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A sphere is inscribed in a straight circular cylinder. The sphere is cut by two parallel poles perpendicular to the...
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the dimensions of the cylinder if its volu...
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the dimensions of the cylinder if its volume is to be maximized. Hints: Let r be the distance from the center of the sphere to the base of the cylinder and let r be the radius of the base of the cylinder. Note that the height of the cylinder is 2r.
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the...
A sphere and a circular cylinder (with its axis perpendicular to the flow) are mounted in the sam...
A sphere and a circular cylinder (with its axis perpendicular to the flow) are mounted in the same freestream. A pressure tap exists at the top of the sphere, and this is connected via a tube to one side of a manometer. The other side of the manometer is connected to a pressure tap on the surface of the cylinder. This tap is located on the cylindrical surface such that the deflection of the fluid in the manometer indicates that...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cyl...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cylinder band) The portion of the cylinder y+z+5)2 25 between the planes x--2 and x-2.
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b)...
Consider a circular cylinder in an ideal flow, with its axis perpendicular to the fiow. Let...
Consider a circular cylinder in an ideal flow, with its axis perpendicular to the fiow. Let p be the angle measured between radi drawn to the leading edge (the stagnation point) and to any abitrary point on the cylinder. The pressure coefficient distribution along the cylindrical surface is given by Cp 1-4sin (m-p). Calculate the drag coefficient for the cylinder, based on projected frontal area of the cylinder. (Round the final answer to three decimal places.) The drag coefricient for...
Two identical circular thin-wire loops carry the same current I=10.4 A and are positioned "parallel" to...
Two identical circular thin-wire loops carry the same current
I=10.4 A and are positioned "parallel" to each
other as illustrated in the figure below. The planes of the loops
are perpendicular to the line connecting their centers
O1 and O2. The radius of the loops
a=1.18 cm and the distance between the loop
planes b=0.944 cm.
What is the magnitude B1 of the
magnetic field at point O1?:
B1= _____ G.
What is the magnitude B2 of the
magnetic field...
Two identical circular thin-wire loops carry the same current I=6.5 A and are positioned "parallel" to...
Two identical circular thin-wire loops carry the same current
I=6.5 A and are positioned "parallel" to each
other as illustrated in the figure below. The planes of the loops
are perpendicular to the line connecting their centers
O1 and O2. The radius of the loops
a=0.46 cm and the distance between the loop
planes b=0.575 cm.
What is the magnitude B1 of the
magnetic field at point O1?:
B1= ______ G.
What is the magnitude B2 of the
magnetic field...
Two identical circular thin-wire loops carry the same current I=5.33 A and are positioned "parallel" to...
Two identical circular thin-wire loops carry the same current I=5.33 A and are positioned "parallel" to each other as illustrated in the figure below. The planes of the loops are perpendicular to the line connecting their centers 01 and 02. The radius of the loops a=1.1 cm and the distance between the loop planes b=2.31 cm. 0-6 What is the magnitude B1 of the magnetic field at point 012: B2- G. What is the magnitude By of the magnetic field...
Prove that in hyperbolic geometry, the following statement is false: Any two parallel hyperbolic straight lines...
Prove that in hyperbolic geometry, the following statement is false: Any two parallel hyperbolic straight lines have a common perpendicular hyperbolic straight line.
Question 2. In this problem we consider the following two surfaces (i) The circular cylinder of...
Question 2. In this problem we consider the following two surfaces (i) The circular cylinder of radius 1/2 and axis of rotation the z-axis (ii) The sphere of radius 1 and centre (-1/2,0,0) These two surfaces intersect in a curve called Viviani's curve. (a) (7 marks) Show that for all real t, (t) = (cos2t -2 curve. (In fact y(t) is a parametrisation of Viviani's curve, but you need not prove this.) (b) (6 marks) Show that y(t) has speed...
Two infinitely long, straight parallel wires perpendicular to the plane of the page carry currents of...
Two infinitely long, straight parallel wires perpendicular to the plane of the page carry currents of l1 = 1.5 A and I2 = 3 A in opposite directions. The smallest distance between the wires is d = 10 cm. Which direction matches the direction of the B-field at a point P midway between the wires?
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the dimensions of the cylinder if its volume is to be maximized. Hints: Let r be the distance from the center of the sphere to the base of the cylinder and let r be the radius of the base of the cylinder. Note that the height of the cylinder is 2r.
8. A right circular cylinder is inscribed in a sphere of radius v3. Find the...
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b) (Circular cylinder band) The portion of the cylinder y+z+5)2 25 between the planes x--2 and x-2.
Q1. Sketch and find a parameterization of the following surfaces (a) (Spherical cap) The portion of the sphere by *+y+-16 cut by the vertical plane y 3, containing the point (0,4,0) (b)...
Consider a circular cylinder in an ideal flow, with its axis perpendicular to the fiow. Let p be the angle measured between radi drawn to the leading edge (the stagnation point) and to any abitrary point on the cylinder. The pressure coefficient distribution along the cylindrical surface is given by Cp 1-4sin (m-p). Calculate the drag coefficient for the cylinder, based on projected frontal area of the cylinder. (Round the final answer to three decimal places.) The drag coefricient for...
Two identical circular thin-wire loops carry the same current
I=10.4 A and are positioned "parallel" to each
other as illustrated in the figure below. The planes of the loops
are perpendicular to the line connecting their centers
O1 and O2. The radius of the loops
a=1.18 cm and the distance between the loop
planes b=0.944 cm.
What is the magnitude B1 of the
magnetic field at point O1?:
B1= _____ G.
What is the magnitude B2 of the
magnetic field...
Two identical circular thin-wire loops carry the same current
I=6.5 A and are positioned "parallel" to each
other as illustrated in the figure below. The planes of the loops
are perpendicular to the line connecting their centers
O1 and O2. The radius of the loops
a=0.46 cm and the distance between the loop
planes b=0.575 cm.
What is the magnitude B1 of the
magnetic field at point O1?:
B1= ______ G.
What is the magnitude B2 of the
magnetic field...
Two identical circular thin-wire loops carry the same current I=5.33 A and are positioned "parallel" to each other as illustrated in the figure below. The planes of the loops are perpendicular to the line connecting their centers 01 and 02. The radius of the loops a=1.1 cm and the distance between the loop planes b=2.31 cm. 0-6 What is the magnitude B1 of the magnetic field at point 012: B2- G. What is the magnitude By of the magnetic field...
Question 2. In this problem we consider the following two surfaces (i) The circular cylinder of radius 1/2 and axis of rotation the z-axis (ii) The sphere of radius 1 and centre (-1/2,0,0) These two surfaces intersect in a curve called Viviani's curve. (a) (7 marks) Show that for all real t, (t) = (cos2t -2 curve. (In fact y(t) is a parametrisation of Viviani's curve, but you need not prove this.) (b) (6 marks) Show that y(t) has speed...
Two infinitely long, straight parallel wires perpendicular to the plane of the page carry currents of l1 = 1.5 A and I2 = 3 A in opposite directions. The smallest distance between the wires is d = 10 cm. Which direction matches the direction of the B-field at a point P midway between the wires?
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