A block of mass M is attached to a spring of negligible mass and can slide on a horizontal surface along the x-direction, as sho
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Answer:
c)
V_local = -x/t^2
V_convec = x/t^2
d)
a = V_local + V_convec = 0
e) When a particle moves towards postive x direction its convective velocity increases, but at the same time the local velocity deacreases (at the same rate) when time increases
Explanation:
Hi!
You can see plots for a) and b) attached on this document
c)
The local acceleration is just teh aprtial derivative of the velocity with respect to t:
And the convective acceleration is given by the product of the velocity times the gradient of the velocity, that is:
d)
Since the acceleration of any fluid particle is the sum of the local and convective accelerations, we can easily see that it is equal to zero, since they are equal but with opposit sign
e)
This is because of teh particular form of the velocity. A particle will move towards areas of higher velocities (convectice acceleration), but as time increases, the velocity is also decreasing (local acceleration), and the sum of these quantities adds up to zero
Answer:
E = 77532.42N/C
Explanation:
In order to find the magnitude of the electric field for a point that is in between the inner radius and outer radius, you take into account the Gauss' law for the electric flux trough a spherical surface with radius r:
(1)
Q: net charge of the hollow sphere = 1.9*10-6C
ε0: dielectric permittivity of vacuum = 8.85*10^-12 C^2/Nm^2
Furthermore, you have that the net charge contained in a sphere of radius r is:
(2)
with the charge density is:
(3)
r2: outer radius = 0.31m
r1: inner radius = 0.105m
The electric field trough the Gaussian surface is parallel to the normal to the surface, the, you have in the integral of the equation (1):
(4)
where you have used the expression for a surface of a sphere.
Next, you replace the expressions of equations (2), (3) and (4) in the equation (1) and solve for E:
you replace the values of all parameters, and with r = 0.17m
The magnitude of the electric field at a distance r=0.17m to the center of the hollow sphere is 77532.42N/C