A proton accelerates from rest in a uniform electric field of 620 N/C. At one later moment, its speed is 1.30 Mm/s (nonrelativistic because v is much less than the speed of light).
(a) Find the acceleration of the proton.
m/s2
(b) Over what time interval does the proton reach this speed?
s
(c) How far does it move in this time interval?
m
(d) What is its kinetic energy at the end of this interval?
J
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I've solved:
1.30Mm x (1m/1000Mm) = .0013
(.0013)(620)/(1.67x10e-27) = 4.826e26,
but I got the wrong answer. What am I doing wrong? If i can get part A right I can do the rest.
To solve part (a), you need to use the equation for the acceleration of a charged particle in a uniform electric field:
acceleration = (electric field strength) / (particle mass)
In this case, the electric field strength is 620 N/C. However, you made an error in converting the speed from Mm/s to m/s.
The correct conversion is 1.30 Mm/s * (10^6 m/1 Mm) = 1.30 * 10^6 m/s.
Now you can plug in the values into the equation:
acceleration = (620 N/C) / (1.67 × 10^-27 kg)
Calculating this gives you:
acceleration = 3.71 × 10^29 m/s^2
Therefore, the acceleration of the proton is 3.71 × 10^29 m/s^2.
To solve part (a), let's analyze the information given in the problem. We know that the proton starts from rest, so its initial velocity, v₀, is 0 m/s. We also know the nonrelativistic velocity, v, is 1.30 Mm/s (which you correctly converted to 0.0013 m/s).
The proton is accelerated by a uniform electric field, and the force it experiences can be calculated using Coulomb's law:
F = q * E
Where F is the force, q is the charge of the proton (which is the elementary charge, 1.6 x 10^(-19) C), and E is the electric field strength (620 N/C).
Since F = m * a (Newton's second law), where m is the mass of the proton (1.67 x 10^(-27) kg), we can set up the equation:
m * a = q * E
Plugging in the values we have, we get:
(1.67 x 10^(-27) kg) * a = (1.6 x 10^(-19) C) * (620 N/C)
a = (1.6 x 10^(-19) C) * (620 N/C) / (1.67 x 10^(-27) kg)
a ≈ 5.961 x 10^6 m/s^2
So, the acceleration of the proton is approximately 5.961 x 10^6 m/s^2.
You did some strange calculations. Your unit factor is silly. Mm is not millimeters, it is Megameters.
F=ma
a= F/m=Eq/m YOu know E (in N/C), you know the mass and charge on a proton.
F*deltaTime= mv
Eq*deltaTime=mv
solve for deltaTime