Answer:
The gauge pressure is ![P_g = 2058 \ P_a](https://tex.z-dn.net/?f=P_g%20%20%3D%20%202058%20%5C%20P_a)
Explanation:
From the question we are told that
The height of the water contained is ![h_w = 30 \ cm = 0.3 \ m](https://tex.z-dn.net/?f=h_w%20%20%3D%20%2030%20%5C%20cm%20%20%3D%20%200.3%20%5C%20m)
The height of liquid in the cylinder is ![h_t = 40 \ cm = 0.4 \ m](https://tex.z-dn.net/?f=h_t%20%20%3D%20%2040%20%5C%20cm%20%20%3D%200.4%20%5C%20m)
At the bottom of the cylinder the gauge pressure is mathematically represented as
![P_g = P_w + P_o](https://tex.z-dn.net/?f=P_g%20%20%3D%20%20P_w%20%2B%20P_o)
Where
is the pressure of water which is mathematically represented as
![P_w = \rho_w * g * h_w](https://tex.z-dn.net/?f=P_w%20%20%3D%20%20%5Crho_w%20%20%2A%20%20g%20%2A%20h_w)
Now
is the density of water with a constant values of ![\rho_w = 1000 \ kg /m^3](https://tex.z-dn.net/?f=%5Crho_w%20%20%3D%201000%20%5C%20kg%20%2Fm%5E3)
substituting values
![P_w = 1000 * 9.8 * 0.3](https://tex.z-dn.net/?f=P_w%20%20%3D%201000%20%2A%20%209.8%20%2A%20%200.3)
![P_w = 2940 \ Pa](https://tex.z-dn.net/?f=P_w%20%20%3D%20%202940%20%5C%20%20Pa)
While
is the pressure of oil which is mathematically represented as
![P_o = \rho_o * g * (h_t -h_w )](https://tex.z-dn.net/?f=P_o%20%20%3D%20%20%5Crho_o%20%2A%20%20g%20%2A%20%20%28h_t%20-h_w%20%29)
Where
is the density of oil with a constant value
![\rho _o = 900 \ kg / m^3](https://tex.z-dn.net/?f=%5Crho%20_o%20%20%3D%20900%20%5C%20kg%20%2F%20m%5E3)
substituting values
![P_o = 900 * 9.8 * (0.4 - 0.3)](https://tex.z-dn.net/?f=P_o%20%20%3D%20%20900%20%2A%20%209.8%20%2A%20%280.4%20-%200.3%29)
![P_o = 882 \ Pa](https://tex.z-dn.net/?f=P_o%20%20%3D%20%20882%20%5C%20Pa)
Therefore
![P_g = 2940 - 882](https://tex.z-dn.net/?f=P_g%20%20%3D%20%202940%20-%20882)
![P_g = 2058 \ P_a](https://tex.z-dn.net/?f=P_g%20%20%3D%20%202058%20%5C%20P_a)
<span>One timing problem
in using fiscal policy to counter a recession is called the “legislative lag”
it occurs between the time the time the need for fiscal action is recognized
and between the time that it is taken in action.</span>
The answer to this would inFact be A
Answer:
alpha=53.56rad/s
a=5784rad/s^2
Explanation:
First of all, we have to compute the time in which point D has a velocity of v=23ft/s (v0=0ft/s)
![v=v_0+at\\\\t=\frac{v}{a}=\frac{(23\frac{ft}{s})}{32.17\frac{ft}{s^2}}=0.71s](https://tex.z-dn.net/?f=v%3Dv_0%2Bat%5C%5C%5C%5Ct%3D%5Cfrac%7Bv%7D%7Ba%7D%3D%5Cfrac%7B%2823%5Cfrac%7Bft%7D%7Bs%7D%29%7D%7B32.17%5Cfrac%7Bft%7D%7Bs%5E2%7D%7D%3D0.71s)
Now, we can calculate the angular acceleration (w0=0rad/s)
![\theta=\omega_0t +\frac{1}{2}\alpha t^2\\\alpha=\frac{2\theta}{t^2}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Comega_0t%20%2B%5Cfrac%7B1%7D%7B2%7D%5Calpha%20t%5E2%5C%5C%5Calpha%3D%5Cfrac%7B2%5Ctheta%7D%7Bt%5E2%7D)
![\alpha=\frac{27}{(0.71s)^2}=53.56\frac{rad}{s^2}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cfrac%7B27%7D%7B%280.71s%29%5E2%7D%3D53.56%5Cfrac%7Brad%7D%7Bs%5E2%7D)
with this value we can compute the angular velocity
![\omega=\omega_0+\alpha t\\\omega = (53.56\frac{rad}{s^2})(0.71s)=38.02\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%3D%5Comega_0%2B%5Calpha%20t%5C%5C%5Comega%20%3D%20%2853.56%5Cfrac%7Brad%7D%7Bs%5E2%7D%29%280.71s%29%3D38.02%5Cfrac%7Brad%7D%7Bs%7D)
and the tangential velocity of point B, and then the acceleration of point B:
![v_t=\omega r=(38.02\frac{rad}{s})(4)=152.11\frac{ft}{s}\\a_t=\frac{v_t^2}{r}=\frac{(152.11\frac{ft}{s})^2}{4ft}=5784\frac{rad}{s^2}](https://tex.z-dn.net/?f=v_t%3D%5Comega%20r%3D%2838.02%5Cfrac%7Brad%7D%7Bs%7D%29%284%29%3D152.11%5Cfrac%7Bft%7D%7Bs%7D%5C%5Ca_t%3D%5Cfrac%7Bv_t%5E2%7D%7Br%7D%3D%5Cfrac%7B%28152.11%5Cfrac%7Bft%7D%7Bs%7D%29%5E2%7D%7B4ft%7D%3D5784%5Cfrac%7Brad%7D%7Bs%5E2%7D)
hope this helps!!
Applying Newtons version of Kepler's third law or the orbital velocity law to the star orbiting 40000 light years from the center of the Milky Way Galaxy allows us to determine the mass of the Milky Way Galaxy that lies within 40000 light years in the galactic center.
<h3>
</h3><h3>What is orbital velocity law?</h3>
The orbital velocity law states that, the orbital velocity is directly proportional to the mass of the body for which it is being calculated and inversely proportional to the radius of the body. Earths orbital velocity near its surface is around 8km/sec if the air resistance is disregarded.
In space exploration, orbital velocity is a crucial topic. Space authorities heavily rely on it to comprehend how to launch satellites. It aids scientists in figuring out the velocities at which satellites must orbit a planet or other celestial body to prevent collapsing into it. The speed at which one body orbits the other body is known as the orbital velocity. The term "orbit" refers to an object's consistent circular motion around the Earth. The distance between the object and the earth's centre determines the orbit's velocity.
To know more about orbital velocity law, refer brainly.com/question/11353717
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