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# In this extended essay, I will be investigating projectile motion via studying the movement of a metal ball bounced off by an unloaded spring. Experimental methods and theoretical models will be used to investigate how the projection height and compressed

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Introduction

Pon Chin Ching (Jensen Pon) 13E Island School

Uploaded By Jensen Pon 9:09 AM 23rd October, 2011

Abstract

In this extended essay, I will be investigating projectile motion via studying the movement of a metal ball bounced off by an unloaded spring. Experimental methods and theoretical models will be used to investigate how the projection height and compressed length of spring affect the projection range of the metal ball.

A spring gun was constructed using a spring and 5 wooden boards. The metal ball served as ammunition for the spring gun. While the simple spring gun was used to launch the metal ball , a zigzag ruler was used to measure the range of horizontal distance travelled by the metal ball at varying ranges of projection height and compressed spring length. The conclusion of this investigation will be drawn by comparing theoretical models and experimental data, considering whether experimental values were less than theoretical values. This may be attributed to air resistance in a vacuum-less environment, therefore it can be seen that gravity isn’t the only factor causing this uncertainty. At the same time, it is should be noted that the elastic potential energy of the spring is converted into work done against friction, work done against air resistance and rotational kinetic energy of metal ball after spring release. Experimental results of the horizontal projection range of the metal ball followed an expected trend, in which the range increases with separate or synchronized  increases of projection height and compressed spring length.  It is discovered that by quadrupling the projection height and doubling the compressed spring length, it results in twice the previous horizontal projection range of the metal ball.

Middle

9.9

10.2

10.1

10.1

Natural length of the spring = 15cm±0.1cm  From the excel, the slope of the curve = 0.050 m/N

Since F=kx (where F is the force applied to the spring, k is the spring constant and x is the compression of the spring) , the slope of the graph=1/k.

Therefore, spring constant k=1/0.050=20.0 N/m

Procedure - Determining range of metal ball by varying projection height

1. Fix the container onto the stand clamp using steel clips. Make sure the stand clamp is fixed tightly using clamps and screws.
2. Tape several recording paper (A4 paper and carbon paper) onto the table using cello tape.
3. Fix a meter rule to the table using a stand clamp and steel clips. Place it behind the muzzle of simple spring gun. Make sure the meter rule is in contact with the table.
4. Attach a 25cm-rule onto the upper wooden board of simple spring gun using cello tapes.
5. Make sure the simple spring is parallel to the surface of the table using a spirit level.
6. Mark a point onto a paper vertically below the muzzle of the spring gun. This will be the starting point of the projectile.
7. Adjust distance height y between the bottom of metal ball and the table to 10cm using the meter rule as reference.
8. Compress the spring and movable wooden block until they are compressed to 5cm of length using the 25cm-rule as reference.
9. Place the metal ball in front of the movable wooden block. Make sure it is touching the movable wooden block.
10. Release the movable wooden block to launch the metal ball.
11. When the metal ball lands, mark the point of impact. It should be a black spot.
12. Measure the distance between the black spot and the starting point using a zigzag ruler.
13. Repeat steps 6 to 11 but vary the height each time. The heights are: 20cm, 30cm, 40cm, 50cm, 60cm, 70cm and 80cm.
14. Tabulate the data and plot a graph of Change of range against the square root of the height.

Now having collected the data we can determine the square root range of the metal ball. The data are listed below along with its corresponding theoretical values. (gravity = 9.81ms-2). Note that the square root values are rounded to two decimal places:

Table 1:

 Height y (cm) ± 0.1cm Square root of height y (cm)± 0.01cm Experimental range (cm)± 0.1cm Theoretical range (cm)± 0.1cm Trial 1 Trial 2 Trial 3 Average Range 10.0 3.16 22.1 21.7 21.8 21.9 24.3 20.0 4.47 30.3 31.5 30.6 30.8 34.3 30.0 5.48 38.2 37.6 39.2 38.3 42.0 40.0 6.32 46.5 45.7 45.8 46.0 48.5 50.0 7.07 48.8 49.5 48.7 49.0 54.2 60.0 7.75 54.6 55.4 53.6 54.5 59.4 70.0 8.37 57.6 58.3 58.1 58.0 64.2 80.0 8.94 65.2 62.3 63.5 63.7 68.6

Conclusion

• More accurate experimental results can be obtained if the experiment is performed in a vacuum since there will be no air resistance acting on the metal ball during flight. However, it requires a high level of technology and advanced apparatuses to help carry out the experiment which cannot be done in a school laboratory.

An investigation on how range is affected when launching the metal ball at different angles is worthy of scholarly inquisition. However, stating a hypothesis proves to be a complicating task as different projection angles leads to different amount of gain in gravitational potential energy during the trajectory of the metal ball. An experiment setup in which the metal ball does not gain gravitational potential energy during its trajectory can be used to investigate this experimental variable- different launch angles, simplifying the investigation. Also, to expand on this investigation, we could introduce another variable, which in this case is surface area and shape. For instance rather than using just metal balls, I could use cylinder shape and bullet shaped projectiles.

Appendix 1

By conservation of energy, during the ejection of the metal ball,

Gain in linear kinetic energy of the metal ball = loss in elastic potential energy of the spring   After the metal ball is projected

Consider the vertical motion of the metal ball,

By     Consider the horizontal motion of the metal ball,

By    Works and Program Cited:

Program:

Microsoft Office Excel 2007

• Microsoft Office Excel 2007 is the basic graphing software from
Microsoft Corporation. It combines graphing, TI calculator data import, curve fitting and other analytical tools into one easy-to-use program.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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