Question

Two charged pith balls are suspended on very light 120 cm strings. Each has a mass of 10.0 g. Assume the angle the threads make from the vertical is 0 -10 and that the balls are in equilibrium. Draw a free-body diagram for one of the pith balls and clearly label all forces with magnitude and direction. Assuming the pith balls are equally charged, what is he charge on each ball? (This qualitative predicti obtained.) is is not a qualitative prediction; a numerical answer must be 120 m

Answer 1

Given data are: length of string (l) = 120 cm i.e l = 1.2 m weight = 10 g = 0.01 kg angle(theta) = 10 degree Free body diagram will be: rightarrow Now calculate the forces on pitch balls, are: Force downwards = mg = F_g electrostatic force(F_e) = F_E = KQ^2/(2r)^2 implies F_E = (9 times 10^9)Q^2/2 times r^2 rightarrow (1) rightarrow From diagram(r) = i sin theta implies 1.2 times sin 10 degree = 0.2083 m r = 0.2083 m \r\n From eq^n (1) we have F_e = 9 times 10^9 times Q^2/2 times (0.2083)^2 F_e = (103.72 times 10^9 times Q^2 And we have forces along x-axis: F_e = T sin theta and along y-axis: F_g = T cos theta rightarrow Now from above two eq^ns Tan theta = F_e/F_g implies F_e = F_g Tan theta = mg Tan 10 degree implies (103.72 times 10^9)Q^2 = (0.01)(9.8) Tan 10 degree implies Q^2 = 0.017280/103.72 times 1069 = 0.000166 times 10^- 9