The mass of a proton is 1836 times the mass of an electron.

[Mdhiggenz]

Homework Statement

The mass of a proton is 1836 times the mass of an electron.

A) A proton is traveling at speed . At what speed (in terms of ) would an electron have the same kinetic energy as the proton?

B) An electron has kinetic energy K . If a proton has the same speed as the electron, what is its kinetic energy (in terms of K )?

Homework Equations

The Attempt at a Solution

The answer for A is 42.85, and to get it here is what I did.

Kp-ke=0

Kp=Ke

1/2mv^2=1/2(1836m)v^2

Ve=squareroot(2*918vp)=42.85

Part B the answer is 1836

But I have no clue on how to get it. Since their velocities are equal I was thinking of setting them both to 1.

1/2m(1)^2=1/2(1836m)(1)^2

I don't know what to do after this.. tried solving for M but that doesn't make sense.

Thank you

 

[tiny-tim]

Hi Mdhiggenz!

Where's the difficulty?

Just call the velocity "v", write out the KE for both particles, and find their ratio …

what do you get? ​

 

[emailanmol]

Hello,

As i see from your previous posts you have a little trouble in solving equations :-)
Don't worry it will go away with practice.

Write the KE=(mv*2)/2

so v^2=2KE/m

now since velocity for proton and electron is given equal we have
2KE(p)/m(p) = 2KE(e)/m(e) (here KE(p) means kinetic energy of proton)

now you have a relation between m(p) and m(e) so equate the two equations above.

 

[Mdhiggenz]

I got Ke(p) = 2ke/me*mp is that correct?

 

[emailanmol]

No, the factor of 2 is extra.
RHS should not have the factor 2.

As i have written 2KE(p)/m(p) = 2KE(e)/m(e)

i.e same as KE(p) = KE(e)/m(e) *m(p)

 

[Mdhiggenz]

Thx email I finally got it. I was missing the mp=1836me relation ship and when you plug and chug using the ration is all makes sense.