- #1
yoyo
- 21
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I am trying to derive an equation for the oscillation of a conical float. There is a conical float with a density of delta 2 and its floating on water with density 1. Find the oscillation of the floating conical float. The final solution should be:
d^2y/dt^2=-g+(g((L-y)/L)^3)/p
where y(t) is the height of the conical float over the water, L is the length of the conical float,g is gravity and p is the ratio of the two density delta1/delta2
what i did was i found the submerge volume: (1/3)r^2(L-y)
then the weight of water displaced by the float is:
(1/3)r^2(L-y)*delta2*g
mass of float m=(1/3)r^2(L)*delta2
using this in Newton's second law i got:
d^2y/dt^2=-g+g*p((L-y)/L) where p=delta1/delta2
i am not getting the solution that my professor gave?...can somebody explain where the cubed part came from?
d^2y/dt^2=-g+(g((L-y)/L)^3)/p
where y(t) is the height of the conical float over the water, L is the length of the conical float,g is gravity and p is the ratio of the two density delta1/delta2
what i did was i found the submerge volume: (1/3)r^2(L-y)
then the weight of water displaced by the float is:
(1/3)r^2(L-y)*delta2*g
mass of float m=(1/3)r^2(L)*delta2
using this in Newton's second law i got:
d^2y/dt^2=-g+g*p((L-y)/L) where p=delta1/delta2
i am not getting the solution that my professor gave?...can somebody explain where the cubed part came from?