- #1
iloveannaw
- 38
- 0
please see my own reply
Last edited:
Efficient Algebra Tips: My Personal Response
- Thread starter iloveannaw
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AI Thread Summary
The discussion focuses on simplifying the algebraic expression involving the Lorentz factor, gamma, and beta. A user seeks assistance in transforming the left-hand side (LHS) to match the right-hand side (RHS) of the equation. Clarifications about the correct representation of gamma and the factorization of the expression 1 - beta^2 are provided. Participants share tips on using LaTeX for better clarity in mathematical notation. The conversation highlights the collaborative effort to resolve algebraic frustrations.
- #2
iloveannaw
- 38
- 0
could someone help me out. how to get from the LHS to the RHS here:
\gamma (1 - \beta) \nu= \sqrt{\frac{1 - \beta}{1 + \beta}} \nu
where \gamma = \frac{1}{\sqrt{1 - \beta^{2}}}
thanks!
so frustrating, i can't get latex do what i want and editing doesn't work. ok that should of course be 1 over the sqrt of 1 - beta^2
\gamma (1 - \beta) \nu= \sqrt{\frac{1 - \beta}{1 + \beta}} \nu
where \gamma = \frac{1}{\sqrt{1 - \beta^{2}}}
thanks!
so frustrating, i can't get latex do what i want and editing doesn't work. ok that should of course be 1 over the sqrt of 1 - beta^2
- #3
phyzmatix
- 313
- 0
iloveannaw said:
It happens
Remember you can write
1-\beta^2 = (1-\beta)(1+\beta)
EDIT: I see it changed again...will still work though.
Last edited:
- #4
iloveannaw
- 38
- 0
doh, i should have seen that - thank you!
- #5
phyzmatix
- 313
- 0
Any time 
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system
$$M(t) = M_{C} + m(t)$$
$$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$
$$P_i = Mv + u \, dm$$
$$P_f = (M + dm)(v + dv)$$
$$\Delta P = M \, dv + (v - u) \, dm$$
$$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$
$$F = u \frac{dm}{dt} = \rho A u^2$$
from conservation of momentum , the cannon recoils with the same force which it applies.
$$\quad \frac{dm}{dt}...
I was told forces are vectors so they can be divided into x and y components, but what about the normal force or the force of static friction? do you divide those into x and y components if say you had a block that was lying on an angled surface?
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