food processing industry ,needed a flouring of a bread with fast transportation. projectile motion is accounted for this problem as a solution as explained

1. HAMMAD-UR-REHMAN
me131013
Assignment: 02 (official)
Engineering Dynamics – Dr. Muhammad Kashif Khan
MANOEUVREMENT THROUGH PROJECTILE MOTION
Objective:
Industrialization is one of the most influenced factors in the development of human races, it has been seen that humans have used their creative thoughts to be able to manufacture or produce mass scale production of goods for the betterment of living standards of the masses. This requires the scientific studies to be used by the engineers to make the automation of good production possible, for fast and quality production. Engineers have been using different forms of motion to be produced through machines for the transportation of goods which is a very basic need for any production. Usually curvilinear motions are produced through conveyer belts but sometimes they have to save money and time and to avoid the complicated mechanisms of conveyer belts, they opt for projectile motion whenever possible, this saves time and its very simple to construct, the only hindrance in this is to make the landing as much accurate and safe.
Abstract:
Nowadays there is an increasing trend, the automated food industry. Here we have to maneuver food stuff (ready and raw materials) throughout the production process and the privilege we have is that the stuff is free to deform and throwing is allowed. I am trying to demonstrate a projectile motion that could be used to transport the food stuff even to add something to food.

2. Construction:
 In the industry to accomplish projectile motion we usually know the range and height for the motion and only need is to device a mechanism for the right velocity and consider the right environmental parameters.
 If I have to flour bread that will fly of the conveyer at some height h and the showering of flour is done at a distance of x, shower is like a thin curtain which applies flour on to the bread uniformly. As this schematic picture depicts.
Governing equations:
 Speed of the conveyer belt.
푽=풓∗흎 흎=ퟐ∗흅∗ 풓풑풎 ퟔퟎ풔풆풄
Where, r= radius of the shaft of motor on which the conveyer moves
 Now when the bread becomes projectile
푽x = 푹 풕 푽풚=품풕 푯= ퟏ ퟐ ∗품∗풕ퟐ 푽풙=푽풄풐풔휽 푽풚=푽풔풊풏휽

3. Assumptions:
 In the above scenario we are assuming air resistance to be negligible because we are working in closed Air conditioned industrial environment where there is no wind flows.
 Flour is almost weight less and due to the fact that only a fraction of the surface of the bread is forced into the flour curtain, there is no effect on the projectile motion or the path of our bread therefore the range of our bread remains the same.
 Value of g is taken negative in projectile motion. And we have to assume right hand xy plane axes system which makes height negative in our case.
Planning the process:
1. Bread is loaded on the supply conveyer and the conveyer took the bread to the end of the conveyer. Where the initial launch velocity of the bread is taken as the tangential velocity of the conveyer.
2. The bread becomes projectile as soon as it leaves the conveyer belt and during the flight it passes through the flour curtain. Here its motion is governed by the gravitational force only.
3. The bread with flour applied lands on the delivery conveyer.
SCENERIO
The distance between end of conveyer and flour curtain is “1 meter” and the distance between the curtain and the next delivery conveyer is “2 meters”. The radius of the conveyer driving shaft is 0.1 meters.
The height of the supply conveyer with respect to delivery conveyer is “3 meters”.
Now for the safety parameter the bread should always land on the delivery conveyer that is “x meters” apart, at “x+0.10x”.
In this case we have landing at least at 3.10meter, height covered is 3 meter here, and the bread has to cross the curtain of flour at 1 meter a head.
o Velocity and rpm of conveyer should be=??
o Time for total flight, time when the brad hits the flour curtain=??
Using 푯= 품푻풕ퟐ ퟐ 푻풕=√ ퟐ푯 품 t=0.7824sec (total time of flight) at that time it drops on delivery conveyer.
Vx= 푅 푇푡 푉푥=3.8343 푚 푠
푉푓=푔푡 푉푓=−9.8∗0.7824 푉푓=−7.66752 푚 푠푒푐
Since we now in this case of 0 degree launching of projectile 푉=푉푥.
푉=푟휔 . 휔= 푉 푟 휔=38.343 푟푎푑 푠 푟푝푚= 60휔 2휋 푟푝푚=366.3397 푟푒푣 푠푒푐
Time to pass throw flour curtain 푇푓:
푇푓= 푅푓 푉푥 푇푓=0.2608037푠푒푐

4.  If we wanted to know that our flour shower is of thickness “y”, let say y=0.1meter in our case then what is the flouring time then??

푇푓= 푦 푉푥 푇푓= 0.13.834 푇푓=0.02608푠푒푐 ,
I.e. if we have 10cm wide flour curtain our bread will remain in it for 0.026sec.
Controlling parameters:
1. First of all we have the design parameters:
i) Total range for the delivery conveyer
ii) Range set for flouring curtain
iii) Height set for supply conveyer
iv) We have fixed radius of driving shaft for the conveyer belt.
2. Bread should always fall in addition of “x” length to the total range of delivery conveyer to avoid dropping out of bread.
3. We have the rpm adjuster setting this allows us to set the certain speed for our supply conveyer.
Mechanical advantages:
To examine the mechanical advantage of our system we can consider the following parameters:
 Now we can increase max height of our system to increase the contact time while covering the small range at slow initial speed.
 We can also set the long range and throw the bread at high speed and increase the width of flour curtain.
Conclusion:
We can have the best of it if we could use all the mathematical results to be engineered in the practical world scenarios and we can see this as done in the above example.
As far as projectile motion is concerned so we can see that a controlled drop of things can save us from designing the complex lifting and carrying mechanisms.