electric potential problem

Question

A small metal sphere of mass 3.9g and charge 9.0 microC is fired with an initial speed of 6.2 m/s directly towards the center of a small metal sphere carrying a charge 7.5 microC and a mass 5.2g held ficed in place. if the spheres are initially at a distance of 50m appart, how close do they get to one another?

 

Hi, I do not know how to solve this problem. I tried to solve this problem by saying that the kinetic energy= energy due to charges but i did not arrive to the correct answer of 6.974m.

 

Thank you in advance.

Answer 1

Use energy conservation.

 

(KE)₁ + (PE)₁ = (KE)₂ + (PE)₂

 

m = 0.0039 kg

q = 9.0 x 10^-6 C

Q = 7.5 x 10^-6 C

d = 50 m

v = 6.2 m/s

x = final distance between the charges = ?

 

mv²/2 + kqQ/d = 0 + kqQ/x = kqQ/x ⇒

 

x = kqQ / (mv²/2 + kqQ/d)

 

kqQ = (9.0 x 10⁹)(9.0 x 10^-6)(7.5 x 10^-6) = 0.6075 Nm²

 

mv²/2 = (0.0039)(6.2)²/2 J = 0.07496 J

 

kqQ/d = 0.6075/50 J = 0.01215 J = 0.01215 Nm

 

x = (0.6075) / (0.07496 + 0.01215) m = 6.974 m