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VEN1102 Engineering Physics 1

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VEN1102 Engineering Physics 1

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Course Code: VEN1102

University: Victoria University

MyAssignmentHelp.com is not sponsored or endorsed by this college or university

Country: Australia

Question:

1.Complete the following Assignment sheet filling in all sections.

2.Write your solution in Section 4, adding more pages as required. The page length of your solution should be reflective of the number of members in the team.

3.All steps in solving the problem must be clearly explained.

4.All formulas and physics concepts must be clearly explained.

5.Where applicable, errors and uncertainties must be included in measurements and calculations.

5.All sources of information must be properly acknowledged or referenced using either the Harvard, APA or IEEE referencing format.

6.Report must be type-written in proper English and not hand-written. Graphs created using plotting software such as MS Excel and must have correct axes and labels. Pages are numbered.

7.Report must be eligible and have no or little spelling/grammar errors.

8.This assignment will be subject to plagiarism checking. Penalties apply for plagiarism and collusion.

9.Submit your group assignment via the VU Collaborate Dropbox. Only one submission per team is required.

Write in your own words what you think the problem that needs solving is and how this can be achieved)

What do you know?

List everything that you know or understand about the problem. What facts are presented in the problem statement? What facts, or knowledge, do you already know about the problem or context in which the problem is set?

What do you need to know?

Determine what information/knowledge is needed in order to solve the problem. This may be information or data as well as physics concepts or other knowledge that may help to analyse or solve the problem. What assumptions are you making? Who will research what? The work should be shared equally amongst the team members. PBL is a group activity where students teach and learn from each other. This can only work when everyone in the team participates.

How did you solve the problem?

Answer:

Section 1: Problem statement

The problem we assumed understand is to measure the acceleration because of gravity by the utilization of a string and mass to make a pendulum. This issue is achievable just by doling out the group individuals to discover fundamental materials that will enable us to find out the best way to determine acceleration due gravity. We will concoct an exact examination to tackle the problem

.Section 2: What we know about the problem

Gravitational pull is the force that brings two bodies towards one another [1], the force that makes celestial bodies to orbit around the sun and also makes things to fall onto the ground level. However, if the object has a greater mass, it possess the strongest gravitational pull. Gravity is amongst the most important forces on earth. This is because it makes object to have weight. For example, when one goes to weigh themselves, the weighing scale tells us the amount of gravity on our bodies. To make this clear, one of the group members went to weigh his body weight and we found out the mass was 55 kilograms.

Isaac Newton built up this theory of universality gravitation in 1960s. The conclusion he made was that every matter was being acted upon by force of gravity. The attraction of every other object is proportional to the product of its masses and inversely proportional to the square of the distance apart. This can be shown as: whereby: is the gravitational pull, r is the apart distance of the objects, represents the two different masses and G represents the gravitational pull constant.

Therefore, gravitational acceleration is the acceleration of the body due to the influence of gravitational pull, denoted ‘g’ [2]. This value is very different for celestial bodies. An example is the acceleration due to gravity for the earth is different from that of the moon. In addition, acceleration possess direction and magnitude hence it is a vector quantity. The direction is towards the centre of earth while the average magnitude of the value g is 9.8 m/s2, which simply means that when an object is falling freely, it experiences that speed that increases every second.

Section 3: What we need to know to solve the problem

The data required in order to take care of the problem include;

Knowledge on gravitational acceleration.

Knowledge on simple pendulum experiment.

Materials needed to perform the experiment.

The correct method to conduct the experiment.

Using excel software to draw graphs.

How to best analyse the results

The work was separated similarly among three of us with the first individual from the group inquiring about on the acceleration due to gravity and inferring the conditions included. The second partner was to find how to perform the experiment by reading about the simple pendulum experiments and furthermore to decide the kind of materials required. Our third member in the group was to find out how to draw diagrams, the factors to be plotted and accompanied the most ideal method for breaking down the outcomes. At that point, as the group individuals we joined and did the analysis together.

All of the research was typed and compiled step by step. We derived the gravitational acceleration as shown. From Newton’s 2nd law of motion, whereby;

F is force acting upon the object

m represents the mass of the body

a is the acceleration

According to Newton’s Law of gravity, we can write the formula as;

Whereby:

Is the gravitational pull

Represents the two different masses

r is the distance apart of the two objects

G represents the gravitational pull constant

h is the height

This is the force of gravity acting on two bodies that are lying in the field of gravitational pull to each other [5]. The two bodies experience same force that is being directed to each other with the same magnitude. In order to find the acceleration due to gravity, we can comfortably use newton’s 2nd law; [4].

Here, the mass of the object is m, and the acceleration due to gravitational pull will be calculated.

When the object is near the surface, the value of the gravitational pull ‘g’ becomes a constant and it does not change [7].

Therefore we get; whereby;

G represents the gravitational pull constant

M is the mass of the objects

R is the distance apart of the masses

Materials needed

The materials needed were listed accordingly;

Stop watch to measure the oscillation time.

Meter rule.

A piece of string.

Metal mass.

The experiment was to be setup as shown by the diagram;

Assumption to be made

The chosen string was non-elastic.

If a metallic pendulum used, the experiment will generate accurate results.

The stand was stable.

Method

One of the group member connected the string to the pendulum and made sure that it was in a position to swing uninhibitedly without making contact.

