Speed Ratio of Particle A to B?

[bmandrade]

Particle A has three times the mass and twice the kinetic energy of particle B. what is the speed ratio Va/Vb

 

[hage567]

You need to show some work before you can receive help. What have you tried so far?

 

[bmandrade]

Well i am working on it and I came up with equations

2k= 1/2*3M*Va
k=1/2*M* Vb

but I got stuck I really don't know what to do with this equations

 

[hage567]

Your equation for kinetic energy is wrong. The velocity is supposed to be squared.

So you have two equations. How do you think you might put them together?

 

[bmandrade]

equal to each other i was thiking maybe dividing the firt equation by 2 so that both equations equal to K

 

[hage567]

OK. Then what?

 

[bmandrade]

equal each other and solve for Va/Vb?

 

[bmandrade]

it gives me 1/6

 

[bmandrade]

sorry 1/36

 

[hage567]

Can you show more of the steps on how you got that number?

 

[bmandrade]

ok so i did it again and i notices i had skipped a step and got a new answer which is square root of 1/3

here is the work

2k= 1/2 3M Va^2 divide by 2
k= (3M Va^2) / 2 set it equal to the other equation
(3M Va^2)/ 2 = 1/2 M Vb^2 muiltiply by 2
3M Va^2 = M Vb^2 divide by Vb^2
3M Va^2/Vb^2 = M divide by 3M
Va^2/ Vb^2 = M/3M M's cancel and take square root
Va/Vb = square root of 1/3!~

 

[hage567]

You are almost right, you are missing a factor of 2 somewhere.

You had

2k= 1/2*3M*Va^2
k=1/2*M* Vb^2

so if you divide the first equation by 2, like you said you were going to do in post #5, you get

k = 1/4*3M*Va^2

right? I think you forgot about the 1/2 on the right side. Do you see that?

So now if you set the two equations equal to each other and solve, what do you get?

 

[bmandrade]

right! i was saw that error
in that case the ratio is square root of 2/3!

 

[hage567]

That looks much better!

 

[bmandrade]

thank you !