Answer:
the formulae is f = mg = vpg
Answer:
2.2 s
Explanation:
Using the equation for the period of a physical pendulum, T = 2π√(I/mgh) where I = moment of inertia of leg about perpendicular axis at one point = mL²/3 where m = mass of man = 67 kg and L = height of man = 1.83 m, g = acceleration due to gravity = 9.8 m/s² and h = distance of leg from center of gravity of man = L/2 (center of gravity of a cylinder)
So, T = 2π√(I/mgh)
T = 2π√(mL²/3 /mgL/2)
T = 2π√(2L/3g)
substituting the values of the variables into the equation, we have
T = 2π√(2L/3g)
T = 2π√(2 × 1.83 m/(3 × 9.8 m/s² ))
T = 2π√(3.66 m/(29.4 m/s² ))
T = 2π√(0.1245 s² ))
T = 2π(0.353 s)
T = 2.22 s
T ≅ 2.2 s
So, the period of the man's leg is 2.2 s
To solve this problem it is necessary to apply the concepts related to Newton's second law, the definition of density and sum of forces in bodies.
From Newton's second law we understand that
Gravity at this case)
Where,
m = mass
a= acceleration
Also we know that
![\rho = \frac{m}{V} \Rightarrow m = \rho V](https://tex.z-dn.net/?f=%5Crho%20%3D%20%5Cfrac%7Bm%7D%7BV%7D%20%5CRightarrow%20m%20%3D%20%5Crho%20V)
Part A) The buoyant force acting on the balloon is given as
![F_b = ma](https://tex.z-dn.net/?f=F_b%20%3D%20ma)
As mass is equal to the density and Volume and acceleration equal to Gravity constant
![F_b = \rho V g](https://tex.z-dn.net/?f=F_b%20%3D%20%5Crho%20V%20g)
![F_b = 1.2*323*9.8](https://tex.z-dn.net/?f=F_b%20%3D%201.2%2A323%2A9.8)
![F_b = 3798.5](https://tex.z-dn.net/?f=F_b%20%3D%203798.5)
PART B) The forces acting on the balloon would be given by the upper thrust force given by the fluid and its weight, then
![F_{net} = F_b -W](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20F_b%20-W)
![F_{net} = F_b -(mg+\rho_H Vg)](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20F_b%20-%28mg%2B%5Crho_H%20Vg%29)
![F_{net} = 3798.5-(9.8*225*9.8*0.179*323)](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%203798.5-%289.8%2A225%2A9.8%2A0.179%2A323%29)
![F_{net} = 1030N](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%201030N)
PART C) The additional mass that can the balloon support in equilibrium is given as
![F_{net} = m' g](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20m%27%20g)
![m' =\frac{F_{net}}{g}](https://tex.z-dn.net/?f=m%27%20%3D%5Cfrac%7BF_%7Bnet%7D%7D%7Bg%7D)
![m' = \frac{1030}{9.8}](https://tex.z-dn.net/?f=m%27%20%3D%20%5Cfrac%7B1030%7D%7B9.8%7D)
![m' = 105Kg](https://tex.z-dn.net/?f=m%27%20%3D%20105Kg)
For this case, what we must do is to rewrite these measurements in the same unit in order to compare them.
By writing the measurements in meters we have:
![30 mm = (30) * (\frac{1}{1000}) = 0.030 m](https://tex.z-dn.net/?f=%2030%20mm%20%3D%20%2830%29%20%2A%20%28%5Cfrac%7B1%7D%7B1000%7D%29%20%3D%200.030%20m%20%20%20)
![30 cm = (30) * (\frac{1}{100}) = 0.30 m](https://tex.z-dn.net/?f=%2030%20cm%20%3D%20%2830%29%20%2A%20%28%5Cfrac%7B1%7D%7B100%7D%29%20%3D%200.30%20m%20%20%20)
![30 dm = (30) * (\frac{1}{10}) = 3 m\\30 Hm = (30) * (100) = 3000 m](https://tex.z-dn.net/?f=%2030%20dm%20%3D%20%2830%29%20%2A%20%28%5Cfrac%7B1%7D%7B10%7D%29%20%3D%203%20m%5C%5C30%20Hm%20%3D%20%2830%29%20%2A%20%28100%29%20%3D%203000%20m%20%20%20)
Therefore, physically the correct measure is:
![0.30 m = 30 cm](https://tex.z-dn.net/?f=%200.30%20m%20%3D%2030%20cm%20%20)
Answer:
the length of a student's textbook most likely is:
30 centimeters
Both systems have benefits and disadvantages.
Benefits of the Metric System
<span>Easier for anything involving conversions.Celsius is based on the the freezing and boiling points of water.Is the most popular system of measurement worldwide. This gives interchangeability internationally.Other systems of measurement, like U.S. standard units, are tied directly to metric units so they can be converted back and forth.<span>You can sell to the government since governments (including the U.S. government) require government contractors to use the metric system for most things.</span></span>