Calculating Proton Kinetic Energy in an Electric Field

[tommyhakinen]

Homework Statement

Two identical parallel metal plates are separated by 8 mm. A voltage of 170V is applied across them. A proton moves in the same direction of electric field between the two plates through a distance of 3mm. If the initial speed of the proton is 1.5 x 10⁵ m/s, what is the final kinetic energy of the proton?

Homework Equations

ΔV = E ΔX
KE = 0.5mv²
ΔPE = -qEΔX

The Attempt at a Solution

Since the proton moves in the same direction of the electric field, the proton gains kinetic energy but lose potential energy. I was thinking that the final kinetic energy:

KE_final = KE_initial + ΔPE

I have found that ΔPE = -1.02 x 10^-17 J

Is this the correct way of solving this problem? Please correct me if I am wrong.

 

[physics girl phd]

Looks good to me!

There is, BTW, another approach too: Finding the field, using the field to write the equations of motion via the acceleration of the proton and your given initial conditions, then relating the equations of motion to find speed at your final distance! (This is WAY more difficult mathematically than your approach, but will result in the same answer... I encourage you to try it too!)

 

[tommyhakinen]

Thanks for the quick reply.

Finding the field, using the field to write the equations of motion via the acceleration of the proton and your given initial conditions, then relating the equations of motion to find speed at your final distance!

Is this what you meant?
∑F = ma
F = qE
E = ΔV / ΔX
then substitute the value of acceleration a into
v_final² = v_initial² + 2aΔx

then find the KE = 0.5mv_final²

 

[physics girl phd]

Yes, except I never have this equation memorized :

v_final² = v_initial² + 2aΔx

I tend to stick with the "raw" a, v, and x equations for motion... so you have to solve the position equation for time (a quadratic equation), use the time to find final velocity, then use that velocity to find the final kinetic energy. ( even IF you use an online quadratic equation root finder to save time!)

You probably did similar comparisons when you worked with dynamics in gravitational fields in mechanics... and found the same: isn't energy conservation so much nicer than using equation of motion, even though BOTH approaches are valid?

 

[tommyhakinen]

Yes. It's the same in mechanics. Thank you very much for the help..