I need help with this problem:
A metal target sphere of 30 cm diameter suspended out in space is given a charge of +1.00 nC. Through what voltage must a distant proton be accelerated from rest (by some sort of space weapon) if it is to arrive at the sphere at a speed of 7.6 x 10^4 m/s? (Neglect any gravitational effects.)
? V
So this is what I did so far..
I figured we need the energy conservation equation so KEi + PEi + Wnc = KEf + PEf
So, KEf= 7.6 x 10^4 m/s; KEi = 0
So, deltaPE = -7.6 x10^4 + Wnc
Wnc = q(deltaV) ; PE = kqq/r ...? But for some reason I can't figure out how to use those equations to solve for V. Help, please. Thank you!!
A metal target sphere of 30 cm diameter suspended out in space is given a charge of +1.00 nC. Through what voltage must a distant proton be accelerated from rest (by some sort of space weapon) if it is to arrive at the sphere at a speed of 7.6 x 10^4 m/s? (Neglect any gravitational effects.)
? V
So this is what I did so far..
I figured we need the energy conservation equation so KEi + PEi + Wnc = KEf + PEf
So, KEf= 7.6 x 10^4 m/s; KEi = 0
So, deltaPE = -7.6 x10^4 + Wnc
Wnc = q(deltaV) ; PE = kqq/r ...? But for some reason I can't figure out how to use those equations to solve for V. Help, please. Thank you!!
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The electric potential at the surface of the sphere is kQ/r = 9 x 10^9 x 1 x 10^-9/.15 = 60V = Vf
KEi + qVi = KEf + qVf
or 1/2 m (7.6 x 10^4)^2 + q Vf = 0 + qVi q = 1.6 x 10^-19 C and m = 1.67 x 10^-27 kg Vf = 60 and vi = 0 m/s
solve for Vi ( I got 90 V )
KEi + qVi = KEf + qVf
or 1/2 m (7.6 x 10^4)^2 + q Vf = 0 + qVi q = 1.6 x 10^-19 C and m = 1.67 x 10^-27 kg Vf = 60 and vi = 0 m/s
solve for Vi ( I got 90 V )