Verify that each of the following force fields is conservative. Then find, for each, a scalar potential ϕ such that F = − ∇ ϕ . F = z 2 sinh y j + 2 z cosh y k .
Verify that each of the following force fields is conservative. Then find, for each, a scalar potential ϕ such that F = − ∇ ϕ . F = z 2 sinh y j + 2 z cosh y k .
If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
Find the acceleration vector.
r(t) = (cos 3t)i + (2 sin t)j
%3D
O a = (-9 cos 3t)i + (-2 sin t)j
O a = (-3 cos 3t)i + (2 sin t)j
O a = (9 cos 3t)i + (-2 sin t)j
O a = (-9 cos 3t)i + (-4 sin t)j
please send complete handwritten solution for Q1
A particle moves along the x-axis from x = 8 to x = 29. Find the work done by the force F(x)
4x2
- 6x
Note: Write the exact answer not the decimal approximation (for example write
not 0.8).
Answer: The work done is
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