Answer:
a) ![1.94 \frac{rad}{s}](https://tex.z-dn.net/?f=1.94%20%5Cfrac%7Brad%7D%7Bs%7D)
b) ![9.12\frac{m}{s}](https://tex.z-dn.net/?f=9.12%5Cfrac%7Bm%7D%7Bs%7D)
c) Towards the center of the centrifuge
Explanation:
a)
Becuse the centrifuge rotates in circular motion, there's an angular acceleration tha simulates high gravity accelerations
![a_{rad}=\omega r^{2}](https://tex.z-dn.net/?f=a_%7Brad%7D%3D%5Comega%20r%5E%7B2%7D%20)
with r the radius and ω the amgular velocity, in or case
so:
and g=9.8![\frac{m}{s^{2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
solving for ω:
![\omega=\frac{3.5g}{r^2}=\frac{3.5*9.8}{4.2^2}](https://tex.z-dn.net/?f=%20%5Comega%3D%5Cfrac%7B3.5g%7D%7Br%5E2%7D%3D%5Cfrac%7B3.5%2A9.8%7D%7B4.2%5E2%7D)
![\omega = 1.94 \frac{rad}{s}](https://tex.z-dn.net/?f=%20%5Comega%20%3D%201.94%20%5Cfrac%7Brad%7D%7Bs%7D)
b) Linear speed (v) and angular speed are related by:
![v=\omega r =(1.94)(4.7)](https://tex.z-dn.net/?f=v%3D%5Comega%20r%20%3D%281.94%29%284.7%29%20)
![v= 9.12\frac{m}{s}](https://tex.z-dn.net/?f=%20v%3D%209.12%5Cfrac%7Bm%7D%7Bs%7D)
c) The apparent weigth is pointing towards the center of the circle, becuse angular acceleration is pointing in that direction.
Answer:
The rate of heat conduction through the layer of still air is 517.4 W
Explanation:
Given:
Thickness of the still air layer (L) = 1 mm
Area of the still air = 1 m
Temperature of the still air ( T) = 20°C
Thermal conductivity of still air (K) at 20°C = 25.87mW/mK
Rate of heat conduction (Q) = ?
To determine the rate of heat conduction through the still air, we apply the formula below.
![Q =\frac{KA(\delta T)}{L}](https://tex.z-dn.net/?f=Q%20%3D%5Cfrac%7BKA%28%5Cdelta%20T%29%7D%7BL%7D)
![Q =\frac{25.87*1*20}{1}](https://tex.z-dn.net/?f=Q%20%3D%5Cfrac%7B25.87%2A1%2A20%7D%7B1%7D)
Q = 517.4 W
Therefore, the rate of heat conduction through the layer of still air is 517.4 W
Answer:
the rate of change in volume with time is 280πr² cm³/min
Explanation:
Data provided in the question:
Radius of the sphere as 'r'
= 70 cm/min
Volume of the sphere, V =
Surface area of the sphere as 4πr²
Now,
Rate of change in volume with time,
=
=
Substituting the value of ![\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D)
=
= 280πr² cm³/min
Hence, the rate of change in volume with time is 280πr² cm³/min
Momentum of the wagon increases by (200 x 3)
= 600 newton-sec
= 600 kg-m/sec