2016.5.8.Sunday

9P Seohyun Lee

Gravity Lab Investigation

Aim: To investigate the value of the acceleration due to the gravitational force on Earth.

Research Question / Rationale

How does the different heights affect the time in relation to the acceleration due to the gravitational force on Earth?

It is related to our lives, because the gravitational force affects all the existing objects and human on the Earth. By understanding and showing how the gravitational force and acceleration works on us, we can understand how our environment is existed and related with the invisible force.

Hypothesis: If I drop the tennis ball to the ground in different heights, the higher heights will take more time than the lower heights. However, the acceleration of the droppings in the different heights will be same, because the acceleration force of the ball is the same as the gravitational acceleration on the surface of the Earth regardless of the height. There is the standard acceleration rate due to the gravity and it is -9.8m/s2.

Variables:

Independent Variable / Dependent Variable
Height (m) / Time (sec)
I will drop the tennis ball in different heights. The range of my independent variable is from 0m to 2.4m and I will measure my independent variable in every 0.6m, which are 0.6m, 1.2m, 1.8m and 2.4m. / I will measure the time taken from right after the ball is released from my hand to the moment when the ball meets the ground by using stopwatch.
Controlled Variables
Weight of the tennis ball (g) / I will grab 1 tennis ball and measure the gram of the tennis ball. I will use that tennis ball for all experiments. The tennis ball is 55.15g.
The place that we conduct the experiment / I will do the experiment in the science class.
Same person drops the ball / I will make the same person to drop the ball and measure the time taken, as that person knows well when they will release the ball from their hands.
Unit of the dependent variable / I will use the same unit, which is the second for the time measurement.

Prediction of the graph:

I will create 3 graphs, which are Position Vs. Time, Velocity Vs. Time, and Acceleration Vs. Time for my experiment. For the graph of Position Vs. Time, my independent variable is position and dependent variable is the time. This graph will show increasing tendency because as the position is higher, the time taken for the ball meeting the ground will be longer. For the graph of Velocity Vs. Time, the independent variable is the velocity and the dependent variable is the time. This graph will show the increasing tendency because the velocity will be increased as the time taken for the ball meeting the ground takes longer. Lastly for the graph of Acceleration Vs. Time, the independent variable is the acceleration and the dependent variable is the time. The graph will shows the constant tendency, as the acceleration remains equal regardless of the time.

Materials needed:

-  1M meter sticks

-  Masking Tape

-  Marker

-  Tennis Ball

-  Stop watch

-  Electronic scale (balance)

-  Chair

Procedure:

1.  Set up the materials that are needed for the experiments.

2.  Measure the height of 0.6m, 1.2m, 1.8m, and 2.4m on the wall.

3.  Label the heights on the wall.

4.  Drop the ball 5 times for each height and measure the time using the stopwatch.

5.  Take the data table for each different height.

Data Table:

Different Heights (m) Vs. Time (sec)
/ 0.6m / 1.2m / 1.8m / 2.4m
Trial 1 / 0.35 / 0.51 / 0.6 / 0.71
Trial 2 / 0.35 / 0.49 / 0.62 / 0.73
Trial 3 / 0.36 / 0.5 / 0.6 / 0.71
Trial 4 / 0.36 / 0.52 / 0.63 / 0.7
Trial 5 / 0.35 / 0.49 / 0.62 / 0.7

Processed Data Table:

Different Heights (m) Vs. Average time taken(sec)
/ Average / Calculation
0.6m / 0.354s / Average time taken = 0.35+0.35+0.36+0.36+0.355
Average time taken = 0.354s
1.2m / 0.502s / Average time taken = 0.51+0.49+0.5+0.52+0.495
Average time taken = 0.502s
1.8m / 0.614s / Average time taken = 0.6+0.62+0.6+0.63+0.625
Average time taken = 0.614s
2.4m / 0.71s / Average time taken = 0.71+0.73+0.71+0.7+0.75
Average time taken = 0.71s
Different Heights (m) Vs. Acceleration (m/s2)
/ Average / Calculation
0.6m / 9.576m/s2 / V= 2dt-u a= v-ut
V= 2(0.6m)0.354s-0m/s a= 3.39m/s-0m/s0.354s
V=3.39m/s- 0m/s a= 9.576m/s2
V= 3.39m/s
1.2m / 9.52m/s2 / a= 4.78m/s-0m/s0.502s
a= 9.52m/s2
1.8m / 9.55m/s2 / a=5.863m/s-0m/s0.614s
a= 9.55m/s2
2.4m / 9.52m/s2 / a= 6.76m/s-0m/s0.71s
a= 9.52m/s2

