Question

1. ¿Cómo se modifica la fuerza gravitatoria o eléctrica entre dos cuerpos en cada uno de los siguientes casos? Explícalo.

Answer 1

Answers:

A) The gravitational force is four times stronger

B) The gravitational force is 1/8 weaker

C) The electric force remains the same

D) The electric force is eight times stronger

Explanation:

In this question we have to deal with two type of forces that depend on the inverse squared distance, Gravitational force $F_{g}$  and Electrostatic force $F_{E}$:

The first one is expressed according to the law of universal gravitation:

$F_{g}=G\frac{m_{1}m_{2}}{r^2}$  (1)

Where:  

$F_{g}$ is the module of the attraction force exerted between both bodies  

$G$ is the universal gravitation constant.  

$m_{1}$ and $m_{2}$ are the masses of both bodies.  

$r$ is the distance between both bodies

As we can see, the gravity force is directly proportional to the mass of the bodies and inversely proportional to the square of the distance that separates them.

The second force is expressed by Coulomb's Law:  

$F_{E}= K\frac{q_{1}.q_{2}}{d^{2}}$  (2)

Where:

$F_{E}$ is the electrostatic force between two point charges

$K$ is a proportionality constant.

$q_{1}$ and $q_{2}$  are point charges

$d$ the distance that separates both point charges

So, when two electrically charged bodies come closer, appears a force that attracts or repels them, depending on the sign of the charges of this two bodies.  

Having this clear, let's start with the answers according to each situation:

A. The mass of one of the bodies quadruples:

According to this situation, the law of universal gravitation equation is:

$F_{g}=G\frac{4m_{1}m_{2}}{r^2}$

Rewritting:

$F_{g}=4G\frac{m_{1}m_{2}}{r^2}$

This means the gravitational force between both masses is increased by 4.

In other words:

The gravitational force is four times stronger.

B. The mass of one of the bodies is doubled, while the distance between the bodies is quadrupled:

According to this situation, the law of universal gravitation equation is expressed as:

$F_{g}=G\frac{2m_{1}m_{2}}{{(4r)}^2}$  

Simplifying:

$F_{g}=\frac{1}{8}G\frac{m_{1}m_{2}}{r^2}$  

This means the gravitational force changes by a factor of 1/8.

In other words:

The gravitational force is 1/8 weaker

C. The electric charge of the two bodies is doubled and the distance between the bodies is doubled:

According to this situation, Coulomb's law is expressed as:

$F_{E}= K\frac{2q_{1}.2q_{2}}{{(2d)}^{2}}$  

Simplifying:

$F_{E}= K\frac{q_{1}.q_{2}}{d^{2}}$  

This means:

The electric force remains the same

D. One of the charges doubles and the distance between the bodies is reduced by half:

According to this situation, Coulomb's law is expressed as:

$F_{E}= K\frac{2q_{1}.q_{2}}{{(d/2)}^{2}}$  

Simplifying:

$F_{E}= 8 K\frac{q_{1}.q_{2}}{d^{2}}$  

This means the electric force is increased by 8.

In other words:

The electric force is eight times stronger