A cylindrical container, 1 meter long and 1 meter in radius, is placed on horizontally on...
A cylindrical container, 1 meter long and 1 meter in radius, is placed on horizontally on its side and filled halfway with water. a) Calculate the horizontal component of the force acting on the cylindrical side-walls? b) Calculate the force acting on each round end? Then we are given the integral solutions of integral h *sqrt(1-h^2)dh = -1/3(1-h^2)^3/2 and integral sin(x)cos(x)dx = -1/2*cos^2 (x) to help out with the problem.
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A cylindrical container, 1 meter long and 1 meter in radius, is
placed on horizontally on...
A cylindrical container, 1 meter long and 1 meter in radius, is placed on horizontally on its side and filled halfway wi...
A cylindrical container, 1 meter long and 1 meter in radius, is placed on horizontally on its side and filled halfway with water. a) Calculate the horizontal component of the force acting on the cylindrical side-walls? b) Calculate the force acting on each round end? Then we are given the integral solutions of integral h *sqrt(1-h^2)dh = -1/3(1-h^2)^3/2 and integral sin(x)cos(x)dx = -1/2*cos^2 (x) to help out with the problem.
Hydrostatic Force Question 1: Consider a trough, 1 meter long, whose cross-section is a semicircle of...
Hydrostatic Force Question 1: Consider a trough, 1 meter long, whose cross-section is a semicircle of radius 2 meters. If the trough is completely filled with water (weight density 9800 N/m^3), what is the total hydrostatic force exerted on one of the semi-circular walls?
1. An amusement park contains a big cylinder of radius R oriented horizontally and rotating with...
1. An amusement park contains a big cylinder of radius R oriented horizontally and rotating with angular velocity o about its horizontal axis. A child of mass m is sitting partway up one side so that she remains at rest a distance h above the bottom of the rotating cylinder. There is the coefficient of kinetic friction u between the child and the cylinder. (a) In terms of R and h, how much is the angle 0? (b) What is...
Concentric Cylindrical Conducting Shells 1 An infiinitely long solid conducting cylindrical shell of radius a =...
Concentric Cylindrical Conducting Shells
1
An infiinitely long solid conducting cylindrical shell of radius
a = 4.8 cm and negligible thickness is positioned with its symmetry
axis along the z-axis as shown. The shell is charged, having a
linear charge density ?inner = -0.35 ?C/m. Concentric
with the shell is another cylindrical conducting shell of inner
radius b = 17.1 cm, and outer radius c = 21.1 cm. This conducting
shell has a linear charge density ? outer =
0.35?C/m....
A frictionless wire is bent into the shape of a cycloid curve, with coordinates given by...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Fi...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
Problem 2 A concrete dam has a curved surface and restrain water (p=1000kg/m3) at a depth...
Problem 2 A concrete dam has a curved surface and restrain water (p=1000kg/m3) at a depth H=2 m. The trace of the surface is a parabola described by the equation: z= 0.2x2 . dam 1- Determine the gage pressure distribution in the water 2- Determine the magnitude of the pressure force F acting on the curved dam surface per unit width (dimension normal to the page) of the gate. [Solution: F=45,780 N] 3-Determine the angle of that force relative to...
An infiinitely long solid conducting cylindrical shell of radius a = 4.8 cm and negligible thickness...
An infiinitely long solid conducting cylindrical shell of radius a = 4.8 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.51 μC/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 15 cm, and outer radius c = 17 cm. This conducting shell has a linear charge density λ outer = 0.51μC/m. 1.What is Ex(P), the x-component...
An infinitely long solid conducting cylindrical shell of radius a = 3.8 cm and negligible thickness...
An infinitely long solid conducting cylindrical shell of radius a = 3.8 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.55 μC/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 13.1 cm, and outer radius c = 17.1 cm. This conducting shell has a linear charge density λ outer = 0.55μC/m. (Please answer #2-5) 1) What...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to th...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
Hydrostatic Force Question 1: Consider a trough, 1 meter long, whose cross-section is a semicircle of radius 2 meters. If the trough is completely filled with water (weight density 9800 N/m^3), what is the total hydrostatic force exerted on one of the semi-circular walls?
1. An amusement park contains a big cylinder of radius R oriented horizontally and rotating with angular velocity o about its horizontal axis. A child of mass m is sitting partway up one side so that she remains at rest a distance h above the bottom of the rotating cylinder. There is the coefficient of kinetic friction u between the child and the cylinder. (a) In terms of R and h, how much is the angle 0? (b) What is...
Concentric Cylindrical Conducting Shells
1
An infiinitely long solid conducting cylindrical shell of radius
a = 4.8 cm and negligible thickness is positioned with its symmetry
axis along the z-axis as shown. The shell is charged, having a
linear charge density ?inner = -0.35 ?C/m. Concentric
with the shell is another cylindrical conducting shell of inner
radius b = 17.1 cm, and outer radius c = 21.1 cm. This conducting
shell has a linear charge density ? outer =
0.35?C/m....
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
Problem 2 A concrete dam has a curved surface and restrain water (p=1000kg/m3) at a depth H=2 m. The trace of the surface is a parabola described by the equation: z= 0.2x2 . dam 1- Determine the gage pressure distribution in the water 2- Determine the magnitude of the pressure force F acting on the curved dam surface per unit width (dimension normal to the page) of the gate. [Solution: F=45,780 N] 3-Determine the angle of that force relative to...
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx +
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...
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