Calculating Work Required to Accelerate an Electron

[AnnieD]

Homework Statement

How much work is required to accelerate an electron from rest to 1.6 x 10 ^8m/s. (m= 9.1 x 10 ^ -31kg)?

The answer should be: 2.7 x 10 ^ -18

Homework Equations

a = Fnet/m
W = F x d
W = E

The Attempt at a Solution

I can't see a way to figure this problem out. It seems I need the distance, but I can't figure it out because I don't have a time to use to figure that out, or the acceleration rate. I tried rearranging a = Fnet/m .. but was again then stuck with the distance/time problem. Am I missing something?

 

[hotcommodity]

The total work done on an object is defined as the objects change in kinetic energy:

$$W_{TOT} = \Delta K$$

where $$\Delta K = 0.5mv^2_f - 0.5mv^2_0$$

All you have to figure out now is the electrons inital and final kinetic energies. Does that help?

 

[fantispug]

You don't know the acceleration (for you are not given how long it takes to accelerate the electron to this speed - if it takes 1 second a=1.6 x 10^8 m/s^2 or if it takes 2 seconds a=0.8*10^8 m/s^2), and you don't know the distance so
W=F d and F = m a are not going to be too helpful.
Look more closely at your 3rd equation - what energy did the electron initially have? What energy does it have finally?
(Warning: This method should work but I got a different result to the one stated - though I am assuming it is in SI units)

 

[AnnieD]

Yes, forgot to mention that I also tried the W = delta E equation.
So E = Ek2 - Ek1
but the answer I ended up getting wasn't the right one.
I ended up with a final answer of 1.1648 x 10 ^ - 14

 

[kudoushinichi88]

You may have copied the question wrongly... or the answer is wrong. I calculated and got $$1.16 \times 10^{-14} J$$ as well.

 

[hotcommodity]

You may have copied the question wrongly... or the answer is wrong. I calculated and got $$1.16 \times 10^{14} ms^{-1}$$ as well.

I believe that should be $$10^{-14}$$ and in units of Joules.

It would be a good idea to double check your values, as kudoushinichi suggested. Text book authors have been know to make errors.

 

[kudoushinichi88]

Oops... typed without thinking much... Sorry...

 

[rl.bhat]

When the electron is moving with the velocity = 1.6*10^8 m/s we have to consider the relativistic mass and energy.

 

[kudoushinichi88]

Oh I totally forgot about relativity... since I haven't really studied that in a formal class...

So we use the equation

$$E_k = (\gamma - 1)mc^2$$

right?

But then I plugged in the values and yielded $$1.49 \times 10^{-14} J$$ instead...

 

[AnnieD]

Thanks everyone for your help! We've come to the conclusion (my physics teacher) that the book is wrong. The correct answer is the one others as well as myself mentioned earlier as the value. I don't know anything about relativity- it's only a gr.12 class, but thank you for trying nonetheless! Much appreciated. :)