Recent orders
TO INVESTIGATE THE WORK ENERGY THEOREM
TO INVESTIGATE THE WORK ENERGY THEOREM
STUDENT NAME
STUDENT NUMBER
Table of Contents
TOC o “1-3” h z u Objectives PAGEREF _Toc24617942 h 3Apparatus PAGEREF _Toc24617943 h 3Theory PAGEREF _Toc24617944 h 3Set up PAGEREF _Toc24617945 h 4Procedure PAGEREF _Toc24617946 h 5Data and Observation PAGEREF _Toc24617947 h 6Calculations PAGEREF _Toc24617948 h 7Results PAGEREF _Toc24617949 h 8Conclusion PAGEREF _Toc24617950 h 10References PAGEREF _Toc24617951 h 11
TO INVESTIGATE THE WORK ENERGY THEOREM
ObjectivesTo investigate the work energy theorem
To investigate Hooke’s law
ApparatusQuantity Equipment Part- Number
1 Motion sensor PS 2103A
1 Hi res force sensor PS-2189
1 Dynamic system ME-6955
1 Elastic bumper ME-8998
1 Elastic cord (in ME 8998)
1 Force bracket CL-6545
1 Braided string SE-8050
1 Balance scale SE-8723
TheoryThe resulting change in the kinetic energy of a body is equal to the work done to the body. This is known as the Work-energy theorem and it can be expressed as;
∆KE=work, this can be derived as W=12mvf2-12mvi2The work done by the sum of all forces acting on a particle equals to the change of the kinetic energy of the particle. It can be extended to the work done on rigid bodies.
The work energy theorem can be derived from Newton’s second law. Work transfers energy from one place to another or from one form to another. In general systems, work can change the potential energy of a mechanical object, electrical energy of an electrical device or heat energy of a thermal object.
Set upThe elastic bumper and the adjustable feet were installed on the track as shown in the figure below.
The force sensor was attached to the track by use of the bracket. The force sensor was attached to the interface and the zero button was pressed to tare the object. The motion sensor was attached and plugged to the interface. The range switch was placed on the cart icon.
Both masses were placed on the cart and the balance was used to measure their masses.
The level of the track was adjusted using adjustable feet. The cart was placed on the track and a small push was given to it away from the motion sensor. The record button was clicked to record the motion.
The level of the track was adjusted using the screw feet so that the cart moved at a constant speed as it moved from the motion sensor. The track was levelled slihtly downhill so as to eleiminate the effects of frictional forces. A short loop of string was tied to the lower tab in the PAScar as shown. A 35 cm long piece of elastic cord was cut between the sensor hook and the loop of string.
ProcedureThe cart was pulled back until stretching the elastic cord until the cart was 20 cm from the sensor. The motion sensor is placed to measure the force on the end of the cart so the hand was placed on the middle and not the end of the cart. The record button was placed and the cart was released.
When the force applied was not positive the data summary was opened and properties icon was pressed for the force sensor and the sign icon was clicked.
The velocity data was checked so that it was smooth. The maximum velocity was to be clearly seen before the motion stopped. One good run was obtained and it was remained two masses. One of the masses was removed from the cart and it was renamed one mass. The masses selection tool was used to display the run for the two masses.
The graph obtained indicated the force against the position which is hook’s law. This is a graph of F against x and it’s a straight line.
The area tool was used to find the area under the graph. The procedure was repeated for the second run.
The run selection tool was used to display the run for the two masses. The maximum velocity of the cart was obtained. The velocity and the cart of the mass were used to calculate the kinetic energy of the cart. This was compared to the elastic cord.
The procedure was repeated for the second run with the masses changed.
Data and ObservationForce for the two masses against time
Time 0 0.1 0.2 0.3 0.4 0.5
Force Mass1 0.0 0.5 1.0 1.5 2.0 2.5
Force Mass2 0.5 1.0 1.5 2.0 2.5 3.0
Velocity of the two masses against time
Time(s) 0 0.1 0.2 0.3 0.4 0.5
Velocity Mass1(m/s) 0.0 0.4 0.9 1.4 1.7 2.0
Velocity Mass 2(m/s) 0.9 1.2 1.4 1.8 2 2.3
Work done by the elastic cord
Time(s) 0 0.15 0.2 0.25 0.3 0.35 0.40
Work done 0 0.5 0.9 1.2 1.5 1.75 1.90
Kinetic energy of the cart
Position (m) 0.1 0.2 0.3 0.4 0.5
Velocity 0.4 0.8 1.1 1.3 1.6
CalculationsVelocity for two masses,
V = 1.36m/s
for the two masses, velocity=1.36ms,W=12mvf2=12×0.754×1.36ms2=1.7J, W=0.307JVelocity for one mass,
V = 1.56m/s
W=12mvf2=12×0.754×1.56ms2=0.917J, W=0.966N/mResultsForce for the two masses against time
Velocity of the two masses against time
Work done by the elastic cord
Kinetic energy of the cart
ConclusionFrom the results obtained from the two exercises, investigating the effect of force on the two masses on the cart and by using the elastic cord, the variation of the kinetic energy of the cart was observed. With variation in the time, the velocity of the cart and the masses increased. In investigating the effect of Hooke’s law, the force applied to the mass attached to the elastic cord was proportional to the displacement of the body. This was evidently expressed graphically from the graph drawn. It was hence observed that the Work Energy Theorem was practically exhibited. The work done by the sum of the forces that were acting on the cart mass was equal to the change in the kinetic energy of the masses.