We first used 40 cm length of the string to perform the experiment. Then, we used 60 cm progressively till 120 cm length of the string. The values accrued were recorded by on the table of results. An angle of 20 degrees was set and the string was released. Tallying the number of oscillations began when the string balanced out. Around 20 oscillations were estimated and the information recorded in the table. Progressive experiment were done in the same while alternating the group members.

The values were tabulated and completed calculations were made amicably.

A graph of independent variable L and dependent variable T² drawn on the x and y axes respectively.

The gradient of the graph was to be found by choosing at least two points within the line.

Precautions

We needed to make sure that the pendulum was released with no of us giving an outer push.

We needed to ensure the string was straight before releasing it.

Section 4: Solution

Results

The experiment was success since we were able to collect data of length with the time for the oscillations made. Results collected were recorded in the table shown below.

Length of string(cm)

Time(t1) (sec)

Time(t2) (sec)

40

25.2

25.1

60

31.0

31.0

80

35.99

36.0

100

40.12

40.14

120

43.98

43.78

The averages of the time for the 20 oscillation were aver aged and tabled. Also the period time was found by squaring the average times collected and recorded in the table.

Length (m)

T1 (sec)

T2 (sec)

Average T

Time for 1 oscillation (sec)

T2

0.40

25.2

25.1

25.2

1.26

1.59

0.60

31.0

31.0

31.0

1.55

2.40

0.80

35.99

36.0

36.0

1.80

3.23

1.00

40.12

40.14

40.2

2.01

4.03

1.20

43.98

43.78

43.8

2.19

4.80

From our table, a graph a graph of the independent variable length in metres was plotted against the dependent variable which in our case is the squared average time of the oscillations. The graph is as shown below

From the graph the gradient can be plotted.

Taking the coordinates (0.4, 1.59) and (1, 4.03)

Therefore, gradient = (4.03-1.59) / (1.0-0.4)

= 4.06

To find the period (T) of the pendulum with its length L is: whereby;

T represents periodic time

is a constant pie of 3.1428

L is the length of the pendulum string

g is the gravitational pull in our case is the slope

Squaring both sides of the equation we get: [3].

From this last equation, we can recall the general equation for a straight line graph. From the straight line graph, m represents the slope of the straight line and with our case, the line passes through the origin (0, 0). Therefore the value of c is 0.

Substituting the terms from the line graph of the pendulum equation which has passed through the origin to since the constant c passes the origin if the straight line is extrapolated further.

One of the group members calculated and it can be shown clearly below;

Slope of the graph = 4.06

L of the pendulum = 4.0

But, slope =

Therefore, g =

= (4 * 3.1428²) / 4.06

g = 9.73 m/sec²

Therefore, 9.73 m/sec² was the gravitational acceleration found.

Error calculation

It is evident from calculation that, there is a slight deviation from the known average value of acceleration due to gravity which is at 9.8 m/sec². We went ahead and our group member suggested to show us how to find the error percentage since already had the theoretical value of acceleration due to gravity and the experimental result which was 9.73 m/sec².

Percentage error = (experimental value – known value) known value * 100%

From our analysis, % error = (9.73 – 9.8) m/sec²

Error = -0.07 m/sec²

= -0.07 m/sec² / 9.8 m/sec²

= 0.007

% error = 0.007 * 100

= 0.7%

Therefore, the percentage error was found to be 0.7%. This is a small error which might b=have been caused during the experiment.

Possible sources of errors

Limiting air friction might have limited the accuracy from the swinging point[6].

One of the members might have given a slight push to the ball since everyone had to participate in the experiment.

Reaction time from the members might have caused errors.

Rotation of the ball due to the effect of revolution of the earth. This might have caused disturbances to the measures of counting the oscillations.

Conclusion

The estimation of the acceleration due to gravity was accomplished effectively fulfilling the problem statement of research. We found the acceleration due to gravity to be 9.73 m/sec² which veered off from the known value with a rate blunder of 0.7%. Thinking about the levels of error, high precision values will be obtained by limiting the response time. More so, the quantity of oscillations will be increased keeping in mind the end goal to decrease the errors due to timing [8].

References

[1]T. Ghose, “What Is Gravity?”, Live Science, 2018. [Online]. Available: https://www.livescience.com/37115-what-is-gravity.html. [Accessed: 05- Oct- 2018].

[2]S. AbdElazem and W. Al-Basheer, “Measuring the acceleration due to gravity using an IR transceiver”, European Journal of Physics, vol. 36, no. 4, p. 4, 2015.

[3]H. Parks and J. Faller, “Simple Pendulum Determination of the Gravitational Constant”, Physical Review Letters, vol. 105, no. 11, p. 15, 2010.

[4]M. Jewess, “Optimising the acceleration due to gravity on a planet’s surface”, The Mathematical Gazette, vol. 94, no. 530, pp. 35=37, 2010.

[5]J. Cutnell and K. Johnson, Introduction to physics. London: John Wiley & Sons, 2010, pp. 102,110.

[6]B. Solomon, “Gravitational acceleration without mass and noninertia fields”, Physics Essays, vol. 24, no. 3, pp. 327-337, 2011.

[7]”Acceleration of Gravity”, Physicsclassroom.com, 2018. [Online]. Available: https://www.physicsclassroom.com/class/1DKin/Lesson-5/Acceleration-of-Gravity. [Accessed: 06- Oct- 2018].

[8]Nano-optics.colorado.edu, 2018. [Online]. Available: https://nano-optics.colorado.edu/fileadmin/Teaching/phys1140/lab_manuals/LabManualM1.pdf. [Accessed: 06- Oct- 2018].

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