Question

An electrically neutral model airplane is flying in a horizontal circle on a 2.5-m guideline, which is nearly parallel to the ground. The line breaks when the kinetic energy of the plane is 50 J. Reconsider the same situation, except that now there is a point charge of +q on the plane and a point charge of -q at the other end of the guideline. In this case, the line breaks when the kinetic energy of the plane is 52.6 J. Find the magnitude of the charges.

q=_____________C

Answer 1

Suppose the centripetal force in case 1 is F_cmax

F_cmax = mv₁² / 2    , KE_max = mv₁² / r

The centripetal force in case 2 is F_c' = F_c + F_q where F_q is the extra force by the charges.

Now, at the breaking point, F_cmax + F_q = mv₁' ² / r

Hence, KE'_max - KE_max = m(v₁' ² - v₁²) / 2 = 2.6 J

and F_q = m(v₁' ² - v₁²) / r

=> kq² / r² = m(v₁' ² - v₁²) / r

=> q² = mr(v₁' ² - v₁²) / k = 2(KE' - KE)r / k = 5.2(2.5)/(9*10⁹) = 14.44*10^-8

=> q = 3.8 * 10^-4C