References BIBLIOGRAPHY Khan. (2010, may). Work energy . Retrieved from Khan Academy.
learning, L. (n.d.). Work Energy theorem. Retrieved from lumenlearning.com: https://courses.lumenlearning.com/boundless-physics/chapter/work-energy-theorem
To Investigate The Relationship Between Force And Acceleration.
TO INVESTIGATE THE RELATIONSHIP BETWEEN FORCE AND ACCELERATION
COURSE CODE
STUDENTS NAME
DATE
Contents
TOC o “1-3” h z u Objectives of the study PAGEREF _Toc23488808 h 3Apparatus PAGEREF _Toc23488809 h 3Theory PAGEREF _Toc23488810 h 4Setup PAGEREF _Toc23488811 h 4Procedure PAGEREF _Toc23488812 h 6Analysis PAGEREF _Toc23488813 h 6Conclusion PAGEREF _Toc23488814 h 11
To Investigate The Relationship Between Force And Acceleration.
Objectives of the studyTo determine the relationship between force and acceleration for a cart mass with different masses.
Determine the variation in acceleration with an increase in force applied for a cart mass with different masses.
ApparatusQuantity Equipment Part number
1 Compact cart mass ME-6755
1 Motion Sensor PS-2103A
1 Force sensor PS-2189
1 Dynamics system ME-6955
1 Balance SE-8723
1 Braided spring SE-8050
1 Mass and hanger set ME-8979
1 Compact Cart mass ME-6755
1 Pulley (part of the CI 6691) ME-9448B
Theory
When a force is applied on a body at rest, it results to a change in its existing state. And when the force is applied on a moving body with uniform velocity, it would result to an acceleration of the body. This exhibits the principle of Newton’s second law of motion. This law states that, “the rate of change of momentum is proportional to the imposed force and goes in the direction of the force.”
SetupThe setup was set as shown in the figure below.
The motion sensor was connected to the interface and attached to the track. The alignment knob was attached to the side of the motion sensor so that it pointed parallel to the track. The switch on the top of the motion sensor was set to cart.
The force sensor was connected to the interface.
The long thumbscrew was used to attach the force sensor to the cart. The Cart/Force assembly was placed on the track.
The pulley was connected to the upper set of holes. The pulley was clamped to the end of the track and placed at the end of the track.
The adjustable feet was placed on both ends of the track to make the track level. A spirit level could be used in this case.
A loop was tied to the end of a one meter string. A mass was hanged on the hanger of the loop. 15g was added to the hanger and a total of 20g. A loop was tied to the other end and it was attached to a force sensor. The mass was hanged over the pulley.
The string was levelled by adjusting the pulley
ProcedureThe string was removed from the force sensor hook and the zero button pressed on the force sensor. The string was then replaced.
The cart was pulled backwards as far as possible without allowing the mass hanger to contact the pulley. The record button was clicked and the cart released.
The force sensor cord was restricted so as not to impede the motion of the cart. This was done by holding the cord at least 30cm above the cart and hand kept directly above the cart as it moves so that the cord did not push or pull the cart.
The STOP button was clicked after the cart stroke the end point. When noise spikes were seen in the velocity data, the angle of the motion sensor was adjusted and all objects moved away from the track.
When a good run was obtained, the data summary was obtained in the left tool palette.
10g was added to the cart and the procedure above was repeated.
The process was repeated for 40g ,50g and 60g
AnalysisThe run select tool was clicked in the graph and 10 g selected.
The statistics tool on the graph was turned on displaying the mean value on the graph. The selection tool was used to restrict the range in which the average value is restricted.
The force values were recorded in the table.
The procedure was repeated for the other values.
F(N)
1 2 3 4 The run select tool was clicked and 10g selected.
A linear curve was selected and the selection tool used to restrict the range.
Acceleration was recorded in the table below.
a (m/s2)
1 2 3 4 The procedure was repeated for the other values.
The graph shows the table values of the applied force and resulting acceleration.
A linear curve fit was selected and the slope determined.
Results and observations
The data was recorded in the tables below.
Force values
F(N)
1 -0.189
2 -0.370
3 -0.453
4 -0.537
A graph of force against time was plotted below.
The acceleration values
a(m/s2)
1 0.481
2 0.837
3 1.170
4 1.240
A graph of acceleration against time was recorded below
From the results, a relationship between the applied force and acceleration was obtained.
F=maWhere F – force
M – the mass
a – acceleration
Conclusion
The relationship between force and acceleration for a cart mass with different masses was found to be directly proportional. Thus an increase in mass lead to an increase in the force.
