Displacement is usually how the messure the rock
Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb = ![157 lb \times \frac{1 kg}{2.2046 lb}](https://tex.z-dn.net/?f=157%20lb%20%5Ctimes%20%5Cfrac%7B1%20kg%7D%7B2.2046%20lb%7D)
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.
![180 \frac{mg}{kg} \times 71.215 kg](https://tex.z-dn.net/?f=180%20%5Cfrac%7Bmg%7D%7Bkg%7D%20%5Ctimes%2071.215%20kg)
= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) = ![\frac{0.65 g}{100 g}](https://tex.z-dn.net/?f=%5Cfrac%7B0.65%20g%7D%7B100%20g%7D)
= ![\frac{0.65 g}{(\frac{100 g}{1.0 g/ml})}](https://tex.z-dn.net/?f=%5Cfrac%7B0.65%20g%7D%7B%28%5Cfrac%7B100%20g%7D%7B1.0%20g%2Fml%7D%29%7D)
= ![\frac{0.65 g}{100 ml}](https://tex.z-dn.net/?f=%5Cfrac%7B0.65%20g%7D%7B100%20ml%7D)
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g = ![\frac{12.8187 g}{\frac{0.65 g}{100 ml}}](https://tex.z-dn.net/?f=%5Cfrac%7B12.8187%20g%7D%7B%5Cfrac%7B0.65%20g%7D%7B100%20ml%7D%7D)
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.
Answer:
- 278.34 kg m/s^2
Explanation:
The rate of the change of momentum is the same as the force.
The force that an object feels when moviming in a circular motion is given by:
F = -mrω^2
Where ω is the angular speed and r is the radius of the circumference
Aditionally, the tangential velocity of the body is given as:
v = rω
The question tells us that
v = 25 m/s
r = 7m
mv = 78 kg m/s
Therefore:
m = (78 kg m/s) / (25 m/s) = 3.12 kg
ω = (25 m/s) / (7 m) = 3.57 (1/s)
Now, we can calculate the force or rate of change of momentum:
F = - (3.12 kg) (7 m)(3.57 (1/s))^2
F = - 278.34 kg m/s^2
Answer:
The time taken is ![t = 0.356 \ s](https://tex.z-dn.net/?f=t%20%3D%20%200.356%20%5C%20s)
Explanation:
From the question we are told that
The length of steel the wire is ![l_1 = 31.0 \ m](https://tex.z-dn.net/?f=l_1%20%20%3D%2031.0%20%5C%20m)
The length of the copper wire is ![l_2 = 17.0 \ m](https://tex.z-dn.net/?f=l_2%20%20%3D%2017.0%20%5C%20m)
The diameter of the wire is ![d = 1.00 \ m = 1.0 *10^{-3} \ m](https://tex.z-dn.net/?f=d%20%3D%20%201.00%20%5C%20m%20%20%3D%20%201.0%20%2A10%5E%7B-3%7D%20%5C%20m)
The tension is ![T = 122 \ N](https://tex.z-dn.net/?f=T%20%20%3D%20%20122%20%5C%20N)
The time taken by the transverse wave to travel the length of the two wire is mathematically represented as
![t = t_s + t_c](https://tex.z-dn.net/?f=t%20%20%3D%20%20t_s%20%20%2B%20%20t_c)
Where
is the time taken to transverse the steel wire which is mathematically represented as
![t_s = l_1 * [ \sqrt{ \frac{\rho * \pi * d^2 }{ 4 * T} } ]](https://tex.z-dn.net/?f=t_s%20%20%3D%20l_1%20%2A%20%20%5B%20%5Csqrt%7B%20%5Cfrac%7B%5Crho%20%2A%20%5Cpi%20%2A%20%20d%5E2%20%7D%7B%204%20%2A%20%20T%7D%20%7D%20%5D)
here
is the density of steel with a value ![\rho_s = 8920 \ kg/m^3](https://tex.z-dn.net/?f=%5Crho_s%20%20%3D%20%208920%20%5C%20kg%2Fm%5E3)
So
![t_s = 31 * [ \sqrt{ \frac{8920 * 3.142* (1*10^{-3})^2 }{ 4 * 122} } ]](https://tex.z-dn.net/?f=t_s%20%20%3D%2031%20%2A%20%20%5B%20%5Csqrt%7B%20%5Cfrac%7B8920%20%2A%203.142%2A%20%20%281%2A10%5E%7B-3%7D%29%5E2%20%7D%7B%204%20%2A%20%20122%7D%20%7D%20%5D)
![t_s = 0.235 \ s](https://tex.z-dn.net/?f=t_s%20%20%3D%200.235%20%5C%20s)
And
is the time taken to transverse the copper wire which is mathematically represented as
![t_c = l_2 * [ \sqrt{ \frac{\rho_c * \pi * d^2 }{ 4 * T} } ]](https://tex.z-dn.net/?f=t_c%20%20%3D%20l_2%20%2A%20%20%5B%20%5Csqrt%7B%20%5Cfrac%7B%5Crho_c%20%2A%20%5Cpi%20%2A%20%20d%5E2%20%7D%7B%204%20%2A%20%20T%7D%20%7D%20%5D)
here
is the density of steel with a value ![\rho_s = 7860 \ kg/m^3](https://tex.z-dn.net/?f=%5Crho_s%20%20%3D%20%207860%20%5C%20kg%2Fm%5E3)
So
![t_c = 17 * [ \sqrt{ \frac{7860 * 3.142* (1*10^{-3})^2 }{ 4 * 122} } ]](https://tex.z-dn.net/?f=t_c%20%20%3D%2017%20%2A%20%20%5B%20%5Csqrt%7B%20%5Cfrac%7B7860%20%2A%203.142%2A%20%20%281%2A10%5E%7B-3%7D%29%5E2%20%7D%7B%204%20%2A%20%20122%7D%20%7D%20%5D)
![t_c =0.121](https://tex.z-dn.net/?f=t_c%20%20%3D0.121)
So
![t = t_c + t_s](https://tex.z-dn.net/?f=t%20%20%3D%20t_c%20%20%2B%20t_s)
![t = 0.121 + 0.235](https://tex.z-dn.net/?f=t%20%3D%20%200.121%20%2B%200.235)
![t = 0.356 \ s](https://tex.z-dn.net/?f=t%20%3D%20%200.356%20%5C%20s)