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Chapter 4: Q73P (page 718)

Imagine two 1.0g bags of protons, one at the earth鈥檚 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脳1023.

Fe=4.9脳105NFg=3.9脳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脳10鈭�3kgandG=6.67脳10鈭�11N.m2kg鈭�2

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

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

Substitution in (1) yields

N=1.0脳10鈭�31.67脳10鈭�27N=6.0脳1023proton

Hence the number of protons is N=6.0脳1023

02

Calculation of electric and gravitational force.

The Electric force is

F=kq2d2鈥�鈥�.=(2)

The charge is given by

q=Ne=6脳1023脳6.67脳10鈭�19=6.9脳104C

The distance is twice as radius of earth

d=2脳6.371脳106=1.3脳107m

Substitute in (2)

Fe=9脳109脳9.6脳10421.3脳1072F胃=4.9脳105N

The gravitational force is given by

F=Gm1m2d2鈥�鈥�..>(3)

Substitute in (3)

Fg=6.67脳10鈭�11脳1.0脳10鈭�321.3脳1072Fg=3.9脳10鈭�31N

03

Conclusion

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

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