The picture above shows the equilibrium position of a ball on a string. This bal

Question

The picture above shows the equilibrium position of a ball on a string. This ball (ball 1) is in a uniform electric field of magnitude E = 400 N/C, which points to the left, as shown. It is also in the usual gravitational field of g = 10 N/kg, directed down. Ball 1 has a positive charge.

(a) When we replace ball 1 by ball 2, which has the same mass as ball 1 but a different amount of positive charge, the equilibrium position of ball 2 is such that the string is at an angle of 2 = 48.0 degrees. What is the ratio of ball 2's charge to ball 1's charge?

(b) Now we replace ball 2 by ball 3. Ball 3 has a mass that is 3 times larger than that of ball 1, and a charge that is 5.5 times larger than that of ball 1. At what angle will the string be when ball 3 is in equilibrium? (in degrees)

(c) If the string breaks, what will the ball do? (select all that apply)

Follow a parabola, curving downward

Follow a parabola, curving to the left

Follow a parabola, curving down and to the left

Move with constant velocity straight down

Move with constant velocity to the left

Move with constant velocity down and to the left, along a line at the same angle the string was at

Move with constant acceleration straight down

Move with constant acceleration to the left

Move with constant acceleration down and to the left, along a line at the same angle the string was at

Explanation / Answer

a.

Fnet,x = Tsin1 - q1E

so

q1E = Tsin1

Fnet,y = Tcos1 - mg

so

mg = Tcos1

thus, the charge q1 is,

q1 = mgtan1 /E

Similarly,

q2 = mgtan2 /E

so, the ratio is,

q2/q1 = tan2 / tan1

= tan48 / tan30

= 1.9236

----------------------------------------------------------

q1 = m1gtan1 /E

q2 = m2gtan2 /E

use these two equations we get the result.

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