A proton with mass 1.67×10−27 kg and charge 1.60×10−19 C accelerates from rest in a uniform electric field of strength 500 N/C. (a) What is the magnitude of the acceleration of the proton? (b) How long does it take the proton to reach a speed of 35,000 m/s? (c) What distance has the proton traveled when it reaches this speed? (d) What is the kinetic energy of the proton at 35,000 m/s?
I have the 1st two answers, I just don't know how to calculate the other two. Everything I have tried comes out with a wrong answer.
(a) 479.04e+8 m/s2
(b) 7.30627923e-7 s
(c) m
(d) J
F = q E = m a
so
a = (q/m)E
= (1.6*10^-19/1.67*10^-27)5*10^2
= 4.79 * 10^10 m/s^2
v = a t
3.5*10^4 = 4.79 * 10^10 t
t = .731 * 10^-6 = 7.31*10^-7 seconds
d = (1/2) a t^2
Ke = (1/2) m v^2
I think you can do c and d
I don't understand what the "^2" means or how to use it in the equation.
The ^2 means squared. v^2 is velocity squared.
what would be the mass of the proton?
To solve this problem, we can use the basic equations of motion and the equations governing the motion of a charged particle in an electric field.
(a) The magnitude of the acceleration of the proton can be found using the equation:
acceleration = force/mass
Given:
Mass of the proton (m) = 1.67×10−27 kg
Electric field strength (E) = 500 N/C
Therefore,
Acceleration (a) = E/m
Substituting the values, we get:
a = 500 N/C / 1.67×10−27 kg
Now, calculating the value of the acceleration will give us the answer.
(b) To find the time taken by the proton to reach a speed of 35,000 m/s, we need to use the equation:
acceleration = change in velocity / time
Rearranging the equation, we get:
time = change in velocity / acceleration
Given:
Initial velocity (u) = 0 m/s (as the proton starts from rest)
Final velocity (v) = 35,000 m/s
Acceleration (a) - calculated from part (a)
Substituting the values in the equation will give us the answer.
(c) The distance traveled by the proton can be calculated using the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time^2
Given:
Initial velocity (u) = 0 m/s
Time (t) - calculated from part (b)
Acceleration (a) - calculated from part (a)
Plugging in the values and calculating will give us the answer.
(d) The kinetic energy of the proton can be found using the equation:
kinetic energy = 1/2 * mass * velocity^2
Given:
Mass of the proton (m) = 1.67×10−27 kg
Final velocity (v) = 35,000 m/s
Substituting the values in the equation and calculating will give us the answer.