FolkIB PhysicsSeptember 26, 2014Projectiles: Bow and Arrow LabAimThis experiment aims to determine the relationship between the extension of a bow and its range.

Background InformationA bow and arrow is a projectile system used for hunting that has been around since recorded history. A bow is an arc which shoots aerodynamic projectiles. Flexible strings at the two ends are drawn back, creating potential energy. When the string is released, the potential energy of the bow will transform into the velocity of the arrow. The velocity of the bow is directly related to the extension of the bow; thus, it is expected that the range of the arrow will be a direct proportion to the extension as governed by the equation (in the form of y=mx) [ where ]. In this experiment acceleration and time will be constants because the arrow will be shot from a constant height.Works Cited http://www.infoplease.com/encyclopedia/history/bow-arrow.htmlApparatus- A toy bow with a maximum extension of 15 cm- 3 one-metre sticks- A toy arrow 20. cm long- 15 cm ruler- Table with height 90. cm

Procedure1. A toy bow is placed on a table 90 cm from the ground2. An arrow is drawn into the bow, stretching the bow with the extension length of 5 cm, then released from the bow.3. The range of the arrow is measured using metre sticks. The arrow is measured from the furthest point from the bow. This is repeated 5 times.4. Steps 2 and 3 are repeated with 6 different extension lengths (5 cm, 7 cm, 9 cm, 11 cm, 13 cm, 15 cm)VariablesIndependent VariableExtension of the bow

Dependent VariableRange of arrow shot from the bow

Controlled VariablesConditions of the arrow (mass, length)Height of table (90 cm)

Results/Data AnalysisTable 1. Cool Title Right HereLength of Extension /cm 1Range /cm Trials 2Average Range /cmStandard Error of the Average Range

Trial 1Trial 2Trial 3Trial 4Trial 5

56571615366633

71251211201151161192

91781881881961841863

112722492372522562536

133293103153353173215

15350410405383365380.10

Sample Calculations of Average range and Standard Error of measurement5 cmAverage Range =Standard Error of the Average Range:

11 cmAverage Range =Standard Error of the Average Range:

15cmAverage Range =Standard Error of the Average Range:

Graph 1. Cool Title Here

The graph above suggests a linear relationship between the range of the arrow and the bows extension. The three calculated slopes in the lines of best fit are 31 (in green), 32 (in red), and 33 (in blue). The average slope is with an error in average slope of .

Conclusion and Error AnalysisThis experiment has successfully determined that the range of the arrow is linear/directly proportional to the bows extension when systematic errors are taken into account.In the theory of , the linear graph (graph 1) should have been a direct proportion with the regression lines passing through the origin. This is caused by systematic errors. In this experiment, we did not pull the bow exactly to the data extension, but instead, we pulled it back 1 cm less than the data value because we realized that the maximum extension was slightly less than 15 cm. For example, for the 13 cm extension length, we actually pulled 12 cm. This problem could be compensated by adding a constant to the ranges (in this experiments case, around 100 cm which is the current y-intercept). An alternative way could be to use a longer bow or change the extension lengths.An error that affected the result as a whole is the effect of air resistance. Air resistance has slowed down all of the arrow trials, making the experimental ranges slower than the theoretical range. This effect could be eliminated by performing the experiment in a tightly controlled environment (in a vacuum). It could also be compensated by adding a constant to the ranges.There are also random and human errors in this experiment. The impreciseness and inaccuracy of measuring the range is one of the most important errors. The error was due to the ruler having such a long length, and the fact that precise measurements of range were wasting experimental time.The bow sliding along the floor when landed was also a big factor contributing to random errors in this experiment. This has caused the floor having low friction and the bow still having horizontal velocity upon landing. This can be compensated by performing the experiment in a more frictious environment or by using technology to determine the exact position of the landing.The bow and arrow itself posed problems leading to some random errors. The arrow shooting off at different angles (in respect to the horizontal plane) each time has altered the range. The arrow occasionally being stuck onto the bow upon shooting (due to the friction from the bow) may have caused the velocity of the arrow to slightly decrease and thus lowering the range.All of the random errors can be reduced by performing the experiment with multiple trials.