a. I've attached a plot of the surface. Each face is parameterized by
• with and ;
• with and ;
• with and ;
• with and ; and
• with and .
b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.
Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.
c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.
where <em>R</em> is the interior of <em>S</em>. We have
The integral is easily computed in cylindrical coordinates:
as expected.
Answer:
The x-component of is 56.148 newtons.
Explanation:
From 1st and 2nd Newton's Law we know that a system is at rest when net acceleration is zero. Then, the vectorial sum of the three forces must be equal to zero. That is:
(1)
Where:
, , - External forces exerted on the ring, measured in newtons.
- Vector zero, measured in newtons.
If we know that , , and , then we construct the following system of linear equations:
(2)
(3)
The solution of this system is:
,
The x-component of is 56.148 newtons.
There’s no picture and what’s the length?