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Shawkify
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Homework Statement
An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation.
d, m, R, t, h are known
http://puu.sh/luare/10352d0479.png
Soccer Ball:
m = 331.2 kg
R = 10.54 cm
t = 2.25 s
d = 0.2805 m
h = 0.0445 m
Homework Equations
Derived from an earlier problem:
a = (g*h)/(d*(1+k))
d = 1/2*a*Δt2
KEtotal = 1/2*m*v2 + 1/2*I*ω2
I = κ*m*R2
U = m*g*h
v = v0 + a*t
The Attempt at a Solution
Ui = KEf
m*g*h = 1/2*m*v2 + 1/2*I*ω2
m*g*h = 1/2*m*v2 + 1/2*κ*m*R2*(v/R)2
g*h = 1/2*v2 + 1/2*κ*v2
κ = (g*h)/v2 - 1
v = (g*h)/(d*(1+k))*t
Solving a system of equations gives me:
v = (2*d)/t
κ = (g*h*t2 - 2*d2)/(2*d2)
Plugging in values gives me v = 1.65 m/s and k = 30.8. Compared to a chart which gives a value of κ = 2/3 for a thin spherical shell, my κ value is extremely large.
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