Uniformly Accelerated Motion Lab Conclusion Essay
PHYSICS DEPARTMENT
PHYS 101 LABORATORY
EXPERIMENT #1:
“KINEMATICS OF HORIZONTAL MOTION”
Prepared by: [Name & Surname, Student No, Department]
Lab Assistant: [Assistant’s Name & Surname]
Experiment Date: [Date]
Lab Group: [Group Name]
Partner: [Name & Surname of the Partner]
INTRODUCTION
The main objective of this experiment is to investigate the relationship between the position, velocity and aceleration of an object, moving in one dimension, along a straight line. The experiment will be carried out under two different circumstances:
(1) a condition with a close approximation to ideal frictionless motion (in other words the is no force acting on the object ideally), and
(2) when a constant force is introduced (gravitational force is acting on the object).
THEORY
Acceleration is the rate of change of an object’s velocity with time. For an object with velocities of v_{1} at time t_{1} and v_{2} at time t_{2}, the average acceleration in the time interval (t_{2}-t_{1}) can be calculated using the below formula:
_{}(1)
If the instantaneous acceleration of the object is constant between t_{2} and t_{1}, the average velocity can be found as follows:
_{}(2)
And if the positions x_{1} and x_{2} of the object, at times t_{1} and t_{2} respectively are known, the average velocity also can be written as:
_{}(3)
Equating equations (2) and (3) above:
_{}(4)
Solving equation (1) for (t_{2}-t_{1}) and substituting the value into equation (4):
_{}(5a)
_{}(5b)
where, Δ means “change in”.
Values measured in the experiment are given with some amount of experimental error, denoted by_{}, where x_{m} is the value measured in the experiment and Δx is the experimental error. Experimental error can be calculated as follows:
_{}(6)
where _{}is the average of the values measured, x_{i} is the value of each measurement and n is the number of measurements.
EXPERIMENT
SETUP
The experimental setup is composed of the following:
(1) a Macintosh computer,
(2) a signal interface,
(3) two photogates,
(4) a picket fence,
(5) a small card and
(6) an ideally frictionless metal track.
PROCEDURE
The velocity of the object, moving on a horizontal plane, is to be measured in the first part of the experiment. In order to do this, the ideally frictionless metal track is placed on the table straightly, so that there is no slope between the table and the track. Then the two photogates are arranged, initially overhanging 20 cm apart as shown in figure (1).
Figure (1) Arrangement of the Photogates
Next, the picket fence is to be placed on the cart and it is checked whether the photogates are analyzing the cart or not by pushing it on the track. After plugging the wires of the photogates into the digital channels 1 and 2, which are on the digital panel of the signal interface as shown in figure (2). And the interface is turned on by means of the switch at its back.
Figure (2) Wire Connections to the Signal Interface
The computer is turned on by pressing the large button on top of the keyboard and the “Science Workshop” program started running automatically. A new file is opened selecting ”New” under the “File” menu and photogate connections are prepared by carrying the “sensor” logo on the “digital channel 1” and “digital channel 2” icons and selecting the “picket fence-photogate”. Then “opaque spacing” is changed settled to 0.01 m by clicking on the “channel 1” and “channel 2” logos. Doing these, the small cart is established on the metal track thus the setup became ready for taking data. By clicking “REC”, and pushing the cart lightly at the same instant, the cart started its motion. After it passed under the second photogate, “STOP” is clicked and data labeled as “Run #1” is obtained. In order to get the result, “Run #1” is marked and “Table” logo is carried over to “channel 1” to have velocities v_{1}. Finally, it is checked whether there are 12 data points or not. This step is repeated for “channel 2” for velocities v_{2} and the whole procedure is repeated twice more for recording data “Run #2” and “Run #3” similarly.
DATA ANALYSIS
SAMPLE CALCULATIONS
Data obtained during Run #1 are tabulated in table (1).
v_{1 }(m/s) | t_{1} (s) | v_{2} (m/s) | t_{2} (m/s) | |
Run #1 | 0.518 | 2.9381 | 0.505 | 3.3132 |
Table (1)
Sample Calculations for Run #1 are as follows:
Δx = 0.2 m (the separation between the photogates)
Δt = t_{2}-t_{1} = 3.3132-2.9381 = 0.375 s
_{}v_{av}^{a}=0.5332 m/s
v_{1+}v_{2} = 0.518+0.505 = 1.023 m/s
_{}v_{av}^{b}=0.5115 m/s
Δv = v_{2}-v_{1} = 0.505-0.518 = -0.013 m/s
_{}a = -0.0346 m/s^{2}
TABLES
Data obtained during the experiment is tabulated in Table (2).
