One particle has a mass of 2.86 x 10-3 kg and a charge of +7.32 μC. A second particle has a mass of 6.41 x 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.127 m, the speed of the 2.86 x 10-3 kg-particle is 116 m/s. Find the initial separation between the particles.
Pls help
To solve this problem, we can use the principle of conservation of mechanical energy. The total mechanical energy of the system (including both particles) is conserved.
1. Let's first find the initial kinetic energy of the system.
- The initial speed of the 2.86 x 10^-3 kg-particle is given as 116 m/s.
- The mass of the 2.86 x 10^-3 kg-particle is given as 2.86 x 10^-3 kg.
- Use the formula: Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * (2.86 x 10^-3 kg) * (116 m/s)^2
2. Now, let's find the electric potential energy between the two particles at the initial separation.
- The electric potential energy between two charges is given by the formula: Electric Potential Energy = (k * q1 * q2) / r
where k is the Coulomb constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the separation distance.
- The charges on the particles are given as +7.32 μC each.
- The separation distance is what we need to find, so let's represent it as "d".
- The electric potential energy at the initial separation is: Electric Potential Energy = (k * q1 * q2) / d
3. Since the total mechanical energy is conserved, the sum of the initial kinetic energy and the initial electric potential energy should be equal to the final kinetic energy.
- Final kinetic energy is zero because the particles come to rest at the maximum separation.
- Therefore, the equation becomes: Initial kinetic energy + Initial electric potential energy = 0
4. Plug in the values we have and solve for the initial separation distance "d".
- Initial kinetic energy = (1/2) * (2.86 x 10^-3 kg) * (116 m/s)^2
- Initial electric potential energy = (k * q1 * q2) / d
- Set the sum equal to zero and solve for "d".
Note: Remember to convert the charge from μC to C by dividing by 10^6 (since 1 μC = 10^-6 C).
I hope this explanation helps you to solve the problem. If you need further assistance, feel free to ask.