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The acceleration, a of an object is given by: a=vf−vit
where vf is the final velocity, vi is the initial velocity, and t is the time interval.
Rearrange this equation to make vi the subject.
vi=at−vf
vi=vf−at
vi=a+t+vf
vi=atvf
vi=a+t−v
E=mgh+12mv2
Rearrange this equation for v
v=√12(Em−gh)
v=√2(Em−gh)
v=√2(E−mgh)
v=√m2(E−gh)
v=√2m(E−gh)
If ω=2πT, and k=mω2, what is T in terms of m and k?
T=2π√km
T=2π√mk
T=√2πkm
T=√2πmk
T=4π2√mk
P_2 = \rho g h + P_1 \ {\rm and} \ Q = \frac{\pi R^4(P_2−P_1)}{8\eta L}. \\ \rm Eliminate \ {\it P_1} \ and \ {\it P_2} \ and \ write \ an \ equation \ for \ {\it h} \ in \ terms \ of \ \it Q, \ R, \ ρ, \ g, \ \eta \ {\rm and} \ L.
h = \frac{8 \eta L Q - \pi R^4}{\rho g}
h = \frac{8 \eta L Q}{\pi R^4 } - \rho g
h = \frac{ \pi R^4 - 8 \eta L Q }{ \rho g}
h = \frac{8 \eta L Q - \pi R^4}{\pi R^4 \rho g}
h = \frac{8 \eta L Q}{\pi R^4 \rho g}
\rm{ Rearrange:}
\sigma_\rho = \frac{\it m}{\it l^3}\sqrt{ \left(\frac{\sigma_{\it m}}{\it m}\right)^2 + 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2}
\rm{for \ \sigma_{\it m}}
\sigma_{\it m} = \it m\sqrt{ \left(\frac{\sigma_\rho l^3}{\it m}\right)^2 - 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2}
\sigma_{\it m} = \it m\sqrt{ \left(\frac{\sigma_\rho l^3}{\it m}\right)^2 + 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2}
\sigma_{\it m} = \sqrt{\it m \left( \left(\frac{\sigma_\rho l^3}{\it m}\right)^2 - 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2 \right)}
\sigma_{\it m} = \frac{\it m}{\it l^3} \sqrt{ \left(\frac{\sigma_\rho l^3}{\it m}\right)^2 - 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2}