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< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
A tank in the shape of an inverted right circular cone has height 5 meters and radius 2 meters. It is filled with 4 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ = 1020 kg/m3. Your answer must include the correct units.
h = 5m
r = 2m
and I am assuming that up to 4m is filled with chocolate
δ = 1020 kg/m3
1. ΔW = F * D = F * y
F = mg
m = δ * V
2. ΔW = ((1020 * V)9.8) * y
Volume of a disk = πr2h = π((-5/2y + 2)1/2)2Δy
r = (my + b)1/2 = (-5/2y + 2)1/2
m = Δy/Δx = -5/2
b = 2
3. ΔW = ((1020 * π((-5/2y + 2)1/2)2Δy )9.8) * y
4. ∫15 = 1020*9.8*π*(-5/4y + 1)2*y*dy
All I want to know is if I am on the right track. I was having difficulties picking out the steps from my professor's examples. (am I approaching things in a logical order?) and obviously I want to know if I'm wrong.
Thank you for your time
A tank in the shape of an inverted right circular cone has height 5 meters and radius 2 meters. It is filled with 4 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ = 1020 kg/m3. Your answer must include the correct units.
h = 5m
r = 2m
and I am assuming that up to 4m is filled with chocolate
δ = 1020 kg/m3
1. ΔW = F * D = F * y
F = mg
m = δ * V
2. ΔW = ((1020 * V)9.8) * y
Volume of a disk = πr2h = π((-5/2y + 2)1/2)2Δy
r = (my + b)1/2 = (-5/2y + 2)1/2
m = Δy/Δx = -5/2
b = 2
3. ΔW = ((1020 * π((-5/2y + 2)1/2)2Δy )9.8) * y
4. ∫15 = 1020*9.8*π*(-5/4y + 1)2*y*dy
All I want to know is if I am on the right track. I was having difficulties picking out the steps from my professor's examples. (am I approaching things in a logical order?) and obviously I want to know if I'm wrong.
Thank you for your time
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