Answer:
The answer would be A. - the temperature remains constant
Explanation:
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0
Answer:
8100W
Explanation:
Let g = 10m/s2
As water is falling from 60m high, its potential energy from 60m high would convert to power. So the rate of change in potential energy is
or 9000W
Since 10% of this is lost to friction, we take the remaining 90 %
P = 9000*90% = 8100 W
Answer:
The angular speed after 6s is
.
Explanation:
The equation
![I\alpha = Fd](https://tex.z-dn.net/?f=I%5Calpha%20%20%3D%20Fd)
relates the moment of inertia
of a rigid body, and its angular acceleration
, with the force applied
at a distance
from the axis of rotation.
In our case, the force applied is
, at a distance
, to a ring with the moment of inertia of
; therefore, the angular acceleration is
![$\alpha =\frac{Fd}{I} $](https://tex.z-dn.net/?f=%24%5Calpha%20%3D%5Cfrac%7BFd%7D%7BI%7D%20%24)
![$\alpha =\frac{22N*0.06m}{(1.5kg)*(0.06)^2} $](https://tex.z-dn.net/?f=%24%5Calpha%20%3D%5Cfrac%7B22N%2A0.06m%7D%7B%281.5kg%29%2A%280.06%29%5E2%7D%20%24)
![\alpha = 244.44\: s^{-2}](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20244.44%5C%3A%20s%5E%7B-2%7D)
Therefore, the angular speed
which is
![\omega = \alpha t](https://tex.z-dn.net/?f=%5Comega%20%20%3D%20%5Calpha%20t)
after 6 seconds is
![\omega = 244.44$\: s^{-2}* 6s](https://tex.z-dn.net/?f=%5Comega%20%3D%20244.44%24%5C%3A%20s%5E%7B-2%7D%2A%206s)
![\boxed{\omega = 1466.67s^{-1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Comega%20%3D%201466.67s%5E%7B-1%7D%7D)
Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)
![x = At^3 + Bt\\m = As^3 + Bs\\m = (\frac{m}{s^3})s^3 + (\frac{m}{s})s](https://tex.z-dn.net/?f=x%20%3D%20At%5E3%20%2B%20Bt%5C%5Cm%20%3D%20As%5E3%20%2B%20Bs%5C%5Cm%20%3D%20%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E3%20%2B%20%28%5Cfrac%7Bm%7D%7Bs%7D%29s)
Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b) ![\frac{dx}{dt} = 3At^2 + B = 3(\frac{m}{s^3})s^2 + \frac{m}{s} = m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%203At%5E2%20%2B%20B%20%3D%203%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E2%20%2B%20%5Cfrac%7Bm%7D%7Bs%7D%20%3D%20m%2Fs)
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.