Velocity of two insulating charged spheres at collision

[intemk9]

Homework Statement

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.200 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m.
(a) How fast will each be moving when they collide?

Homework Equations

The Attempt at a Solution

I know i need to use the conservation of energy for the potential and kinetic forces, but I cannot figure out how to appropriately set up the equation in order to do so.

 

[tiny-tim]

welcome to pf!

hi intemk9! welcome to pf!

don't forget you can also use conservation of momentum

 

[Simon Bridge]

Can you argue through the conservation of energy and momentum in words? What sort of energy does each sphere start out with, and what kind does it have at the end of the motion? Do you know the equations for kinetic and potential energy?

 

[nasu]

I think that the question is about velocity just before collision and not after collision.
The wording is a little ambiguous. If the rest of the problem were given, I suppose it will become more clear.
For part (a) conservation of energy may be enough.

 

[Nickie]

I would approach this problem by first considering the forces acting on the two spheres. The charged spheres will experience a repulsive force due to their charges, which will cause them to accelerate towards each other. Additionally, the spheres will also experience a gravitational force due to their masses, which will cause them to accelerate towards each other.

Next, I would use the principle of conservation of energy to solve for the velocities of the spheres at the moment of collision. This principle states that the total energy of a system remains constant, and can only be transferred between different forms. In this case, the initial potential energy of the system (due to the separation between the spheres) will be converted into kinetic energy as the spheres accelerate towards each other.

To set up the equation, I would first calculate the initial potential energy of the system using the formula U = kq1q2/r, where k is the Coulomb's constant, q1 and q2 are the charges on the spheres, and r is the initial separation between the centers of the spheres.

Next, I would use the conservation of energy equation, where the initial potential energy is equal to the final kinetic energy of the system (since there is no friction or other external forces acting on the system). This can be written as:

U = 1/2mv1^2 + 1/2mv2^2

Where m is the mass of each sphere, and v1 and v2 are the velocities of the spheres at the moment of collision.

Using this equation, I can solve for the velocities of the spheres at the moment of collision, and thus answer the question of how fast each sphere will be moving when they collide.

In summary, as a scientist, I would approach this problem by considering the forces acting on the spheres and using the principle of conservation of energy to solve for the velocities at the moment of collision.