Combining Equations: How to Combine Fc=mv²/r and Fg=qvb?

[music_lover12]

How do I combine these two equations?

Fc=mv(squared)/r
Fg=qvb

 

[cristo]

You need to make an effort yourself, and furthermore, defined your symbols. For example, on the LHS of each equation, you have Fc and Fg, respectively. Are these Fxc and Fxg, or are they different variables F_c and F_g?

 

[music_lover12]

It is with the smaller c and g.

 

[cristo]

Well, in that case, can you rearrange the second equation to get it into the form v=... ?

 

[music_lover12]

Yeah, it would be v=f/qB...

 

[music_lover12]

...also I'm trying to combine the two equations to find m, which is mass.

 

[cristo]

Yeah, it would be v=f/qB...

Ok, so you now have F_c=mv²/r and v=F_g/qB. Now, can you substitute the second equation into the first? [i.e. replace v^2 in the first with F_g/qb]

...also I'm trying to combine the two equations to find m, which is mass.

Right, well if you manage to do the substitution above, then you need to rearrange the equation you obtain to get it in the form m=...

 

[music_lover12]

Okay, so I substituted the second equation into the first and I got Fc=m*fg/qB/R. Is that right?

 

[cristo]

Okay, so I substituted the second equation into the first and I got Fc=m*fg/qB/R. Is that right?

No, v is squared in the first equation, and thus substituting the second into the first should yield $$F_c=\frac{m}{r}\left(\frac{F_g}{qB}\right)^2$$. Can you rearrange this?

 

[music_lover12]

No, v is squared in the first equation, and thus substituting the second into the first should yield $$F_c=\frac{m}{r}\left(\frac{F_g}{qB}\right)^2$$. Can you rearrange this?

m=Fcr*qB/Fg^2

 

[cristo]

m=Fcr*qB/Fg^2

Well, you're missing a square on q and B; adding parentheses like this m=Fcr*(qB/Fg)^2 gives the correct solution.

 

[music_lover12]

Oh okay. I see. Thank you very much!

 

[cristo]

You're welcome.