Now consider the general case for a droplet on a surface: ?2 + (? +- ℎ)2...
Now consider the general case for a droplet on a surface: ?2 + (? +- ℎ)2 = 1, where h is the
height of the centre of the droplet either above or below the x-axis. Derive expression(s) for the
general case relating h and ?. Use your expression to find the height of a droplet that makes a
contact angle of ? = 25 deg with the solid surface.
Homework Answers
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Now consider the general case for a droplet on a surface:
?2 + (? +- ℎ)2...
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е....
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е. where M is the mass and R is the radius of the spherical mass, and m is the mass of some object at the surface. Show that the difference between this potential and that of an object a distance h above the surface is mgh, where g is a constant that is the same for any m or h. Derive an expression for g...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
Question 2. Boundary conditions (and more on hyperbolic functions). Consider an arch of the type described above, posit...
Question 2. Boundary conditions (and more on hyperbolic functions). Consider an arch of the type described above, positioned on a horizontal surface. Let us take as our reference point the left base of the arch (where the left side of the arch makes contact with the supporting surface). The right base is 2L metres away from the left base. (o) Sketch this situation and mark on your diagram all nformation b) Write down a boundary condition involving y(0). Also, given...
I would like a step by step solution please and clear to read. Surface Tension and...
I would like a step by step solution please and clear to
read.
Surface Tension and Bubbles Surface tension is a force caused by the attraction of liquid molecules on a boundary surface for each other. It acts tangential to the surface and is modeled as a single number, the surface tension Consider a square film on a wire frame. The bottom edge is movable and, when the frame is vertical, as shown, the surface tension of the film pulls...
6. Consider a cylinder with a surface area of 2 m2. Find the radius r and...
6. Consider a cylinder with a surface area of 2 m2. Find the radius r and height h of such a cylinder so that the volume of the cylinder is a maximum. Given: For a cylinder, the surface area is S = 2^r2 + 2trh and the volume is V = arh (where r is the radius and h is the height of the cylinder). I (5)
I am having trouble with #2 X() xy = 1, y=0, x = 1, x =...
I am having trouble with #2
X() xy = 1, y=0, x = 1, x = 2, about 3 = -1. #2 Find the volume of the frustrum of a cone (i.e. the result of re- moving a smaller cone from the top of a larger cone) with height h, lower radius R and upper radius r. h R (Hint: Turn the cone on its side and draw a set of axes with the x axis piercing the centre of...
please explain the answer 2) A ball is dropped from rest at a height H. At...
please explain the answer
2) A ball is dropped from rest at a height H. At height h (below H) the ball bounces off a surface with no loss in speed. The surface is tilted at 45°, so the ball bounces off horizon- tally. Derive an expression for the distance the ball travels in the horizontal direction. Plot the distance traveled in the horizontal direction as a function of h where h varies between O and H. 3) Imagine an...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
Consider a wide, nearly flat square with uniform charge density p. The square is centered at...
Consider a wide, nearly flat square with uniform charge density p.
The square is centered at the origin and is lying parallel to the
xy plane. It has side length a and thickness h h<<a, so the
top surface of the square is at z=h/2 and the bottom is at z=-h/2.
Find a simple approximate (monomial) expression for the magnitude
of the electric field on the z-axis for
(1). 0 < z < h/2
(2). h/2 < z << a...
Question 2 A small car is driving in a horizontal circle on the inside surface of...
Question 2 A small car is driving in a horizontal circle on the inside surface of a cone as shown. The car has mass M and is moving with a constant speed of V. Assume there is no friction acting on the car. The horizontal circle is located at a height H above the point of the cone as shown. The angle between the centre of the cone and the side (the half angle) is ? as shown. a) Draw...
Consider the expression for potential energy at the surface of a spherical mass GMm R. Р.Е. where M is the mass and R is the radius of the spherical mass, and m is the mass of some object at the surface. Show that the difference between this potential and that of an object a distance h above the surface is mgh, where g is a constant that is the same for any m or h. Derive an expression for g...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
Question 2. Boundary conditions (and more on hyperbolic functions). Consider an arch of the type described above, positioned on a horizontal surface. Let us take as our reference point the left base of the arch (where the left side of the arch makes contact with the supporting surface). The right base is 2L metres away from the left base. (o) Sketch this situation and mark on your diagram all nformation b) Write down a boundary condition involving y(0). Also, given...
I would like a step by step solution please and clear to
read.
Surface Tension and Bubbles Surface tension is a force caused by the attraction of liquid molecules on a boundary surface for each other. It acts tangential to the surface and is modeled as a single number, the surface tension Consider a square film on a wire frame. The bottom edge is movable and, when the frame is vertical, as shown, the surface tension of the film pulls...
6. Consider a cylinder with a surface area of 2 m2. Find the radius r and height h of such a cylinder so that the volume of the cylinder is a maximum. Given: For a cylinder, the surface area is S = 2^r2 + 2trh and the volume is V = arh (where r is the radius and h is the height of the cylinder). I (5)
I am having trouble with #2
X() xy = 1, y=0, x = 1, x = 2, about 3 = -1. #2 Find the volume of the frustrum of a cone (i.e. the result of re- moving a smaller cone from the top of a larger cone) with height h, lower radius R and upper radius r. h R (Hint: Turn the cone on its side and draw a set of axes with the x axis piercing the centre of...
please explain the answer
2) A ball is dropped from rest at a height H. At height h (below H) the ball bounces off a surface with no loss in speed. The surface is tilted at 45°, so the ball bounces off horizon- tally. Derive an expression for the distance the ball travels in the horizontal direction. Plot the distance traveled in the horizontal direction as a function of h where h varies between O and H. 3) Imagine an...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
Consider a wide, nearly flat square with uniform charge density p.
The square is centered at the origin and is lying parallel to the
xy plane. It has side length a and thickness h h<<a, so the
top surface of the square is at z=h/2 and the bottom is at z=-h/2.
Find a simple approximate (monomial) expression for the magnitude
of the electric field on the z-axis for
(1). 0 < z < h/2
(2). h/2 < z << a...
Question 2 A small car is driving in a horizontal circle on the inside surface of a cone as shown. The car has mass M and is moving with a constant speed of V. Assume there is no friction acting on the car. The horizontal circle is located at a height H above the point of the cone as shown. The angle between the centre of the cone and the side (the half angle) is ? as shown. a) Draw...
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