Answer:
Scandium with an ion charge of +3
Explanation:
Answer:
Radius, r = 0.00523 meters
Explanation:
It is given that,
Magnetic field, ![B=2\ mT=2.2\times 10^{-3}\ T](https://tex.z-dn.net/?f=B%3D2%5C%20mT%3D2.2%5Ctimes%2010%5E%7B-3%7D%5C%20T)
Current in the toroid, I = 9.6 A
Number of turns, N = 6
We need to find the radius of the toroid. The magnetic field at the center of the toroid is given by :
![B=\dfrac{\mu_oNI}{2\pi r}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_oNI%7D%7B2%5Cpi%20r%7D)
r = 0.00523 m
or
![r=5.23\times 10^{-3}\ m](https://tex.z-dn.net/?f=r%3D5.23%5Ctimes%2010%5E%7B-3%7D%5C%20m)
So, the radius of the toroid is 0.00523 meters. Hence, this is the required solution.
The gravitational force would get stronger because the farther the two masses are separated the more gravitational force will be used to pull them together the closer they are the less gravitational pull is used to pull them together
We need to consider for this exercise the concept Drag Force and Torque. The equation of Drag force is
![F_D = c_D A \frac{\rho V^2}{2}](https://tex.z-dn.net/?f=F_D%20%3D%20c_D%20A%20%5Cfrac%7B%5Crho%20V%5E2%7D%7B2%7D)
Where,
F_D = Drag Force
= Drag coefficient
A = Area
= Density
V = Velocity
Our values are given by,
(That is proper of a cone-shape)
![A = 9m^2](https://tex.z-dn.net/?f=A%20%3D%209m%5E2)
![\rho = 1.2Kg/m^3](https://tex.z-dn.net/?f=%5Crho%20%3D%201.2Kg%2Fm%5E3)
![V = 6.5m/s](https://tex.z-dn.net/?f=V%20%3D%206.5m%2Fs)
Part A ) Replacing our values,
![F_D = 0.5*9*\frac{1.2*6.5^2}{2}](https://tex.z-dn.net/?f=F_D%20%3D%200.5%2A9%2A%5Cfrac%7B1.2%2A6.5%5E2%7D%7B2%7D)
![F_D = 114.075N](https://tex.z-dn.net/?f=F_D%20%3D%20114.075N)
Part B ) To find the torque we apply the equation as follow,
![\tau = F*d](https://tex.z-dn.net/?f=%5Ctau%20%3D%20F%2Ad)
![\tau = (114.075N)(7)](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%28114.075N%29%287%29)
![\tau = 798.525N.m](https://tex.z-dn.net/?f=%5Ctau%20%3D%20798.525N.m)
Answer:
Explanation:
Given
Volume of bucket ![V=10\ gallon](https://tex.z-dn.net/?f=V%3D10%5C%20gallon)
Time taken to fill the bucket ![t=50\ s](https://tex.z-dn.net/?f=t%3D50%5C%20s)
so volume flow rate is ![\dot{V}=\frac{10}{50}=0.2\ gal/s](https://tex.z-dn.net/?f=%5Cdot%7BV%7D%3D%5Cfrac%7B10%7D%7B50%7D%3D0.2%5C%20gal%2Fs)
1 gal is equivalent to ![0.133\ ft^3](https://tex.z-dn.net/?f=0.133%5C%20ft%5E3)
![\dot{V}=0.0267\ ft^3/s](https://tex.z-dn.net/?f=%5Cdot%7BV%7D%3D0.0267%5C%20ft%5E3%2Fs)
mass flow rate ![\dot{m}=\rho \times \dot{V}](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%3D%5Crho%20%5Ctimes%20%5Cdot%7BV%7D)
![\dot{m}=62.4\times 0.0267](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%3D62.4%5Ctimes%200.0267)
![\dot{m}=1.668\ lbs](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%3D1.668%5C%20lbs)
(b)Average velocity through nozzle exit
![\dot{V}=Av_{avg}](https://tex.z-dn.net/?f=%5Cdot%7BV%7D%3DAv_%7Bavg%7D)
![v_{avg}=\dfrac{0.0267}{\frac{\pi}{4}\times (0.0262)^2}](https://tex.z-dn.net/?f=v_%7Bavg%7D%3D%5Cdfrac%7B0.0267%7D%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%5Ctimes%20%280.0262%29%5E2%7D)
![v_{avg}=49.51\ ft/s](https://tex.z-dn.net/?f=v_%7Bavg%7D%3D49.51%5C%20ft%2Fs)