Question
At1=0, a proton is projected in the positive x-direction into a region of a uniform electric field of E=-6x1051. The proton travels 7.00 cm as it comes to rest. Determine Its initial speed.
in the simplest steps
in the simplest steps
Answers
GPT 3.5
To determine the initial speed of the proton, we can use the equation of motion for an object in a uniform acceleration:
vf^2 = vi^2 + 2ax
Where vf is the final velocity (0 m/s since the proton comes to rest), vi is the initial velocity (unknown), a is the acceleration (caused by the electric field), and x is the displacement (7.00 cm or 0.07 m).
Given that the electric field E = -6x10^51 N/C, we can calculate the acceleration of the proton using Newton's second law:
F = ma
Where F is the force acting on the proton and m is the mass of the proton. The force acting on the proton is given by:
F = qE
Where q is the charge of the proton. The charge of the proton is the elementary charge e:
q = e = 1.6x10^-19 C
Substituting this into the equation:
Fe = ma
qE = ma
Solving for the acceleration:
a = qE/m = (1.6x10^-19 C)(-6x10^51 N/C)/(1.67x10^-27 kg) = -9.6x10^-7 m/s^2
Substituting the known values into the equation of motion:
(0 m/s)^2 = vi^2 + 2(-9.6x10^-7 m/s^2)(0.07 m)
0 = vi^2 - 1.344x10^-8 m^2/s^2
Solving for vi:
vi^2 = 1.344x10^-8 m^2/s^2
vi = sqrt(1.344x10^-8 m^2/s^2) ≈ 3.6667x10^-4 m/s
Therefore, the initial speed of the proton is approximately 3.67x10^-4 m/s.
vf^2 = vi^2 + 2ax
Where vf is the final velocity (0 m/s since the proton comes to rest), vi is the initial velocity (unknown), a is the acceleration (caused by the electric field), and x is the displacement (7.00 cm or 0.07 m).
Given that the electric field E = -6x10^51 N/C, we can calculate the acceleration of the proton using Newton's second law:
F = ma
Where F is the force acting on the proton and m is the mass of the proton. The force acting on the proton is given by:
F = qE
Where q is the charge of the proton. The charge of the proton is the elementary charge e:
q = e = 1.6x10^-19 C
Substituting this into the equation:
Fe = ma
qE = ma
Solving for the acceleration:
a = qE/m = (1.6x10^-19 C)(-6x10^51 N/C)/(1.67x10^-27 kg) = -9.6x10^-7 m/s^2
Substituting the known values into the equation of motion:
(0 m/s)^2 = vi^2 + 2(-9.6x10^-7 m/s^2)(0.07 m)
0 = vi^2 - 1.344x10^-8 m^2/s^2
Solving for vi:
vi^2 = 1.344x10^-8 m^2/s^2
vi = sqrt(1.344x10^-8 m^2/s^2) ≈ 3.6667x10^-4 m/s
Therefore, the initial speed of the proton is approximately 3.67x10^-4 m/s.
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