).
- The distance between the two planets is labeled as \( 6L \).
- The spaceship is positioned exactly in the middle between the two planets.
- An arrow labeled \( +x \) points towards the right.

### Answer Choices:

A list of multiple-choice answers is provided to determine the \( x \)-component of the net gravitational force on the spaceship:

- \( \frac{7GMm}{18L^2} \)
- \( \frac{GMm}{6L} \)
- \( \frac{7GMm}{6L} \)
- \( -\frac{GMm}{18L^2} \)
- \( \frac{GMm}{18L^2} \)
- \( -\frac{7GMm}{18L^2} \)

### Explanation of the Diagram:

The diagram helps visualize the positions and masses of the planets relative to the spaceship. The forces due to gravitational attraction exerted by each planet on the spaceship need to be calculated to find the net \( x \)-component of the gravitational force acting on the spaceship.

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