Variable Isolation - August 20, 2012

Isolating Variables

Michael Matias

August 20, 2012

I wasn't sure whether, when taking the square root of a number, the solution will be + and -. 

Example: v² = 2E/m --> v = sqrt(2E/m)

Are there two solutions to the equation, one with a negative value?

Solve the following equations from the variable(s) requested

1.       E = 1/2mv² for m and v

2E = mv² à 2E/m = v² à v = sqrt(2E/m)

2E = mv² à m = 2E/v²

2.       E = mgh for h

h = E/mg

3.       1/f = 1/d_o + 1/d_i for d_o

d_od_i = fd_i + fd_o à fd_i = d_od_i – fd_o à fd_i = d_o(d_i -f) à d_o = fd_i /(d_i -f)

4.       s_o/s_i = d_o/d_i for s_i

d_i s_o = d_o s_i à s_i = d_i s_o / d_o

5.       P=Fd/t for d

Pt = Fd à d = Pt/F

6.       E = hf -W_o for W_o and h

E – hf = - W_o à W_o = hf – E

E + W_o = hf à h = (E + W_o)/f

7.       v = square root of TL/m for T

v = sqrt(TL/m) à v² = TL/m à v²m = TL à T = v²m/L

8.       F = Kq₁q₂/r² for r

Fr² = Kq₁ q₂à r² = Kq₁ q₂/F à r = sqrt(K q₁ q₂/F)

9.       R = pl/A for A

AR = pl à A = pl/R

10.   a_c = mv²/r for v

a_c r = mv² à v² = a_c r/m à v = sqrt(a_c r/m)