F- [y - yz sin x,x + z cos x,y cos x] from OstsT/2 where the path is defined as follows x- 2t y = (1 + cost)2 z- 4(sint)3 m. F= [8xy®z, 12x2y®z, 4x2yaj from (2,0,0) to (0,2,π/2). The path is a helix of radius 2 advancing 1 unit along the positive z axis in one period of 2Tt. We were unable to transcribe this image
F- [y - yz sin x,x + z cos x,y cos x] from...
The path integral of a function f(x, y) along a path e in the xy-plane with respect to a parameter r is given by 2. fex,y)ds= f(x),ye) /x(mF +y(t" dr , where a sr sb. (a) Show that the path integral of f(x, y) along a path c(0) in polar coordinates where r=r(0), α<θ<β, is Sf(r cos 0,rsin e) oN+( de. (b) Use this formula to compute the arc length of the path r 1+cos0, 0<0 27
The path integral...
A particle moves on a counter clockwise, origin-centered circular path in the x y-plane at a constant rate. The radius of the circle is r, the mass of the particle is m, and the particle completes one revolu tion in time τ a) Neatly draw the following things 1. The path of the particle 2. A dot on the path when the particle is at 00 90° and 210° where 0 is mea sured from the x-axis (posi tive counter-clockwise)...
Question 1 Let R be the region enclosed by the positive x-axis, the positive y-axis, and the curve y = (9- x2,1/2. A solid is generated by rotating about x-axis. What is the volume of the solid? give exact answer in term of Pi.(example:a pi) Y Y = 19 22 R 0 3
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A car is going with a constant tangential acceleration (i.e. increasing speed) in a circular path. As seen from above, the path is counter-clockwise. It crosses the point 'A' at time 0.00, at which point its speed is known. Find the direction of its centripetal acceleration at some time after it crosses the point A:Write your answer in degrees. Given: Speed when it crosses point 'A' - V-3.6 m/s, tangential acceleration a 3.6 m/s2, radius of path...
A solid sphere of mass m and radius R rolls down a parabolic path PQR from height H without slipping (assume R « H) as shown in the figure below. Path PQ is rough (and so the shell will roll on that path), whereas path QR is smooth, or frictionless (so the shell will only slide, not roll, in this region). Determine the height h above point Q reached by the shell on path QR. (Use the following as necessary:...
X(s) R(s) ms Hardware gain PID controller Plant (a) PID in Forward Path X(s) R(s)+ ms Kas (b) PI in Forward Path, D in the return path A regulator is a class of control systems that aim to hold the output value at a designated level. The input to a regulator is a set point which changes infrequently. When change occurs, it takes the form of a step. PID controllers used regulate a quantity will typically use the method of...
5. Define R as the region bounded by the graph of y=2x-r and by the x-axis over the interval [0,2]. Find the volume of the solid of revolution formed by revolving R around the y-axis. Hint: Use Shell Method s
from the +x-axis) from the +x-axis) of the electric force on q. as the force in part (b). but opposite direction as the field in part (a).
The Moon orbits the Earth in an approximately circular path. The position of the Moon as a function of time is given by x(t) = r cos(ωt) y(t) = r sin(ωt), where r = 3.84 108 m and ω = 2.46 10-6 radians/s. What is the average velocity of the Moon measured over the interval from t = 0 to t = 3.28 days? Find its magnitude, in m/s, and find its direction, given as an angle measured counterclockwise from...