Need help with physics questions with charges and velocity

[tripz1196]

Need help with physics questions with charges and velocity!

Hi,
I need some help with a couple problems from my AP physics class regarding charges and velocity.

1. Two insulating spheres having radii 0.41 cm and 0.61 cm, masses 016 kg and 0.78 kg and charges -2 micro coulombs and 4 micro coulombs are released from rest when their centers are separated by 0.5 meters. how fast is the smallest sphere moving when they collide. Answer in m/s.

i'm not quite sure how to tie in momentum to this question because you're given mass and need to find final velocity...but how do you connect the charges and radii into the problem? do you find the electrical force between the two..?

i have no idea how to solve it.


2.when a potential difference of 198V is applied to the plates of a parallel-plate capacitor the plates carry a surface charge density of 14nC/cm^2. The permittivity of a vacuum is 8.85419 10^-12 C^2/N*m^2. What is the spacing between the two plates? Answer in units of micrometers.

any help would be great.thanks!

 

[blechman]

Hi,

1. Two insulating spheres having radii 0.41 cm and 0.61 cm, masses 016 kg and 0.78 kg and charges -2 micro coulombs and 4 micro coulombs are released from rest when their centers are separated by 0.5 meters. how fast is the smallest sphere moving when they collide. Answer in m/s.

i'm not quite sure how to tie in momentum to this question because you're given mass and need to find final velocity...but how do you connect the charges and radii into the problem? do you find the electrical force between the two..?

i have no idea how to solve it.

You can use energy conservation: the spheres have potential energy but no kinetic energy at the start, and they have both potential and kinetic at the time of collision. Since Coulomb force is conservative, the total energy is conserved. That's one equation.

Normally, you can only use momentum conservation when there are no forces (since the time change of momentum is force by Newton's second law), but this case is nice: Newton's third law gives us that the forces on sphere 1 by sphere 2 is equal and opposite to the force on sphere 2 by sphere 1, so therefore the momentum of sphere 1 is equal and opposite to the momentum of sphere 2; can you prove it with math and not words? That's the second equation.

Two equations, two unknowns (v1 and v2). You're all set!

2.when a potential difference of 198V is applied to the plates of a parallel-plate capacitor the plates carry a surface charge density of 14nC/cm^2. The permittivity of a vacuum is 8.85419 10^-12 C^2/N*m^2. What is the spacing between the two plates? Answer in units of micrometers.

Recall the definition of capacitance: Q=CV. You know what C is in terms of the geometry of the problem. The rest is manipulating terms.

Hope this helps. Have fun!