Hi Can i have the answer on a paper please QUESTION 2 A liqu

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)

Solution

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

--------------------

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