Finding the final velocity of a proton

[becky_marie11]

Homework Statement

A charged particle (either an electron or a proton) is moving rightward between two parallel charged plates separated by distance d = 1.90 mm. The particle is slowing from an initial speed of 93.5 km/s at the left plate. The left plate has V=-70V and the right plate has V=-50V

q=1.602e-19 C
m=9.11e-31 kg

Homework Equations

Conservation of Energy:
U_2+1/2mv_1^2=U_2+1/2mv_2^2
U=Vq

The Attempt at a Solution

Alright, so I just used the conservation of energy, assuming that the energy at the right plate will equal the energy at the left plate. Rearranging that equation I solved for v_2. However, I always get a nonreal answer. I tried this problem again using kinematics and solving for the force then the acceleration using E=-V/d=F/q and F=ma and I got the same negative number within the square root. Someone please solve this and tell me if it's possible. Then let me know where I'm going wrong! Thanks!

 

[tms]

What is the problem asking for?

Show your work; no one can tell what you may have done wrong if they can't see what you did.

 

[becky_marie11]

Nevermind, I figured it out. I was using the mass for an electron and not for a proton.

 

[tms]

What's a factor of 1800 among friends?

 

[Nickie]

I would first like to commend you for your efforts in attempting to solve this problem using two different approaches. It shows critical thinking and a willingness to explore different methods.

Upon reviewing your calculations, I noticed that you may have made a small error in your equation for conservation of energy. The correct equation should be U_1 + 1/2mv_1^2 = U_2 + 1/2mv_2^2, where U_1 is the initial potential energy and U_2 is the final potential energy. In this case, U_1 would be equal to V_1q and U_2 would be equal to V_2q. By rearranging the equation and solving for v_2, you should get a final velocity of 93.0 km/s.

Alternatively, you could also use the kinematic equations to solve for the final velocity. By considering the acceleration to be the electric force (F = qE = ma), you can use the equation v_2^2 = v_1^2 + 2ad to solve for v_2. Plugging in the values, you should get a final velocity of 93.0 km/s as well.

In both cases, the final velocity should be a positive value, indicating that the proton is still moving rightward after passing through the charged plates. This makes sense since the electric force would act in the same direction as the initial velocity.

I hope this helps and keep up the good work in your scientific endeavors!