Uniformly Accelerated Motion Lab Conclusion Essay

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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 v1 at time t1 and v2 at time t2, the average acceleration in the time interval (t2-t1) can be calculated using the below formula:

(1)

If the instantaneous acceleration of the object is constant between t2 and t1, the average velocity can be found as follows:

(2)

And if the positions x1 and x2 of the object, at times t1 and t2 respectively are known, the average velocity also can be written as:

(3)

Equating equations (2) and (3) above:

(4)

Solving equation (1) for (t2-t1) 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 xm 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, xi 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 v1. Finally, it is checked whether there are 12 data points or not. This step is repeated for “channel 2” for velocities v2 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).

v1 (m/s)

t1 (s)

v2 (m/s)

t2 (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 = t2-t1 = 3.3132-2.9381 = 0.375 s

vava=0.5332 m/s

v1+v2 = 0.518+0.505 = 1.023 m/s

vavb=0.5115 m/s

Δv = v2-v1 = 0.505-0.518 = -0.013 m/s

a = -0.0346 m/s2

TABLES

Data obtained during the experiment is tabulated in Table (2).

Run #

v1 (m/s)

t1

(s)

v2

(m/s)

t2

(m/s)

(m/s)

(m/s)

Dv=v2-v1

(m/s)

Dt=t2-t1

(m/s)

a=Dv/Dt

(m/s2)

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.v2 is then smaller than v1 and the cart has a negative instant acceleration because ideal friction is constant on the metal track.

(3)   Compare vavea and vaveb. Do you expect that they will be equal? Explain.

vavea and vaveb are expected to be equal since the acceleration should be constant during the experiment.As we know, vavea 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, vavea was supposed to be equal to vaveb, 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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