QUESTION
PEC120 S1 2012 Assignment 2
Real-world Physics is not about solving idealised problems from a textbook it is about applying what
you have learned to real world situations with all the complicating factors like friction, air resistance,
humidity, inelastic collisions, open systems…
For this assignment we want you to take the first steps to becoming a real-world scientist or
engineer. To do this you have to think like an expert not a novice. The following table may give you
some insight into how each thinks.
Novice Expert
Content forms isolated pieces of information
that need memorising.
Mental models are used but they are treated as
though they are reality and there is no
understanding of their limitations.
Knowledge in the discipline is fixed and handed
down from some expert higher authority –
lecturer, tutor, textbook.
Problem solving is approached by recognising
patterns and memorising recipes for finding
solutions.
Your report will be focused on one of the following areas:
Topic 2 – Linear Motion
Topic 3 – Newton’s Laws and Vectors
Topic 5 – Gravity and Projectile Motion
Where Do You Start?
There is a coherent structure to the content
where relationships are clearly seen and pulled
together under overarching concepts.
Mental models are used to help with understand
and the realisation that a model is being used is
retained. The limitations of those models are
clearly understood.
The knowledge in the discipline describes
nature, is discovered by observation and
established by experiment.
There is a systematic approach to problem
solving which includes self checking, sense
making and reflection upon the topic.
You start by understanding what you want to get out of this exercise then you go on to do it. You
need to show that you can:
• Investigate and explain the underlying physics of an observed real-world situation
• Write a scientific report
• Evaluate the quality of your work
This report is worth 6% of your marks so if 100 marks equates to 150hrs of work (15 weeks at 10 hrs
per week) then 5 marks should take you around 9 hrs. Or a bit over a full working day.
Investigate and Explain the Underlying Physics of an Observed Real-world
Situation
1.
Observation
Spend a day or two analysing the world around you in terms of Linear Motion / Newton’s Laws /
Vectors / Gravity / Projectile Motion. Choose one aspect you would like to investigate further e.g.
apples falling from a tree.
2. Link observations to prior understanding
Make a note of what you have found interesting in your observations and what you think the
underlying physics may be. Then check your explanation using a valid source of information and
modify your explanation accordingly if necessary.
3. Do some tests / collect some detailed information
Try and capture some data / information about the situation that demonstrates the underlying
physics. You can use this information in your report. You will need to collect some actual information
and measurements for this section.
4. Analyse the information
See if the detailed information / data you have captured supports or refutes your original
explanation of the underlying science. Or perhaps your explanation needs to be modified slightly to
explain all the data you observed. Make notes on this stage to help you with writing up your report.
5. Reflect on the process
Ask yourself questions about the process and jot down some notes which may be of use when
writing up your report. The types of questions you might ask could include “Was this the best way to
illustrate the physics of the situation? Are there other ways it could have been done and what are
the merits of each? Are there other interesting aspects of the situation that could also be
investigated?
Write a Scientific Report
The report should be coherent, cohesive, comprehensive and concise. We are expecting around 3
pages of text plus any pictures, diagrams, tables of data, audio or video material relevant to your
study. A report is usually broken up into a series of sections with different headings and purposes.
Headings for the report which should be used:
• Introduction (put this at the beginning but write it last)
• Initial Observation
• Initial Explanation
• Detailed Observations and Documentation
• Discussion and Analysis (modified explanation goes in this bit)
• Reflection on the Process
• Conclusion (restates the interesting observation and the polished explanation of the
underlying physics)
A good report tells one story and is logically set out i.e. it flows. The report should look professional
and it should have been proof read for spelling and grammatical errors.
Learn how to use the reference checking software
Run your finished assignment through TurnItIn to see if you have missed any references. The
TurnItIn report should be attached to your assignment before you submit it.
Evaluate the quality of your work
This is the difficult bit. The marking criteria are going to be partially determined by you during the
tutorials preceding the assignment deadline and the discussion will be continued on the unit website
so external students can contribute. Each tutorial will determine what makes a good report and from
these guidelines the marking key will be constructed. The marking key will then be posted on LMS.
This allows you to judge the quality of your work before it is submitted and marked.
SOLUTION
Observation
The projectile motion describes the behavior of body, when launched from a height or with certain finite velocity. This dynamics is determined by the
1. Physical dimensions of the body
2. Gravitational pull of the earth (and the other objects surrounding it.)
3. The air drag, might play a bigger role, depending on the dimensions of the object .This effect may become louder if the air is in motion.
The observation, under consideration, is the effect of the air drag on the bodies in motion. Like the motion of sheet of paper, when left to free fall. It is quite difficult to tell time period of the fall, even after numerous experiments, would repeat under similar conditions.(Claymore , 2012)
The classical theories of physics tell that all the masses would fall through a given height in the same amount of time. The only factor determining the fall is small g.
Underlying Physics
The objects under consideration in the classical physics are, in general considered as the point masses. This work in the ideal conditions, and is helpful in providing important insights.
However, the sheet of paper cannot be considered a point mass but a distributed one .The air-drag felt by it would have to be calculated in an aggregate effect
Effect of Air-drag on point mass
The air drag increases with the velocity of the body, though it shows a parabolic trend . It is given as ,
Drag (D) = (1/2)C*r*A*(V^2)
Where, C=is the drag coefficient
r=density of air
A=area of the body in contact
V=the velocity of the object
As, has been found the constant C, is the function dependent on, u the viscosity of air, r the density of the air, d the diameter of the body in motion and V the velocity. So,
C=f (u,r,d,v)
The factors density, viscosity, speed, diameter contributing to the coefficient of drag can be combined into a constant called Reynolds number Re.
Re= (rVd)/u
Where, variable’s have their meaning, in natural sense.
