Velocity of insulating sphere before colliding with other insulatin spherre

• phymateng
In summary, the problem involves two insulating spheres with different radii, masses, and charges, released from rest and separated by a distance of 1.3 m. The question asks for the velocity of the smaller sphere at the moment of collision. The suggested equations for solving this problem are conservation of energy and conservation of total momentum.
phymateng

Homework Statement

Two insulating spheres having radii 0.47 cm and 0.67 cm, masses 0.13 kg and 0.89 kg, and charges −4 μC and 2 μC are released from rest when their centers are separated by 1.3 m. How fast is the smaller sphere moving when they collide? Answer in units of m/s.

Homework Equations

What techique or conceptual understading can help me attack this problem? Am I missing something?

The Attempt at a Solution

I tried to use the conservation of energy. But there are two problems, because they don't hit and stop, so they must both be independet from each other (unless the problem would tell me that they collide and their final velocity is 0. I don't know how to relate the two spheres. I do know that they have charges that attract each other and that I could use the force of the electric field if I treat them as point charges. But with the force of the electric field I don't know if it can be useful because I can't use it to find the velocity. If I use kinematics it won't work since there is no time given.

Last edited:
phymateng said:
I tried to use the conservation of energy. But …

Hi phymateng!

Yes, you do need an extra equation …

use conservation of total momentum …

momentum is always conserved.

1. What is the equation for calculating the velocity of an insulating sphere before colliding with another insulating sphere?

The equation for calculating the velocity of an insulating sphere before colliding with another insulating sphere is v = (m1 * v1 + m2 * v2) / (m1 + m2), where v is the final velocity, m is the mass, and v1 and v2 are the initial velocities of the two spheres respectively.

2. How does the mass of the insulating spheres affect the velocity before collision?

The mass of the insulating spheres directly affects the velocity before collision. As the mass increases, the velocity decreases according to the equation v = (m1 * v1 + m2 * v2) / (m1 + m2). This is because the larger mass will have a greater influence on the final velocity.

3. What is the role of initial velocity in determining the final velocity of the insulating spheres?

The initial velocity of the insulating spheres plays a significant role in determining the final velocity. The equation v = (m1 * v1 + m2 * v2) / (m1 + m2) shows that the initial velocity of each sphere is directly related to the final velocity. The higher the initial velocity, the higher the final velocity will be.

4. How does the velocity of the insulating spheres change after collision?

The velocity of the insulating spheres changes after collision according to the law of conservation of momentum. This means that the total momentum before the collision will be equal to the total momentum after the collision. Therefore, the velocities of the spheres will change, but their total momentum will remain the same.

5. What factors can affect the velocity of insulating spheres before collision?

There are several factors that can affect the velocity of insulating spheres before collision. These include the mass and initial velocity of the spheres, as well as any external forces acting on the spheres. Other factors such as air resistance and friction can also have an impact on the velocity.

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