Two spheres, fastened to “pucks” riding on a
frictionless airtrack, are charged with +2 ×
10
−8
C, and +6 × 10
−8
C, respectively. Both
objects have the same mass. As they repel
this makes no sense.
each other, the smaller charged sphere moves to the right with a certain velocity while the larger charged sphere moves to the left with another velocity.
To find the velocities of the spheres, we can use the principles of conservation of momentum and conservation of electric potential energy.
Let's denote the velocities of the smaller and larger spheres as v1 and v2, respectively.
1. Conservation of momentum:
According to conservation of momentum, the total momentum before the interaction should be equal to the total momentum after the interaction.
Since the smaller sphere moves to the right and the larger sphere moves to the left, their velocities have opposite directions.
Thus, we can write the equation as:
(mass of smaller sphere * velocity of smaller sphere) + (mass of larger sphere * velocity of larger sphere) = 0
2. Conservation of electric potential energy:
According to conservation of electric potential energy, the total electric potential energy before the interaction should be equal to the total electric potential energy after the interaction.
The electric potential energy of a charged object is given by the equation U = k * (q1 * q2) / r, where k is the electrostatic constant, q1 and q2 are the charges of the spheres, and r is the distance between them.
Since the spheres are fastened to pucks on a frictionless airtrack, the distance between them remains constant.
Thus, we can write the equation as:
(k * (q1^2) / r) + (k * (q2^2) / r) = (k * (q1 * q2) / r) + (k * (q1 * q2) / r)
By solving these two equations simultaneously, we can find the velocities v1 and v2 of the spheres.