Physics/Algebra problems?
Physics/Algebra problems?
So i'm taking a physics class and there is some algebra involved and I have had an algebra class in years so I'm trying some practice problems, but can't tell if i'm doing them right. I will list the problems below. Please show all of the steps as I'm trying to figure out how to do them, not just get the answer. Thank you.
I'm solving for the variable that is after semicolon
1. V=4/3(Pi)r^3;r
2..E=1/2mv^2+1/2kx^2;v
3.m1v1+m2v2=(m2-m1)v;v the 1 and 2 are subscripts
4.m1v1+m2v2=(m2-m1)v;m2 subscripts again
5. 0= -1/2gt^2+vt;t
Thanks in advance.
Comments
1. V = 4/3 πr^3
3V/4π = r^3 (multiply both sides by 3/4π)
(3V/4π)^(1/3) = r (take cube roots on both sides).
2. E = 1/2 mv^2 + 1/2 kx^2
E - 1/2 kx^2 = 1/2 mv^2 (subtract 1/2 kx^2 from both sides)
2E/m - kx^2 = v^2 (multiply both sides by 2/m)
+/- √(2E/m - kx^2) = v (take square roots on both sides).
√(2E/m - kx^2) = v (v is never negative).
3. m1 v1 + m2 v2 = (m2 - m1) v
(m1 v1 + m2 v2)/(m2 - m1) = v (divide both sides by m2 - m1).
4. m1 v1 + m2 v2 = (m2 - m1)v
m1 v1 + m2 v2 - (m2 - m1)v = 0 (subtract (m2 - m1)v from both sides)
m1 v1 + m2 v2 - m2 v + m1 v = 0 (distribute -v in -(m2 - m1)v)
m1(v1 + v) + m2 (v2 - v) = 0 (combine like terms and factor)
m2 (v2 - v) = -m1(v1 + v) (subtract m1(v1 - v) from both sides)
m2 = -m1(v1 + v)/(v2 - v) (divide both sides by v2 - v)
m2 = [(v + v1)/(v - v2)] m1 (distribute the negative in -(v2 - v)).
5. 0 = -1/2 gt^2 + vt
0 = 1/2 gt^2 - vt (multiply both sides by -1)
0 = t(1/2gt - v) (factor out the t)
t = 0 or 1/2gt - v = 0 (no zero divisors)
t = 0 or 1/2 gt = v (add v to both sides of the second equation)
t = 0 or t = 2v/g (multiply 2/g on both sides of the second equation).