Hence, the drag coefficient comes out to be dependent on Reynolds number:
C=f (Re).
As, the drag force is by nature against increase in the velocity of the body in motion. Assuming that the body moves, in a two dimension reference frame, we can take help of the differential calculus, in order to frame the equation of motion .The variables used ahead, all have the same meaning in the context as, earlier. The variables u’ and v’ are the horizontal and the vertical rate of change of distance with time, i.e., the velocities corresponding to each of the axes.
(dx/dt)=u’;
(dy/dt)=v’;
(du’/dt)= -(CRe/24T)u’;
(dv’/dt)= -(CRe/24T)v’-g;
The T is proportional to the mass m, and inversely proportional to diameter and the Viscosity u of the air.
Projectile Motion plots
The projectile motion plots can vary with the different types of drag force.
The body in projectile motion, would travel an ideal path of a projectile motion,
If gravity is the only acting force. As the objects behave differently in nature, the projectiles seen in the figure below, end-up with shorter ranges. Even if the projectiles are shot with same velocities and with same angle with the horizontal, they have smaller range as compared to the ideal range
The projectile motion with the blue color is the ideal curve. While the black and the brown curves have increasingly high drag force behind them.(Barakat, 2007)
The projectile motion
To understand the motion of a body in projectile motion, the velocity of the body would have to be resolved into horizontal and vertical components. The projectile is thrown into air at a certain angle with respect to the horizontal direction. There is a constant pull of the gravitation of the earth, as a result it tends to be in the parabolic path .The figure in the above picture clearly illustrates this fact.
Even the extended complicated objects tend to be in following roughly the same trajectory.
The projectile motion may also depend on the height of the body in motion. If the projectile is thrown from cliff or a tall building the range of the projectile may decrease.
The two variants of major concern with projectile is that, it may have either larger range (or maximum horizontal distance travelled by the projectile before falling) , on the other hand if it has maximum height achieved.
Another important feature of the projectile is the time duration of its flight, before it comes to the ground.
The horizontal motion is given by the Newton’s formula as,
X(t)=Vx*t
While, the vertical motion is calculated as:
Y(t)=Vy*t-(1/2)gt^2
The vertical component of the velocity becomes zero as the object reaches its maximum height. This equation is required while calculating the maximum height. (Charles, 2008)
The angle also determines the range and the maximum height. There is actually a trade-off between the two factors. The maximum angle being the 90 degrees, when the distance traversed by the projectile is almost null in the horizontal direction. The other angles, being between (0-90) degrees, 45 degree angle from the horizontal ensure that object is thrown at maximum range.
So, in order that the object (projectile) is thrown at the farthest distance, the angle of the projectile from the horizontal should be 45 degrees.
Even the rockets carrying satellites, are launched into the sky at such an angle and that velocity, the range of the rocket is always greater than the view. As a result, the rocket keeps rotating round the Earth.
The Gravity
The gravity or the gravitational force is a very important factor affecting the flight of the object. So, let us have a brief look over the topic, in the next few pages.
The laws of gravitation are universal in nature, as it stems from the basic fact that there is a basic tendency of two objects, two attract each other. This tendency in turn, comes from the electrostatic nature of the objects. However, going into that many details would derail us from our main focus, so let’s look into the aspects of gravitation.
It was the laws of, Sir Isaac Newton that explained the planetary motions into details. On the basis of several experiments and mathematical conclusion, he reached to the Newton’s law of gravity, as the force between two point masses is directly dependent on the product of their masses; however the force between them is weakened by the distance between them. I order to correlate the results of experimental evidence and his law, Newton came up with a factor called the Newton’s constant G .If you separate two objects each of mass 1kg, by 1m of distance the objects would pull each other with a force equal to 6.67×10^(-11) N. This is the value of his constant.
This value may seem to be insignificant but is an important result that lets us predict, why the force is so strong enough to result in the large celestial bodies and the mysteries of Black hole. It should be also taken a note, that if there is a mighty force pulling a small ball towards the earth, the newton’s third law guaranties us the small ball also pulls the earth with the same amount of force. Seems unbelievable but true!
The gravitational force between two objects is a vector quantity like velocity, acceleration, and as any other force. So it has a direction along with a physical value. This is always in the direction towards the body for which we intend to calculate the force.(Julia,2009)
It has been always felt that a body with greater weight shall be falling faster than a lesser weight object, even true from the newton’s law, but Galileo demystified the misconception. He proved it experimentally that a coin and paper disc with same weight would be falling with same velocity if the experiment be conducted in vacuum. This was established that since, the mass of all the objects on planet earth are negligible compared to the later, the force is decided only by the earth.
Thus a new concept of gravitational acceleration (g) was coined .If calculated at different places on the earth the values of it would be calculated. The reason is again the electrostatic forces, again! However, 9.8m/s^(2) is a very largely accepted value. As you move away from the earth this force(gravitational) continues to become smaller, and in space new values of the force, would come to light.
Conclusion
The Study of the projectile suggests that the body follows a parabolic trajectory, as long as the air-drag acting on the body in motion is not considerable enough to act as an important factor deciding the range of the body. The body makes a nose-dive, as much the air drag factor comes into the figure. This decreases the range of the body in flight.
The dynamics of the lighter bodies are still different because of the buoyancy present in the air. This makes it keep floating in the air.
References
1. Claymore, viewed on 16th april 2012,Claymore.engineer.gvsu.edu
2. Barakat , N 2007,”Professional and Soft Skills for the Engineers”,Seattle.
3. Charles W. Misner & Kip S Thorne 2008, Gravitation
4. Steven (John Wiley & Sons) ,Gravitation and cosmology , Weinberg
5. Julian B. Barbour 2009, The Discovery of Dynamic .
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