A charged sphere with an initial speed v0 has a final speed 2v0 when accelerated through a potential difference ΔV0 . What potential difference is needed to accelerate the same charged sphere from an initial speed 2v0 to a final speed 4v0 ?

Answer 1

Problem 1
work done on sphere = kinetic energy gained = .5 m (4 vo^2 - vo^2) = QVo
Q Vo = .5 m (3 vo^2)
Problem 2
work done on sphere = kinetic energy gained =.5 m (16 vo^2-4vo^2) = Q Vf
Q Vf = .5 m (12 vo^2)
12/3 = 4