A small sphere of mass m = 6.70 g and charge q 1 = 28.2 nC is attached to the en

Question

A small sphere of mass m = 6.70 g and charge q1 = 28.2 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = 58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure.

A small sphere of mass m = 6.70 g and charge q1 = 28.2 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = ?58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure. (a) Find the tension in the string. N (b) If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks? cm

Explanation / Answer

a) The mass is being pulled down with 2 force, gravity and electric attraction, and pulled up with tension of rope. Since it is not moving, we can say up force equals down force, or:

T = mg + Fe

To find Fe, the force of electricity, we use coloumbs law:

Fe = kq1q2/r2
Fe = (9e9)(28.2e-9)(58e-9) / (.02)2
Fe = .0368 N

So we put it into the first equation:

T = mg + Fe
T = ( .0067)(9.8) + .0368 N
T = .10246 N

b) We, we know T and mg, but Fe unknown, so:

T = mg + Fe
.180 N = (.0067)(9.8) + Fe
Fe = .11434 N

We now plug this into coloumbs law and solve for r:

Fe = kq1q2/r2
.11434 N = (9e9)(28.2e-9)(58e-9) / (r)2
r = .01135 m or 1.135 cm

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