Question

An electrically neutral model airplane is flying in a horizontal circle on a 3.5-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 53.5 J. Find the magnitude of the charges.

Answer 1

For the centripetal force, we have

F_c = m v² / r = (2 K.E) / r

so,

T_max + k_e |q|² / r² = (2 K.E)_charged / r                                           { eq.1 }

And

T_max = (2 K.E)_uncharged / r                                                { eq.2 }

subtracting eq.2 from eq.1 and we get -

k_e |q|² / r² = 2 [(K.E)_charged - (K.E)_uncharged] / r

solving for |q|, we have

|q| = 2r [(K.E)_charged - (K.E)_uncharged] / k_e

|q| = 2 (3.5 m) [(53.5 J) - (50 J)] / (9 x 10⁹ Nm²/C²)

|q| = [(24.5 Nm²) / (9 x 10⁹ Nm²/C²)]

|q| = 5.21 x 10^-5 C