Please help solve the following question with steps. Thank you!
Please help solve the following question with steps. Thank you! 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine t...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
(1 point) Find the work done by the force field F(x, y, z) = 5xi + 5yj + 3k on a particle that moves along the helix r(t) = 1 cos(t)i + 1 sin(t)j + 5tk, 0 < t < 21.0
all questions clearly solved please (2) If the point of application of a force F: R3 R moves along a curve C, then the work done by the force is W F.dr. (a) Find the total work done on an object that traverses the curve c(t) (cos(t), 2 sin(t), (b) Find the total work done on an object that traverses the straight line from (1,0,-2) (c) Explain why the answers in the previous two questions coincide and provide a way...
The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minimizes the work done on the object by the force field. Please use the line work integral, and optimization
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m 3. [10 Marks] Find the work done by the force F(z, y)-(e 2019y 233 cos(sin(4y )) 2 + + 1)y,-r + e 2019r 233 sin χ -(2 along the cardioid r 3+3 sin 0, 0 (0, 2m
9. (8 marks) Let F be an inverse force field given by k F(r,y,z) r13 r, where k is a constant. Find the work done by F on an object as its point of application moves along the -axis from A(1,0, 0) to B(2,0,0) 9. (8 marks) Let F be an inverse force field given by k F(r,y,z) r13 r, where k is a constant. Find the work done by F on an object as its point of application moves...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
1. Suppose a gas has the velocity field v(x,y,z) = xi + zj + yk. Find the circulation along the helix r(t) - <cos(t), sin(t), > for Osts. [10]
QUESTION 4 Suppose a fourth field and path: F= <cos(z), sin(z), xy > and r= <sin(t), cos(t), t-> when Osts 21 What does this field look like? What does the path look like? Find ff. dr (use a calculator), what does it represent? Explain.