Answer:
Part a)
![\tau = 23.1 Nm](https://tex.z-dn.net/?f=%5Ctau%20%3D%2023.1%20Nm)
Part b)
![\tau = 17.05 Foot pound force](https://tex.z-dn.net/?f=%5Ctau%20%3D%2017.05%20Foot%20pound%20force)
Explanation:
As we know that torque is defined as the product of force and its perpendicular distance from reference point
so here we have
![\tau = \vec r \times \vec F](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%5Cvec%20r%20%5Ctimes%20%5Cvec%20F)
now we have
![\tau = (0.140)(165)](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%280.140%29%28165%29)
![\tau = 23.1 Nm](https://tex.z-dn.net/?f=%5Ctau%20%3D%2023.1%20Nm)
Part b)
Now we know the conversion as
1 meter = 3.28 foot
1 N = 0.225 Lb force
now we have
![\tau = 23.1 Nm](https://tex.z-dn.net/?f=%5Ctau%20%3D%2023.1%20Nm)
![\tau = 23.1 (0.225 Lb)(3.28 foot)](https://tex.z-dn.net/?f=%5Ctau%20%3D%2023.1%20%280.225%20Lb%29%283.28%20foot%29)
![\tau = 17.05 Foot pound force](https://tex.z-dn.net/?f=%5Ctau%20%3D%2017.05%20Foot%20pound%20force)
I'm stuck on the same question, as well :(
Answer:
a = v^2/r centripetal acceleration
v = (a * r)^1/2 = (42 * .23)^1/2 = 3.1 m/s
Physical changes are those which do not affect the chemical properties of a substance. For example, when a paper is cut, the two pieces obtained are still paper. The chemical properties have not changed. Only, physically when one piece is cut to two. A chemical change occurs when the chemical properties change and a new substance with different chemical properties is obtained. For example, when the paper is burnt, it turns to ashes. Hence, this is a chemical change.
When a substance undergoes a physical change, the physical properties of the substance changes like the state (solid to liquid during melting), shape, size, volume etc. Many physical changes are reversible whereas, in general many chemical changes are irreversible.
Answer:
1402.73 m
Explanation:
Mass of Azurite=3.25 lb
Percent of copper in AZurite mineral=55.1%
Diameter of copper wire,d=0.0113 in
Radius of copper wire=![r=\frac{d}{2}=\frac{0.0113}{2}=0.00565 in=\frac{565}{100000}=\frac{565}{100}\times \frac{1}{1000}=5.65\times 10^{-3}in](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7B0.0113%7D%7B2%7D%3D0.00565%20in%3D%5Cfrac%7B565%7D%7B100000%7D%3D%5Cfrac%7B565%7D%7B100%7D%5Ctimes%20%5Cfrac%7B1%7D%7B1000%7D%3D5.65%5Ctimes%2010%5E%7B-3%7Din)
![\frac{1}{1000}=10^{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1000%7D%3D10%5E%7B-3%7D)
Density of copper=![\rho=8.96g/cm^3](https://tex.z-dn.net/?f=%5Crho%3D8.96g%2Fcm%5E3)
1 lb=454 g
3.25 lb=![3.25\times 454=1475.5 g](https://tex.z-dn.net/?f=3.25%5Ctimes%20454%3D1475.5%20g)
Mass of Azurite=![1475.5 g](https://tex.z-dn.net/?f=1475.5%20g)
Mass of copper=![\frac{55.1}{100}\times 1475.5=813 g](https://tex.z-dn.net/?f=%5Cfrac%7B55.1%7D%7B100%7D%5Ctimes%201475.5%3D813%20g)
Density=![\frac{Mass}{volume}](https://tex.z-dn.net/?f=%5Cfrac%7BMass%7D%7Bvolume%7D)
Using the formula
![8.96=\frac{813}{volume\;of\;copper}](https://tex.z-dn.net/?f=8.96%3D%5Cfrac%7B813%7D%7Bvolume%5C%3Bof%5C%3Bcopper%7D)
Volume of copper wire=![\frac{813}{8.96}=90.7cm^3](https://tex.z-dn.net/?f=%5Cfrac%7B813%7D%7B8.96%7D%3D90.7cm%5E3)
Radius of copper wire=![5.65\times 10^{-3}\times 2.54=14.35\times 10^{-3} cm](https://tex.z-dn.net/?f=5.65%5Ctimes%2010%5E%7B-3%7D%5Ctimes%202.54%3D14.35%5Ctimes%2010%5E%7B-3%7D%20cm)
1 in=2.54 cm
Volume of copper wire=![\pi r^2 h](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%20h)
![\pi=3.14](https://tex.z-dn.net/?f=%5Cpi%3D3.14)
Using the formula
![90.7=3.14\times (14.35\times 10^{-3})^2\times h](https://tex.z-dn.net/?f=90.7%3D3.14%5Ctimes%20%2814.35%5Ctimes%2010%5E%7B-3%7D%29%5E2%5Ctimes%20h)
![h=\frac{90.7}{3.14\times (14.35\times 10^{-3})^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B90.7%7D%7B3.14%5Ctimes%20%2814.35%5Ctimes%2010%5E%7B-3%7D%29%5E2%7D)
![h=140273 cm](https://tex.z-dn.net/?f=h%3D140273%20cm)
1 m=100 cm
![h=\frac{140273}{100}=1402.73 m](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B140273%7D%7B100%7D%3D1402.73%20m)
Hence, the length of copper wire required=1402.73 m