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!

 

[ogb p]

Hi there,

It seems like you are struggling with some basic concepts in electrostatics and electricity. Don't worry, we can work through these problems together.

For the first problem, you are correct in thinking that momentum plays a role in solving this. Remember that momentum is equal to mass times velocity (p=mv). In this case, we have two spheres with different masses and charges, so we need to use the conservation of momentum principle. This states that the total momentum before the collision is equal to the total momentum after the collision. So, we can set up an equation:

(m1v1 + m2v2) = (m1v1' + m2v2')

Where m1 and m2 are the masses of the spheres, v1 and v2 are their initial velocities (which are both zero since they are released from rest), and v1' and v2' are their final velocities (which we are trying to find). We also know that the electrical force between the spheres will cause them to accelerate towards each other, and this force is given by Coulomb's Law:

F = k * (q1 * q2) / r^2

Where k is the Coulomb's constant, q1 and q2 are the charges of the spheres, and r is the distance between their centers (which is given as 0.5 meters). We also know that force equals mass times acceleration (F=ma), so we can set up another equation:

ma = k * (q1 * q2) / r^2

Now, we can solve for acceleration (a) and plug it into our conservation of momentum equation, along with the given values for masses and charges:

(0.016 * 0 + 0.78 * 0) = (0.016 * v1' + 0.78 * v2')

And solving for v1' (since that is the velocity of the smaller sphere):

v1' = (0.78 * 0.41^2 * 4 * 10^-6) / (0.5 * 0.016)

v1' = 0.016 m/s

So, the final velocity of the smaller sphere is 0.016 m/s when they collide.

For the second problem, we can use the formula for capacitance (C = Q/V) to find the charge (Q) on the plates. We know that