Electrostatics, finding velocity of proton

[physics604]

1. A moving proton has 6.4 x 10-16 J of kinetic energy. The proton is accelerated by a potential difference of 5 000 V between parallel plates. The proton emerges from the parallel plates with what speed?

a) 1.3 x 10⁶ m/s
b) 8.8 x 10⁵ m/s
c)1.8 x 10⁶ m/s
d) 9.8 x 10⁵ m/s

Homework Equations

$\Delta$E_k + $\Delta$E_p = 0

The Attempt at a Solution

E_ki + E_kf = -E_p
6.4×10^-16 + 1/2mv² = -Q$\Delta$v

v= √ [(-1.6x10^-19×-5000)-6.4x10^-16 ×2 / 1.67x10^-27] = 437740.5241...

My answer doesn't match with any of the responses. What did I do wrong?

 

[Simon Bridge]

Looks like you have misplaced a minus sign or three.
I suspect you have applied the formula without understanding it.

Derive the relation you need using:
Gain in kinetic energy = loss in potential energy

Hint:
what is the initial speed of the proton?
should the final speed be greater than or less than this?
what does this say about the final kinetic energy vs the initial kinetic energy?
how does this relate to the change in potential energy (careful)?

 

[physics604]

Okay, I get it!

$\Delta$E_k = E_kf - E_ki

I just used that part of the formula wrong.

 

[Simon Bridge]

Though had you gone to the physics first, you wouldn't have needed to know how to use any particular formula.
You can get a long way just looking for equation to stick the numbers you have into - but that way of thinking will always bite you eventually.

But "no worries" aye?

 

[Nickie]

It looks like you have the right approach, but there may be a calculation error. Here is the correct solution:

First, we can use the equation for electric potential energy to find the initial kinetic energy of the proton:

Ep = qΔV

Where q is the charge of the proton (1.6x10^-19 C) and ΔV is the potential difference (5000 V).

Ep = (1.6x10^-19 C) (5000 V) = 8.0x10^-16 J

Next, we can use the conservation of energy equation to find the final kinetic energy of the proton:

Eki + Ekf = Ep

Where Eki is the initial kinetic energy (unknown) and Ekf is the final kinetic energy (also unknown).

8.0x10^-16 J + 6.4x10^-16 J = Eki + Ekf

Eki + Ekf = 1.4x10^-15 J

Since the proton is moving in a straight line, we can assume that there is no change in the potential energy (ΔEp = 0). Therefore, all of the initial kinetic energy is converted into final kinetic energy.

Eki = Ekf

1.4x10^-15 J = 2Ekf

Ekf = 7.0x10^-16 J

Finally, we can use the equation for kinetic energy to find the final velocity of the proton:

Ekf = 1/2mv^2

Where m is the mass of the proton (1.67x10^-27 kg) and v is the final velocity (unknown).

7.0x10^-16 J = 1/2 (1.67x10^-27 kg) v^2

v^2 = (2)(7.0x10^-16 J)/(1.67x10^-27 kg) = 8.4x10^11 m/s^2

v = √(8.4x10^11 m/s^2) = 9.2x10^5 m/s

Therefore, the correct answer is d) 9.8 x 10^5 m/s.