Combine these formulas without q and get an expression of U

Question

qU=1/2mv²   and r=mv/qB

Answer 1

I can't quite read the expressions you wrote, but if you set each one = to Q you will the be able to set them equal to each other.

 

for example: qt=Rv

divide by t to get q alone

 

q=Rv/t

 

q/2p=4g

 

multiply both sides by 2p to get q=8gp

 

now each expression is equal to q so they can be combined to: Rv/t=8gp

Answer 2

solve both formulas for q, and then set the solutions equal to each other.

 

First formula:

q=(1/2mv²)/U

= mv²/(2U)

 

Second formula:

r = mv/qB

1/r = qB/mv

q=mv/Br

 

Setting the solutions equal to each other:

 

mv²/(2U) = mv/Br.  We can cancel m and a power of v on both sides:

 

v/(2U) = 1/Br