In lecture demonstrations, we do
measurements of the drag force on different objects. The objects are placed in a uniform airstream created by a fan. Calculate the Reynolds number and the drag coefficient.
The calculus of velocity-dependent frictional forces
When a body slides across a surface, the frictional force on it is approximately constant and given by
Unfortunately, the frictional force on a body moving through a liquid or a gas does not behave so simply. This drag force is generally a complicated function of the body’s velocity. However, for a body moving in a straight line at moderate speeds through a liquid such as water, the frictional force can often be approximated by
where
b is a constant whose value depends on the dimensions and shape of the body and the properties of the liquid, and
v is the velocity of the body. Two situations for which the frictional force can be represented this equation are a motorboat moving through water and a small object falling slowly through a liquid.
Let’s consider the object falling through a liquid. The free-body diagram of this object with the positive direction downward is shown in
[link] . Newton’s second law in the vertical direction gives the differential equation
where we have written the acceleration as
As
v increases, the frictional force –
bv increases until it matches
mg . At this point, there is no acceleration and the velocity remains constant at the terminal velocity
From the previous equation,
so
We can find the object’s velocity by integrating the differential equation for
v . First, we rearrange terms in this equation to obtain
Assuming that
integration of this equation yields
or
where
are dummy variables of integration. With the limits given, we find
Since
and
we obtain
and
Notice that as
which is the terminal velocity.
The position at any time may be found by integrating the equation for
v . With
Assuming
which integrates to
Effect of the resistive force on a motorboat
A motorboat is moving across a lake at a speed
when its motor suddenly freezes up and stops. The boat then slows down under the frictional force
(a) What are the velocity and position of the boat as functions of time? (b) If the boat slows down from 4.0 to 1.0 m/s in 10 s, how far does it travel before stopping?
Solution
With the motor stopped, the only horizontal force on the boat is
so from Newton’s second law,
which we can write as
Integrating this equation between the time zero when the velocity is
and the time
t when the velocity is
, we have
Thus,
which, since
we can write this as
Now from the definition of velocity,
so we have
With the initial position zero, we have
and
As time increases,
and the position of the boat approaches a limiting value
Although this tells us that the boat takes an infinite amount of time to reach
the boat effectively stops after a reasonable time. For example, at
we have
whereas we also have
Therefore, the boat’s velocity and position have essentially reached their final values.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life