Question 466.
Three 3.37-g Styrofoam balls of radius 2 cm are coated with carbon black to make them conducting and then are tied to 1.27-m-long threads and suspended freely from a common point. Each ball is given the same charge, q. At equilibrium, the balls form an equilateral triangle with sides of length 24.38 cm in the horizontal plane. Determine the absolute value of q.
Answer 466. Consider any one of the three balls.
Three forces act on it.
i ) its weight, mg, downwards
ii ) tension in the thread, T, in the direction from the ball
to the point of suspension and
iii ) the resultant of the two forces of repulsion from the remaining two balls.
Let O be the point of suspension, A the position of the ball
and C the center of the equilateral triangle formed by the three balls.
OA = 1.27 m
AC cos30° = 24.38/2 cm = 0.1219 m
=> AC = (0.1219)/cos30° = 0.141 m
=> OC = √[(1.27)^2 - (0.141)^2] m = 1.262 m
=> m∠AOC = arctan[(0.141)/(1.262)] = 6.38°
Vertical component of T balances weight mg
=> Tcos6.38° = 3.37 x 10^-3 x 9.81
=> T = 0.03327 N
Horizontal component of T balances the resultant of the two forces of repulsion
from the remaining two balls
=> 0.03327sin6.38° = 2 * kq^2/(0.2438)^2 * cos30°
=> q^2 = (0.2438)^2 * 0.03327 sin6.38° / (2 * 9 x 10^9 x cos30°)
=> q^2 = 1.409669 x 10^(-14) C
=> q = 0.1187 μC.
Link to YA!
Three 3.37-g Styrofoam balls of radius 2 cm are coated with carbon black to make them conducting and then are tied to 1.27-m-long threads and suspended freely from a common point. Each ball is given the same charge, q. At equilibrium, the balls form an equilateral triangle with sides of length 24.38 cm in the horizontal plane. Determine the absolute value of q.
Answer 466. Consider any one of the three balls.
Three forces act on it.
i ) its weight, mg, downwards
ii ) tension in the thread, T, in the direction from the ball
to the point of suspension and
iii ) the resultant of the two forces of repulsion from the remaining two balls.
Let O be the point of suspension, A the position of the ball
and C the center of the equilateral triangle formed by the three balls.
OA = 1.27 m
AC cos30° = 24.38/2 cm = 0.1219 m
=> AC = (0.1219)/cos30° = 0.141 m
=> OC = √[(1.27)^2 - (0.141)^2] m = 1.262 m
=> m∠AOC = arctan[(0.141)/(1.262)] = 6.38°
Vertical component of T balances weight mg
=> Tcos6.38° = 3.37 x 10^-3 x 9.81
=> T = 0.03327 N
Horizontal component of T balances the resultant of the two forces of repulsion
from the remaining two balls
=> 0.03327sin6.38° = 2 * kq^2/(0.2438)^2 * cos30°
=> q^2 = (0.2438)^2 * 0.03327 sin6.38° / (2 * 9 x 10^9 x cos30°)
=> q^2 = 1.409669 x 10^(-14) C
=> q = 0.1187 μC.
Link to YA!
No comments:
Post a Comment