Hi, Can i have the answer on a paper please? QUESTION 2 A liquid in a capillary

Question

Hi,
Can i have the answer on a paper please? QUESTION 2 A liquid in a capillary tube forms a meniscus that can be described by the function y-ar+bx+c, where the x and y axes are oriented as shown in the figure below. F= 15mN -0.5 0.5 (a) Use the information given, and the diagram to determine a, b and e and hence write the function describing the meniscus. (b) Find the derivative of the function, and hence determine the angle in degrees. (c) The force F with magnitude F and direction represents the total surface tension force around the circum- ference on the liquid in the tube. The vertical component of F holds up the liquid in the tube above the liquid outside the tube. What is this vertical component? (8 marks)

Explanation / Answer

a)   The points on the parabola of the meniscus are : (0,0) , (0.5 , 0.5) , (-0.5, 0.5)

y = ax^2 +bx +c ; y = ax^2 +bx

Plug the remaining two points to form the equation:

0.5 = 0.025a + 0.5b

0.5 = 0.025a - 0.5b

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1 = 0.05a ----> a = 20

b = 0

So, y = 20x^2

b) derivative : y' = 40x

at x =0.5 ; y' = 40*0.5 = 20

So, tan(theta) = 20 ;

sin(theta) = 20/sqrt(401) = 20.02

c) So, vertical component : Fy = (15x10^-3)*(20.02)

= 0.3 Nt

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