Run # | v_{1 }(m/s) | t_{1} (s) | v_{2} (m/s) | t_{2} (m/s) | _{}(m/s) | _{}(m/s) | Dv=v_{2}-v_{1} (m/s) | Dt=t_{2}-t_{1} (m/s) | a=Dv/Dt (m/s^{2}) |
1 | 0.518 | 2.9381 | 0.505 | 3.3132 | 0.5332 | 0.5115 | -0.013 | 0.3751 | -0.0346 |
2 | 0.654 | 2.7432 | 0.641 | 3.0386 | 0.6770 | 0.6475 | -0.013 | 0.2954 | -0.0440 |
3 | 0.461 | 2.1295 | 0.444 | 2.5540 | 0.4711 | 0.4525 | -0.017 | 0.4245 | -0.0400 |
_{}
Table (2)
DISCUSSION
QUESTIONS & ANSWERS
(1) After giving a slight push to the cart, what sort of a motion would you expect from the cart on an ideal frictionless horizontal track? Explain.
The cart is expected to reach a constant velocity and then continue moving at the same speed along the same direction from then on. The average velocity of the cart is will be equal to the instant velocity and the acceleration will be zero since there is no force acting on the cart during its motion on the ideal frictionless track.
(2) Considering that friction exists in reality between the cart and the track, what deviations would you expect from your answer to question 1?
In fact there exists friction between cart and the track.As a result, the motion does not happen as expected.The velocity of the cart decreases after being pushed since friction acts negatively on the cart.v_{2} is then smaller than v_{1} and the cart has a negative instant acceleration because ideal friction is constant on the metal track.
(3) Compare v_{ave}^{a }and v_{ave}^{b}. Do you expect that they will be equal? Explain.
v_{ave}^{a }and v_{ave}^{b} are expected to be equal since the acceleration should be constant during the experiment.As we know, v_{ave}^{a} can be equal to average velocity only if acceleration is constant during the motion because the area under graph of velocity in velocity and time graph of inconstant accelerating motion is not equal to the area under graph of velocity in the velocity and time graph of constant accelerating motion.
(4) Do your results confirm your predictions in questions 1-3? Comment on possible results.
Results do not confirm the predictions completely.For instance, v_{ave}^{a} was supposed to be equal to v_{ave}^{b}, however they did not come out to be equal since the acceleration was not constant.Also the environment can not be idealized due to the inconstant friction between the track and the cart, the air resistance acting on the cart or the rotation of the earth around itself. Additionally experimental errors may rise during the experiment such as, small measuring errors.
(5) Comment on the sign of a.
The sign of acceleration came out to be negative for all 3 runs, meaning that the cart is slowing during its motion. Acceleration in positive direction means that the object is accelerating in the direction of motion or slowing down opposite to the direction of motion at that time.Acceleration in negative direction means that object is slowing down in the direction of motion or accelerating opposite to the direction of motion.
CONCLUSIONS
During the experiment, the relationship between the position, velocity and acceleration of an object, moving in one dimension, along a straight line is investigated. The experiment was carried out under a condition with a close approximation to ideal frictionless motion (in other words there is no force acting on the object ideally), and when a constant force is introduced (gravitational force is acting on the object).
Initial and final velocities of the cart in certain time intervals are measured for 3 different runs. And using the data obtained ,the average velocity of the cart is calculated using two different ways, using equations (2) and (3) mentioned in the theory part. The results obtained were expected to be equal to each other. However they came out to be different since there exists friction between the cart and the track in fact in the real case.
Finally the acceleration of the cart is calculated and found out to be negative, meaning that the cart is slowing down in the positive direction of motion. This acceleration is introduced since the metal track, which assumed to be ideal, is not frictionless in fact and the force acting on the cart is not zero as a consequence.
The results obtained in the experiment are reasonable but there may be errors due to the misreading of data or inaccuracies in measurements.
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