A pressure P acts on an area A, which is enclosed by a curve C1 and another curve C2. To find the total force F, the area A must first be calculated. Suppose the equation of C1 is y = (1/√￣8)x^2 and the equation of C2 is y = √￣x
i) Find the intersection points of C1 and C2
ii) Calculate the area A
iii) Determin the total force F in terms of P
數學一問(M1/M2)!!?
2015-12-07 4:21 pm
回答 (1)
2015-12-07 9:56 pm
We have
C1(x)=(1/sqrt(8))x^2=sqrt(2)x^2/4
C2(x)=sqrt(x)
(i) By inspection, C1 and C2 intersect at x=0 and x=2.
(ii) the area A can be obtained by integrating (C(2)-C(1)) over (0,2) with respect to x.
A=(2x^(3/2) /3 - x^3/(3sqrt(8)) for x=0 to 2 = (2/3)sqrt(2)
(iii)Force = Area * Pressure = AP=(2/3)sqrt(2)*P
C1(x)=(1/sqrt(8))x^2=sqrt(2)x^2/4
C2(x)=sqrt(x)
(i) By inspection, C1 and C2 intersect at x=0 and x=2.
(ii) the area A can be obtained by integrating (C(2)-C(1)) over (0,2) with respect to x.
A=(2x^(3/2) /3 - x^3/(3sqrt(8)) for x=0 to 2 = (2/3)sqrt(2)
(iii)Force = Area * Pressure = AP=(2/3)sqrt(2)*P
參考: Basic calculus principles.
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