Show that the solid angle subtended by a plane rectangle of sides 2a, 2b, at a point distance l a...
Show that the solid angle subtended by a plane rectangle of sides 2a, 2b, at a point distance l along the normal through its centre can be written
![\int_{-b}^{b}\int_{-a}^{a} ldxdy/ \sqrt[3]{x^2+y^2+l^2}](http://img.homeworklib.com/images/bea4f869-0b6d-4d29-b1dc-aa0adcd58b17?x-oss-process=image/resize,w_560)
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Show that the solid angle subtended by a plane rectangle of sides 2a, 2b, at a point distance l a...
Let S be a smooth parametric surface and let P be starts at P intersects S at most once. The solid angle (S) subten...
Let S be a smooth parametric surface and let P be starts at P intersects S at most once. The solid angle (S) subtended by S at P is the set of lines starting at P and passing through S. In this problem, we define the measure of the solid angle (in steradians) as a point such that each line that r n dS, where r is the position vector from P to any point on S, l, and the...
2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A str...
2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q where L intersects the xy-plane. b) Find the angle that the line through (0,-1,1) and (√3,1,4) makes with a normal vector to the xy-plane. c) Find the distance from the point (3,1,-2) to the plane x-2y+z=4. d) Find a Cartesian equation for the plane containing (1,1,2), (2,1,1) and (1,2,1)
A rod of length 2a is constrained to move with its ends on the perimeter of a circle of radius ....
A rod of length 2a is constrained to move with its ends on the perimeter of a circle of radius . This circle lies in the horizontal plane and is fixed. A small insect whose mass is equal to that of the rod moves along the rod, starting from its mid-point and maintaining a constant relative speed V, then show that in time t, the rod will turn through an angle 2 V3 We were unable to transcribe this image...
#1 and #3 I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer...
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
Slove 4.3.8 please axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
A uniform thin wire of mass M is bent into the form of a square OPQR of side 2a. Show that the moment of inertia of the wire about an axis through O perpendicular to the plane of the square is 10Ma2/3...
A uniform thin wire of mass M is bent into the form of a square OPQR of side 2a. Show that the moment of inertia of the wire about an axis through O perpendicular to the plane of the square is 10Ma2/3 . The wire frame can rotate freely in the vertical plane about a smooth pivot at O. It is held with P vertically above O and is released from rest. Find the initial acceleration of the point P....
A source of strength m, which by itself produces radial streamlines as indicated by the dashed ar...
A source of strength m, which by itself produces radial
streamlines as indicated by the dashed arrows, is placed a distance
L away from a vertical wall (occupying the yz-plane), at point S
(x=L,y= 0). To compute the flow field in the presence of the wall,
the method of images can be employed: A second source of strength m
is placed a distance L from the wall on the other side, at S′
(x=−L,y= 0). The combined flow field of...
show all steps please (1 point) Suppose a pendulum with length L (meters) has angle 0...
show all steps please
(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
Reflection from Plane & Convave Mirrors Snell's n sin 02 Law n2 sine, For the plane...
Reflection from Plane & Convave Mirrors Snell's n sin 02 Law n2 sine, For the plane mirror, we assume the mirror is placed on this page so that it stands vertically along the blue line below, with its length parallel to the page. Take the light source and arrange it to emit a ray of light that lies in the plane of this page. Cast the light ray onto the mirror, so that the ray hits the mirror at an...
Let S be a smooth parametric surface and let P be starts at P intersects S at most once. The solid angle (S) subtended by S at P is the set of lines starting at P and passing through S. In this problem, we define the measure of the solid angle (in steradians) as a point such that each line that r n dS, where r is the position vector from P to any point on S, l, and the...
2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the...
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
A source of strength m, which by itself produces radial
streamlines as indicated by the dashed arrows, is placed a distance
L away from a vertical wall (occupying the yz-plane), at point S
(x=L,y= 0). To compute the flow field in the presence of the wall,
the method of images can be employed: A second source of strength m
is placed a distance L from the wall on the other side, at S′
(x=−L,y= 0). The combined flow field of...
show all steps please
(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
Reflection from Plane & Convave Mirrors Snell's n sin 02 Law n2 sine, For the plane mirror, we assume the mirror is placed on this page so that it stands vertically along the blue line below, with its length parallel to the page. Take the light source and arrange it to emit a ray of light that lies in the plane of this page. Cast the light ray onto the mirror, so that the ray hits the mirror at an...
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