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Suppose you had two small boxes, each containing 1.0 g of protons. (a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why? (b) What gravitational force would each box of protons exert on the other box?

Short Answer

Expert verified
  1. The tension in the string is 560 N .
  2. The gravitational force exerted by one box on the other box is 4.5×1034N .

Step by step solution

01

Step 1: Concept of Coulomb’s Law

According to the Coulomb’s law, the force between two charges spaced at a distance is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them.

Coulomb’s law of force between two charges is,

F=kq1q2r2 ..... (1)

Here, the Coulomb’s constant, k=8.99×109N.m2/C2,ris the distance between two charges q1and q2.

(a) Determination of the tension in the string.

The data required in this problem are,

Mass of box, m=1.00×10-3kg

Mass of proton, mp=1.67×10-27kg

Charge of a proton, e=1.60×10-19C.

The distance between the earth and the moon, r=3.84×108m.

To determine the total charge, the number of atoms in the box is required. Therefore

N=mmp=1.0×10-3kg1.67×10-27kg=5.99×1023

Define the total charge as below.

q=Ne=5.99×10231.60×10-19C=9.58×104C

Determine the electrical force from equation (1) by substituting all known values.

F=8.99×109N.m2/C29.58×104C3.84×108m2=560N=130lb

Hence, the force is repulsive in nature and this force is equal to the tension in the string.

02

(b) Determination of the gravitational force exerted by one box on the other box.

The gravitational force expression is given as,

Fg=Gm1m2r2

Here, Fg is the gravitational force, G is the gravitational constant, ris the distance between two masses m1and m2.

Here, m1=m2

Substitute all the values in the above equation,

F=6.67×10-11Nm2/kg21.0×10-3kg23.84×108m2=4.5×10-34N

Hence, the gravitational force is much less than the electrical force which makes it negligible in comparison.

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