Graph:

This is an additional graph for the change in velocity. The reason why I create this change in velocity graph is that I used change in velocity when I calculate the acceleration.

Conclusion:

According to the generated data, I calculated the acceleration speed by the basic formula of acceleration; a= v-ut. When I dropped the ball in 2.4m, the average time taken for the ball meeting the ground was 0.71s. In this case, the acceleration is 9.52m/s2. When I dropped the ball in 1.8m, the average time taken was 0.612s and the acceleration was 9.55m/s2. When I dropped the ball in 1.2m, the average time taken was 0.502s and the acceleration was 9.52m/s2. Lastly, when I dropped the ball in 0.6m, the average time taken was 0.354s and the acceleration was 9.576m/s2. Overall, as the height of the dropping position is increased, the time taken was also increased, so the graph showed the ascending curved line. The average rate of the acceleration for each experiment was between 9.5m/s2 and 9.6m/s2, thus the graph showed the constant line of best fit. Lastly, the velocity is increased as the time taken for the ball meeting the ground took longer. So, the graph showed the increasing tendency even though there were slight changes in the actual speed, which was 0.695m/s.

As a conclusion, the data that I collected from the experiment mostly supported my hypothesis but there is some part that did not support my hypothesis, which is the acceleration. The data proved my first hypothesis that if I dropped the tennis ball in the higher heights, it took longer time to meet the ground. However, my prediction for the acceleration was not supported by the data, because I predicted the acceleration rate for each experiment would be same, which is -9.8m/s2. But my data showed that the accelerations for the experiments were between -9.5m/s2 and -9.6m/s2. To analyze and prove why my result came out different with the standard gravitational force rate, I conducted some researches on the factors that change the gravitational force on Earth.

There are three major factors that change the gravitational force depending on where it is measured; Latitude, Longitude and Altitude. Jeju Island is the place that I conducted the experiments and Jeju Island is located in 33.489°N in latitude and 126.4983°E in longitude on Earth. As the place measured the standard gravitational force is different from where Jeju Island is located on Earth that could change the results. This is because the Earth is not a perfect sphere; rather the Earth is more like ellipse-like shape. Thus, the distance between the center of the Earth and the surface the Earth is different according to the position. To be more specific, the radius of the place that the standard gravitational force is measured is different from the radius of the place that I measured the gravitational force. Thus even if I measured the gravitational force on the surface of the Earth, there inevitably are differences between my results compared to the standard gravitational force. In addition to that, the altitude also changes the gravitational force that as the distance from the center of the Earth increases, the altitude increases. This means that the geology of the surface of the Earth changes the altitude that affects the gravitational force, because as the total distance of the radius with the altitude increases, the gravitational force decreases. In this respect, my results from the data could be accurate in relation to the place on the Earth, where the gravitational acceleration in Jeju Island and other countries could be different.

In addition to that, Newton’s 2nd law is “F=ma”, which means “m” is the mass of the object and “a” is the gravitational acceleration. This formula calculates the total force by multiplying ‘m’ and ‘a’ and it is considered the net force of an object. If I conduct the same experiments on the assumption of using the same ball in other region or other country, where there are different radius and altitude, then the total force of the ball could be different because the gravitational acceleration is slightly different according to the position on the Earth.

