Question

Comparison of electric & gravity forces: Two identical blocks are placed 5 m apart. Each has a mass of 2 kg, is electrically neutral, and is made entirely of copper. Note: One copper atom has a mass of 1.055·10-25 kg and contains 29 protons. a.) How many electrons must a neutral copper atom have? 29 Correct: Your answer is correct. electrons b.) Estimate the percentage of a copper atom's mass that is due to: electrons: 0.025 Correct: Your answer is correct. % protons: 45.9 Correct: Your answer is correct. % Do a proton & electron have an equal amount of charge? Of mass? Also, what constitutes the remaining mass of these copper atoms? c.) Estimate how many electrons each of these blocks has within it. 5.50e26 Correct: Your answer is correct. electrons What is the total charge of all these electrons? -8.8e7 Correct: Your answer is correct. C And what is the total charge of all the protons in a block? +8.8e7 Correct: Your answer is correct. C So what is the net charge of each block? 0 Correct: Your answer is correct. C d.) You now remove an equal amount of electrons from each block, so the electric repulsion of the blocks cancels their gravitational attraction to each other. (Note: You may assume the mass of the blocks is not significantly reduced when removing these electrons-- why?) What is the net charge of each block now? 1.72e-10 Correct: Your answer is correct. C How many electrons were removed from each block? Give a number, and then also express this as a percentage of the total number in the block. % Did your answers for this part depend on the distance between the blocks?

Answer 1

a)

To be electrically neutral , the number of electron and the number of protons must be equal

Number of electron = Number of proton = 29

b)

m = mass of atom = 1.055 x 10^-25

n_e = number of electrons = 29

n_p = number of protons = 29

m_e = mass due to electrons = n_e (9.1 x 10^-31) = (29)(9.1 x 10^-31)

m_p = mass due to protons = n_e (1.67 x 10^-27) = (29)(1.67 x 10^-27)

percentage of mass of electron is given as

percentage = m_e x 100/m = (29)(9.1 x 10^-31) (100)/(1.055 x 10^-25 ) = 0.025

percentage of mass of proton is given as

percentage = m_p x 100/m = (29)(1.67 x 10^-27) (100)/(1.055 x 10^-25 ) = 45.9

yes the amount of charge on electron and proton would be same as they have same number and same magnitude of charge.

c)

n = number of atoms = given mass/ atomic mass = 2/(1.055 x 10^-25) = 1.896 x 10²⁵

N = number of electrons = 29 n = 29 x 1.896 x 10²⁵ = 5.5 x 10²⁶

Q_e = total charge of electrons = Ne = (5.5 x 10²⁶) (- 1.6 x 10^-19) = - 8.8 x 10⁷ C

Q_p = total charge all the protons = - Q_e = - ( - 8.8 x 10⁷ C) = 8.8 x 10⁷ C

Net charge = Q = Q_e + Q_p = - 8.8 x 10⁷ C + 8.8 x 10⁷ C = 0 C

d)

q = charge on each block

r = distance between the blocks = 5 m

m = mass of each block = 2 kg

electric force between the blocks = gravitational force

kq²/r² = Gm² /r²

kq² = Gm²

(9 x 10⁹) q² = (6.67 x 10^-11) (2)²

q = 1.72 x 10^-10 C

q = ne where n = number of electrons removed

1.72 x 10^-10 = n (1.6 x 10^-19)

n = 1.075 x 10⁹

percentage = n x 100/N = (1.075 x 10⁹ ) (100)/(5.5 x 10²⁶) = 1.95 x 10^-16

since the distance "r" cancelled out , hence distance between the blocks play no role