A 2.70 C charged 1.00 g cork ball is suspended vertically on a 0.800 m long ligh

Question

A 2.70 C charged 1.00 g cork ball is suspended vertically on a 0.800 m long light string in the presence of a uniform downward-directed electric field of magnitude E = 4.60x105 N/C. If the ball is displaced slightly from the vertical, it oscillates like a simple pendulum. (a) What would be the period be if there was no electric field?

(b) Find the magnitude of the electric force on the ball due to the electric field.

(c) Determine the acceleration of the ball due to the combined effects of the gravitational and electric fields. That is, what is the effective acceleration due to both gravity and the electric field? (What is the new "g" that you should use in the period equation?)

(d) Determine the period of the ball's oscillation in the electric field.

Explanation / Answer

a) if there is no electric field

time period = 2pi * sqrt(L/g)

time period = 2pi * sqrt(0.80/9.80)

time period = 1.79 s

b) magnitude of electric force on the ball = q * E

magnitude of electric force on the ball = 2.7 *10^-6 * 4.6 *10^5

magnitude of electric force on the ball = 1.242 N

c)

let the acceleration after net combination is a

m * a = 1.242 + m * g

a = 2.142/(0.001) + 9.8

a = 2151.8 m/s^2

the acceleration of the ball is 2151.8 m/s^2

d)

period of the ball's oscillation in the electric field = 2pi * sqrt(L/a)

period of the ball's oscillation in the electric field = 2pi * sqrt(0.80/2151.8)

period of the ball's oscillation in the electric field = 0.121 s

the period of the ball's oscillation in the electric field is 0.121 s

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