In conclusion, my hypothesis is proven to be invalid through my experiments and the researches. Through the research, I learned that the gravitational force would be different depending on the longitude, latitude and altitude. Because as the Earth is not a perfect sphere shape, the distance between the center of the Earth and the surface of the Earth would be different according to the position, meaning that the gravitational acceleration will be different depending on the place and the altitude of dropping the ball. Therefore, my hypothesis was not supported by the results of the experiment I conducted and it proves that my hypothesis is not valid.

Evaluation:

There might be some mistakes even though I did the experiments several trials and collected the valid data for accuracy. However, there were some difficulties that I cannot control even though my method was valid. First, although the same person dropped the ball and measured the time with stopwatch at the same time, the ability of the person to react could not be exactly same for every trial, because we measured the time at the same time drop the ball. Therefore, it could affect our data during the experiment. Also the air resistance is one of the factors that could affect the data. The standard gravitational acceleration is measured without any air resistance, so if I drop the ball without any air resistance, the ball would fall down faster than my result because tennis ball has some air resistance.

There possible improvements that I would make when collecting the data is that I could use a ball that is less affected by the air resistance like a golf ball or a streamlined shape of the objects with less air resistance lesser. Tennis ball is known to be comparatively less in air resistance, but it could be the cause of different result of my data from the standard gravitational acceleration. For more accuracy of collecting the data, I could take video of the process of dropping the ball and analyze the video using editing programs like iMovie and then I can figure out how long the ball takes to meet the ground in the unit of second. In this way, I could reduce the miss calculation during the process. If I have time to do the experiments again, I want to do the experiment using different ball with different mass to compare the results of the gravitational acceleration in same heights. Through this comparison, I could prove my experiment results are accurate or not.

Bibliography:

"Does Gravity Vary across the Surface of the Earth? (Intermediate) - Curious About Astronomy? Ask an Astronomer."Does Gravity Vary across the Surface of the Earth? (Intermediate) - Curious About Astronomy? Ask an Astronomer. N.p., n.d. Web. 07 May 2016. <http://curious.astro.cornell.edu/about-us/42-our-solar-system/the-earth/gravity/93-does-gravity-vary-across-the-surface-of-the-earth-intermediate>.

"Falling Object with Air Resistance."Falling Object with Air Resistance. N.p., n.d. Web. 07 May 2016. <https://www.grc.nasa.gov/www/k-12/airplane/falling.html>.

"Free Fall and Air Resistance."Free Fall and Air Resistance. N.p., n.d. Web. 07 May 2016. <http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Free-Fall-and-Air-Resistance>.

"Gravity Applications."Gravity Applications. N.p., n.d. Web. 07 May 2016. <http://www.astronomynotes.com/gravappl/s6.htm>.

"Gravity of Earth."Wikipedia. Wikimedia Foundation, n.d. Web. 07 May 2016. <https://en.wikipedia.org/wiki/Gravity_of_Earth>.

"Newton's Laws of Motion."Wikipedia. Wikimedia Foundation, n.d. Web. 07 May 2016. <https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion>.

"Newton's 3 Laws of Motion."Newton's 3 Laws of Motion. N.p., n.d. Web. 07 May 2016. <http://teachertech.rice.edu/Participants/louviere/Newton/law2.html>.

"Newton's Law of Universal Gravitation."Wikipedia. Wikimedia Foundation, n.d. Web. 07 May 2016. <https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation>.

"Newton's Second Law."Newton's Second Law. N.p., n.d. Web. 07 May 2016. <http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law>.

"Standard Gravity."Wikipedia. Wikimedia Foundation, n.d. Web. 07 May 2016. <https://en.wikipedia.org/wiki/Standard_gravity>.

"Variations of Gravity over the Earth's Surface."Variations of Gravity over the Earth's Surface. N.p., n.d. Web. 07 May 2016. <http://geol-amu.org/notes/m10-1-1.htm>.

(Korean Website about Gravitational Force)

"중력가속도.": 지식백과. N.p., n.d. Web. 07 May 2016. <http://terms.naver.com/entry.nhn?docId=1261202&cid=40942&categoryId=32229>.