- #1
Ush
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Homework Statement
this isn't really a word problem, it's part of a series of calculations from a physics lab
in this lab,
Ug = energy at initial position
Ug -> Ekrot + Ek at final position
I need to calculate
1. Ekrot
2. Moment of Inertia
3. angular velocity
Homework Equations
Ug = mgh
Ekrot = ½Iѡ²
Ek = ½mv²
ѡ = v/r
v = 2h/t (in this case)
m = 0.100m ± 0.0005
g = 9.8m/s²
h = 0.800m ± 0.0005
v = 0.21m/s ±0.01
r = 0.004m ± 0.002
t = 7.66s ± 0.08
The Attempt at a Solution
mgh = Ekrot + ½mv²
Ekrot = mgh - ½mv²
Δmgh = |dy/dm mgh| + |dy/dh mgh|
= |dy/dm gh| + |dy/dh mg|
= |dy = ghΔm| + |dy = mgΔh|
relative error = Δmgh / mgh
= |ghΔm / mgh| + |mgΔh / mgh|
= |Δm/m| + |Δm/h|
similarly, the relative uncertainty of ½mv² is..
Δ½mv²/½mv² = |Δm/m| + |2Δv/v|so... now what?
We're not allowed to add relative uncertainties, i really don't know what to do here
We can add absolute uncertainty but I have no knowledge on how to calculate absolute uncertainty.
also, the angular velocity, ѡ, = v/r. There is an uncertainty on v and an uncertainty on r. so how do I calculate moment of inertia (I) after I have the uncertainty of Ekrot?? The uncertainties of ѡ and r weren't used when when calculating uncertainty of Ekrot (unless my steps above are way off.. which i doubt)
I'm very confused, any help would be appreciated
thank you
~Ush
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