Question

Three identical small Styrofoam balls of mass 1.89 g are suspended from a fixed point by three nonconducting threads, each with a length of 59 cm and negligible mass. At equi- librium the three balls form an equilateral triangle with sides of 30.6 cm.

What is the common charge carried by each ball? The acceleration due to gravity is 9.8 m/s2 and the value of Coulomb’s con- stant is 8.98755 × 109 N · m2/C2 .

1. 0.190953 2. 0.180562

3. 0.131962
4. 0.127213
5. 0.169465
6. 0.265633
7. 0.194387
8. 0.18699
9. 0.215062
10. 0.198498
Answer in units of ?C.

Answer 1

distance from cornet to centroid l = (s/2)/cos30 = (30.6/2)/cos30 = 17.7 cm = 0.177 m

angle made by the thread with horzontal = theta

costheta = l/L

costheta = 17.7/59

theta = 72.576

net electric force acting on ball Fe = 2*k*q*q*cos30/s^2

In equilibrium for the ball

along vertical

Fnet = 0

T*sintheta - m*g = 0

T*sintheta = m*g

along horizontal

Fnet = 0

T*costheta - Fe = 0

T*costheta = 2*k*q^2*cos30/s^2

tantheta = m*g*s^2/(2*k*q^2*cos30)

tan72.576 = 1.89*10^-3*9.8*0.306^2/(2*8.98755*10^9*q^2*cos30)

q = 0.18699 uC <<<------------ANSWER