The source of error in the experiment could come from the instruments used. The certainty of the results largely depends on the accuracy of the precision of the apparatus. These errors could come in the measurements when the time, length and the mass of the variables are measured. This error can be limited by doing multiple experiments and getting the average of the results. In doing similar experiments the use of stopwatches to measure the acceleration time within a given distance is encouraged while motion sensors can be used when plotting the graph of velocity against time.
The Evolutionary Step In Communication
The Evolutionary Step In CommunicationThe earliest forms of art were naturalistic, or in other words, a “cave man”, an upper Paleolithic Homeo Sapien- Sapien, found an existing shape in his “ sacred space”, saw the similarities between that and of an animal, like a bison, and decided to trace around it in ochre. Hence the recognition of a shape and the literal transformation of something real into a picture to convey a message to the collective.After this, the identification, the idea of making an image evolved to something more of a document. For example, later cave paintings are not of the naturalistic form, but rather formalized animal drawings (Cooke, 15). Rather than seeing a pre-existing form, man is creating from his imagination, not literally creating something, but the idea being lent from the indigenous animals of the region, of course not limited to animals, but primarily concentrated on (Coke, 105). Showing us that man was trying, or was indeed, comunicating through the use of images.
I know I am leaving out other steps in the evolution of this idea, but it is clearly too broad of an investigation, if I were to go in that direction. None of my instances are to be examined in one place. They are a collective evaluation of the start of communication and how the man who gave birth to this idea of an image, interprets it as a phenomena of some greater deity. The very first cave paintings represent the first existence of the modern day man, in terms of thinking (Bataille, 12). The homeo- sapiean- sapiean was very similar to the modern day man. In the upper Paleolithic time period, man lived in an unconscious state, but was not with out understanding, he perceived his environment in a naïve manner (Lommel, 12). When creating something as revolutionary such as a representation of something in reality, he feels a vigor and freshness. Meaning, this new idea of drawing, is subject to interpretation. The interpretation of use and the interpretation of its creation.
The modern, or most common interpretation of “the use”, is the idea of religious icons for the purpose of representing deities, whether they be animals, humans or both (Bataille, 35). I have no evidence to disagree with that basic, common interpretation. Yet, for some reason I am unsatisfied with this level of understanding. Of course there are unlimited possibilities and evidence to support all of them substantially, so I try here not to make this some personal philosophical inquiry. But, rather to prove my point, that the cave paintings were the enlightening event that created the human mind, not to say this has not been stated before. I was generally disappointed when doing the research to discover that most pre-historians actually believe the idea that the cave paintings were religious symbols.They were not symbols, but rather the identification of an entity, as to communicate to another being, “ hey look, this looks like this thing”. Then after they all agreed, it became practiced. As a counter argument, one could ask, why were they only found in the caves, “the sacred space”, where the dead were buried and the shaman practiced or some say, lived there, if it was to communicate to the collective? Well, as to a lack of a better devise to prove my point, I would reply to the questioning by explaining the brilliance and majesty of a pictorial representation of something. Especially if the cave made it for them. I could also say that is why the cave was sacred to them, because of these images they saw. Nevertheless, not to speculate too much, after the evolution of these communicative ideas, we see them turn to something different, a symbol or an icon. Used freely, not restricted to areas that already have a pre-existing shape.
This practice is limited to the shaman, because he or she is the only one who spends their time in the caves. So, to the villagers, this drawing thing is something of a wonder. It has to be something of a spiritual nature, to them, it is something never seen or thought of before. Perhaps they thought that since their sacred space was making images of animals, that the animals had some sort of spiritual over rule, leading them to be animists. However that might be or not, they had still created the first step in the evolution of communication, through drawing. Many, or all cultures, picked up characteristics from this time period. The Egyptian hieroglyphic characters, Persian cuneiform, all share the same pictorial elements. The actual reference to an object was expressed through visually representing that object, but of course it progressed into a more diversified skill, with more complicated drawings, with a more specific meaning. The “cave men” were not aware of the monumental technology that they had discovered, and we as interpreters of their creation greatly discard the most logical explanation and seem to run a little far with our speculations. It is truly a phenomenon of how we have evolved from that to present day.
Bibliography
1. Pedro A. Saura Ramos The Cave of Altaira. Harry Abrams,Inc.,Spain; 1999.
2. Budge, E.A. Walls. An Egyptian Hieroglyphic Dictionary. Dover, New York; 1978.
3. Baring, Anne. The Myth of The Goddess. London, Great Britain; 1993.
4. Bataille, Georges. Lascaux or The Birth of Art.Skira, Switzerland; 1976.
5. Lee, D.N.. Art on the Rocks of Southern Africa. Purnell, London; 1970.
6. Lommel, Andreas. Prehistoric and Primitive Man. McGraw Book Co., Neherlands; 1966.
7. Cooke, C.K. Rock Art of Southern Africa. Africa, Books of Africa; 1969.