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Physics / Physics with MasteringPhysics 4 / Chapter 19 / Problem 93GP

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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IP Suppose a charge +Q is placed on the Earth, and another

Chapter 19, Problem 93GP

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QUESTION:

Problem 93GP

IP Suppose a charge +Q is placed on the Earth, and another charge +Q is placed on the Moon. (a) Find the value of Q needed to "balance" the gravitational attraction between the Earth and the Moon. (b) How would your answer to part (a) change if the distance between the Earth and the Moon were doubled? Explain.

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QUESTION:

Problem 93GP

IP Suppose a charge +Q is placed on the Earth, and another charge +Q is placed on the Moon. (a) Find the value of Q needed to "balance" the gravitational attraction between the Earth and the Moon. (b) How would your answer to part (a) change if the distance between the Earth and the Moon were doubled? Explain.

ANSWER:

Solution 93GP

Step 1 of 3

(a)

Here we need to find the value of charge $Q$ that is necessary to balance the gravitational attraction between the Earth and the Moon. In the given case, the charge $Q$ is placed on the Earth and another charge $Q$ is placed on the Moon.

The gravitational force should be balanced by the electrostatic force between charges, that is

${F}_{G}={F}_{e}$

Using the respective definitions,

$\frac{G\ {M}_{e}{M}_{m}}{{R}^{2}}=\frac{k{Q}^{2}}{{R}^{2}}$

Where ${M}_{e}$ and ${M}_{m}$ are the masses of Earth and Moon, $R$ is the distance between Earth and Moon.

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