Question

The solution to a problem is represented by the following equation:

(9.0×109N⋅m2/C2)(+20.0×10−9C)(+50.0×10−9C)/(5cm)=12(10g)v2x+(9.0×109N⋅m2/C2)(+20.0×10−9C)(+50.0×10−9C)/(20cm)

Describe a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

Answer 1

Using conservation of energy, we have

P.E_initial + K.E_initial = K.E_final + P.E_final

(k_e q₁ q₂ / r_i) + 0 = (1/2) m v² + (k_e q₁ q₂ / r_f)

[(9 x 10⁹ Nm²/C²) (20 x 10^-9 C) (50 x 10^-9 C)] / (0.05 m) = (1/2) (0.01 kg) v² + (9 x 10⁹ Nm²/C²) (20 x 10^-9 C) (50 x 10^-9 C)] / (0.2 m)

[(9 x 10^-6 Nm²) / (0.05 m)] = (0.005 kg) v² + [(9 x 10^-6 Nm²) / (0.2 m)]

(1.80 x 10^-4 J) = (0.005 kg) v² + (4.50 x 10^-5 J)

[(1.80 x 10^-4 J) - (4.50 x 10^-5 J)] = (0.005 kg) v²

[(1.35 x 10^-4 J) / (0.005 kg)] = v²

v = _$\sqrt{}$0.027 m²/s²

v = 0.164 m/s