A proton is projected in the positive x direction into a region of uniform electric field E = (-6.80 * 10^5 N/C at t = 0. The proton travels 6.80 cm as it comes to rest.
(a) Determine the acceleration of the proton.
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To determine the acceleration of the proton, we can use the equation F = ma, where F is the force acting on the proton, m is the mass of the proton, and a is the acceleration.
In this case, the only force acting on the proton is the electric force, given by F = qE, where q is the charge of the proton and E is the electric field.
Given that E = -6.80 * 10^5 N/C and q is the charge of a proton (which is the elementary charge e = 1.602 * 10^-19 C), we can substitute these values into the equation to find the force:
F = (1.602 * 10^-19 C) * (-6.80 * 10^5 N/C)
F ≈ -1.090 * 10^-13 N
Since the force acting on the proton is in the opposite direction of motion (positive x direction), the acceleration of the proton will also be in the opposite direction.
Now, applying Newton's second law (F = ma) and rearranging the equation, we can solve for the acceleration:
a = F / m
The mass of a proton is approximately 1.67 * 10^-27 kg. Substituting this value along with the force we calculated earlier:
a = (-1.090 * 10^-13 N) / (1.67 * 10^-27 kg)
a ≈ -6.527 * 10^13 m/s^2
Therefore, the acceleration of the proton is approximately -6.527 * 10^13 m/s^2 in the negative x direction.