An incompressible flow field F in a 3D cartesian grid with components u,v,w:
F = u + v + w
where u,v,w are functions of x,y,z
Must satisfy:
∇·F = du/dx + dv/dy + dw/dz = 0
We have a field F defined:
F = u+v+w, u = ax+byz, v = cy+dxz
du/dx = a, dv/dy = c
Recall ∇·F = 0:
∇·F = du/dx + dv/dy + dw/dz = 0
a + c + dw/dz = 0
dw/dz = -a-c
Solve for w by separation of variables:
w = ∫(-a-c)dz
w = -az - cz + f(x,y)
f(x,y) is some undetermined function of x and y
The question states that w is not a function of x and y, therefore f(x,y) = 0...
w = -az - cz
Answer:
The neutron loses all of its kinetic energy to nucleus.
Explanation:
Given:
Mass of neutron is 'm' and mass of nucleus is 'm'.
The type of collision is elastic collision.
In elastic collision, there is no loss in kinetic energy of the system. So, total kinetic energy is conserved. Also, the total momentum of the system is conserved.
Here, the nucleus is still. So, its initial kinetic energy is 0. So, the total initial kinetic energy will be equal to kinetic energy of the neutron only.
Now, final kinetic energy of the system will be equal to the initial kinetic energy.
Now, as the nucleus was at rest initially, so the final kinetic energy of the nucleus will be equal to the initial kinetic energy of the neutron.
Thus, all the kinetic energy of the neutron will be transferred to the nucleus and the neutron will come to rest after collision.
Therefore, the neutron loses all of its kinetic energy to nucleus.
Answer:
t = 0.0735 m
Explanation:
Angular acceleration of the flywheel is given as
now after t = 8 s the speed of the flywheel is given as
now rotational kinetic energy of the wheel is given as
now we have
Answer:
m is expressed in kilograms and r in metres, with I (moment of inertia) having the dimension kilogram-metre square.
About 13.7 billion years ago
The Big Bang Theory states that the universe started about 13.7 billion years ago, and before that, everything was in 1 singularity.
