A free electron and a free proton are exactly 1.0 com apart. Find the magnitude and direction of (a) the acceleration of the proton and (b) the acceleration of the electron.
How far is a com? Do you mean centimeter (cm) ?)
Use Coulomb's Law for the force, F.
F = ke^2/d^2
For the acceleration a, use
a = F/m
m = electron mass
yeah I meant cm. so for F= 8.99*10^9(9.11*10^-31)/ .01m^2 ?
NO. Instead of the square of the elctron charge, e^2, in units of coulomb^2, you have used the electron mass,in kg.
To find the magnitude and direction of the acceleration of the proton and the electron, we need to apply Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Given:
Distance (r) = 1.0 cm = 0.01 meters
Charge of the electron (qe) = -1.6 x 10^-19 C
Charge of the proton (qp) = +1.6 x 10^-19 C
Mass of the electron (me) = 9.1 x 10^-31 kg
Mass of the proton (mp) = 1.7 x 10^-27 kg
Using Coulomb's law, the formula for the electric force (F) between two charged particles is given by:
F = k * (|qe| * |qp|) / r^2
where k is the Coulomb constant (k = 9 x 10^9 N m²/C²).
a) Acceleration of the proton:
To find the acceleration of the proton, we need to calculate the force acting on it and then divide it by the mass of the proton (Newton's second law, F = ma).
1. Calculate the electric force between the proton and the electron:
Fp = k * (|qe| * |qp|) / r^2
2. Calculate the acceleration of the proton:
ap = Fp / mp
b) Acceleration of the electron:
To find the acceleration of the electron, we can follow the same steps as above.
1. Calculate the electric force between the electron and the proton:
Fe = k * (|qe| * |qp|) / r^2
2. Calculate the acceleration of the electron:
ae = Fe / me
Now, substitute the given values into these formulas, solve for Fp, ap, Fe, and ae, and then determine their magnitudes and directions using the given charges and distances.