# Potential Energy of two spheres

• lcam2
In summary, two small metal spheres, A and B, with masses of 5.5 g and 9.4 g respectively, have equal positive charges of 8 μC. They are connected by a non-conducting string of length 1 m. The electrical potential energy of the system can be found using the equation U = K Q1Q2/R. If the string is cut, the acceleration of each sphere can be found using the equation F=ma. After a long time, the momentum of each sphere can be found using the conservation of energy and momentum equations.

## Homework Statement

Two small metal spheres, A and B, of mass mA = 5.5 g and mB = 9.4 g have equal positive charges of 8 μC. The spheres are connected by a non-conducting string of negligible mass and with length d = 1 m, which is much greater than the radii of the spheres.
a) What is the electrical potential energy of the system?
b) Suppose you cut the string. At that instant, what is the magnitude of the acceleration of each sphere?
c) After a very long time, what is the magnitude of the velocity of each sphere?

## Homework Equations

U=Electrical potential Energy
USystem = K Q1Q2/R

U =-W = -Fd; W= work

F=ma

P= Momentum; P=ma
Pi = pf

## The Attempt at a Solution

a) it is just the electrical potential energy of system.
USystem = K Q1Q2/R

b) U=-Fd
Using electric potential energy found in part a, find the force F.
Then F=ma, solve for masses of a and b, respectively.

c) momentum initial= final momentum, inital momentum of both spheres is zero, given that they were released from rest, when connected by the string.

ma*va = -mb*vb

I need another equation, to solve the problem
But i don't know what equation to use.

Use conservation of energy. At infinity potential energy is zero.

## What is the definition of potential energy?

Potential energy is the stored energy an object has due to its position or state. It is the energy that an object has the potential to convert into other forms of energy, such as kinetic energy, when it is released.

## What factors affect the potential energy of two spheres?

The potential energy of two spheres is affected by their masses, the distance between them, and the gravitational constant. The larger the masses of the spheres, the greater their potential energy. The greater the distance between the spheres, the lower their potential energy. The value of the gravitational constant, which is a constant number, also affects the potential energy of the spheres.

## How is the potential energy of two spheres calculated?

The potential energy of two spheres is calculated using the formula PE = G * (m1 * m2) / d, where PE is the potential energy, G is the gravitational constant, m1 and m2 are the masses of the spheres, and d is the distance between them.

## What happens to the potential energy of two spheres as they move closer together?

As two spheres move closer together, their potential energy decreases. This is because the distance between them decreases, and according to the formula for potential energy, a smaller distance results in a smaller potential energy. Therefore, as the spheres move closer, their potential energy is converted into kinetic energy, causing them to accelerate towards each other.

## Can the potential energy of two spheres be negative?

Yes, the potential energy of two spheres can be negative. This occurs when the spheres are very close to each other, resulting in a negative value for the potential energy according to the formula. A negative potential energy indicates that the spheres are bound together by a strong force, such as gravity, and will require a greater amount of energy to separate them.