1). Consider an object with a mass of 10.3 kg. Assume that it\'s made up of equa
ID: 1777677 • Letter: 1
Question
1). Consider an object with a mass of 10.3 kg. Assume that it's made up of equal numbers of protons, neutrons and electrons. Remember that protons and neutrons each individually have the same mass namely 1.7 x 10^-27 kg. Electrons have negligible mass by comparison; and that the charge of an individual proton ( or electron) has a magnitude of 1.6 x 10^-19 C. a) how many protons does the object contain? b) Imagine taking all the protons out of the object and stuffing them into a box. Also take all of the electrons out of the object and stuff them in a second box. How much charge is contained in each box? c) Now imagine separating the two boxes. One containing all the protons, the other containing all the electrons. Let's put them at a distance of 6.4 m from one another. What will be the strength of the force of attraction between the two boxes. d) Suppose that you now want to take the two boxes and move them even further apart. You moved them from 6.4 m apart to 8.6 m apart. How much work (energy) would you have to expend to pull the boxes that much further apart, fighting against the electrostatic attraction between them? e) From this new distance of 8.6 m, if you were to release the clump of protons from their box, how much acceleration would the clump of protons undergo due to its attraction to the clump of electrons in the other box?
Explanation / Answer
a)
m = given mass = 10.3 kg
n = number of proton = number of neutron
m' = mass of each proton and neutron = 1.7 x 10-27 kg
n = m/(2m') = 10.3/(2 x 1.7 x 10-27) = 3 x 1027
b)
Q = n q = (3 x 1027)(1.6 x 10-19) = 4.8 x 108 C
c)
r = 6.4 m
F = k q2/r2 = (9 x 109) (4.8 x 108)2 /(6.4)2 = 5.0625 x 1025 N
d)
W = k q2 (1/r1 - 1/r2) = (9 x 109) (4.8 x 108)2 (1/6.4 - 1/8.6) = 8.3 x 1025 J
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