A positive charge of 5.10 C is fixed in place. From a distance of 3.70 cm a particle of mass 6.80 g and charge +2.60 C is fired with an initial speed of 70.0 m/s directly toward the fixed charge. How close to the fixed charge does the particle get before it comes to rest and starts traveling away?
Particle 1 carrying -4.0 μC of charge is fixed at the origin of an xy coordinate system, particle 2 carrying +8.0 μC of charge is located on the x axis at x = 4.0 m , and particle 3, identical to particle 2, is located on the x axis at x = -4.0 m .
What is the vector sum of the electric forces exerted on particle 3? Determine the x and y components of the vector sum.
Express your answers separated by a comma.
To solve this problem, we can use the principle of conservation of energy. The initial kinetic energy of the particle is converted into electric potential energy as it moves closer to the fixed charge, and eventually comes to rest before moving away.
Here are the steps to find the distance where the particle comes to rest:
1. Calculate the initial kinetic energy of the particle using the formula:
KE = (1/2) * mass * velocity^2
Substituting the given values:
KE = (1/2) * 6.80 g * (70.0 m/s)^2
Convert the mass from grams to kilograms:
KE = (1/2) * 0.00680 kg * (70.0 m/s)^2
Calculate the result to find the initial kinetic energy.
2. Calculate the electric potential energy when the particle comes to rest. At this point, all of the initial kinetic energy is converted to electric potential energy. Thus, we have:
PE = electrical potential energy
3. The electric potential energy can be calculated using the formula:
PE = (k * |q1 * q2|) / r
where:
k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2),
q1 is the charge of the fixed charge (5.10 C),
q2 is the charge of the particle (+2.60 C),
and r is the distance between the charges at rest (which we need to find).
4. Substitute the values into the formula and solve for r:
(k * |q1 * q2|) / r = PE
Rearrange the equation to solve for r:
r = (k * |q1 * q2|) / PE
Substitute the known values to find the distance r at which the particle comes to rest.
By following these steps, you can find the distance at which the particle comes to rest before moving away from the fixed charge.