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Imagine two 1.0g bags of protons, one at the earth’s north pole and the other at the south pole.

(a) How many protons are in each bag?

(b) Calculate the gravitational attraction and the electric repulsion that each bag exerts on the other.

(c) Are the forces in part (b) large enough for you to feel if you were holding one of the bags?

Short Answer

Expert verified

The number of protons is N=6.0×1023.

Fe=4.9×105NFg=3.9×10-31N

The gravitational force is so small to be delectated but the electric force is so large.

Step by step solution

01

Number of protons.

Given d=2Re,mb=1.0×10−3kgandG=6.67×10−11N.m2kg−2

a) The mass of proton is mp=1.67×10-27kg so the total number of protons

mb=Nmp....=>(1)

Substitution in (1) yields

N=1.0×10−31.67×10−27N=6.0×1023proton

Hence the number of protons is N=6.0×1023

02

Calculation of electric and gravitational force.

The Electric force is

F=kq2d2…….=(2)

The charge is given by

q=Ne=6×1023×6.67×10−19=6.9×104C

The distance is twice as radius of earth

d=2×6.371×106=1.3×107m

Substitute in (2)

Fe=9×109×9.6×10421.3×1072Fθ=4.9×105N

The gravitational force is given by

F=Gm1m2d2……..>(3)

Substitute in (3)

Fg=6.67×10−11×1.0×10−321.3×1072Fg=3.9×10−31N

03

Conclusion

Hence the gravitational force is so small to be delectated but the electric force is so large.

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