-- The potential energy of a 12-lb bowling ball up on the shelf
doesn't have anything to do with the temperature of the ball or
the shelf.
-- The potential energy of a jar full of gas does depend on the
temperature of the gas. The warmer it is, the greater its pressure
is, and the more work it can do if you let it out through a little hole
in the jar. If it gets hot enough, it'll have enough potential energy
to blow the jar to smithereens.
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:
Points downward, and its magnitude is 9.8 m/s^2
Explanation:
The motion of a projectile consists of two independent motions:
- A uniform horizontal motion, with constant velocity and zero acceleration. In fact, there are no forces acting on the projectile along the horizontal direction (if we neglect air resistance), so the acceleration along this direction is zero.
- A vertical motion, with constant acceleration g = 9.8 m/s^2 towards the ground (downward), due to the presence of gravity wich "pulls" the projectile downward.
The total acceleration of the projectile is given by the resultant of the horizontal and vertical components of the acceleration. But we said that the horizontal component is zero, therefore the total acceleration corresponds just to its vertical component, therefore it is a vector with magnitude 9.8 m/s^2 which points downward.
The energy is 3.06 electronvolts, E = 3.06eV
1eV = 1.6 * 10^-19 J
3.06 eV = 3.06* 1.6 * 10^-19 J = 4.896 * 10^-19 J
