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(View from short end of the bath) (View from above)
Andy's having a bath with his favourite duck called Tony. The bath has curved sides and is filled to the top with water; it has a height of 0.8m and is 1.5m in length. The sides of the bath have a curve of radius 0.4m.
a) What is the force exerted on one side of the bath along the curved edge?
Solution:
Vertical Force-
W1= Vρg = (0.4 x 0.4 x 1.5) x 1000 x 9.81 = 2354 N
W2=>
Volume = 1/4πr2l = 1/4 x π x 0.42 x 1.5 = 3/50 π
Weight = Vρg = (3/50 x π) x 1000 x 9.81 = 1849 N
Vertical force= Total weight = 2354 + 1849 = 4203 N
Horizontal force-
Fh = Fx = PA = ρghA = 1000 x 9.81 x 0.6 x (0.4 x 1.5) = 3531.6 N
Total resultant force-
FR = √((FH)2 + (FV)2) = √((3531.6)2 + (4203)2) = 5490 N
b) Using your answer from the previous question, what angle is the force exerted at?
Solution:
tan(a) = Fv/FH
a = tan-1(4203/3531.6) = 50o
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