hsc physics notes online

8/13/2019 HSC Physics Notes Online

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Determining the Average MuzzleVelocity of a Water Pistol

Andrew Harvey12 PHYSICS


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Aim:To determine the average muzzle velocity of a water pistol.

Variables:

Independent(Change) Dependent(Measure) Control (Sam

e/Constant)

Nothing. Distance(horizontal)

Value of g (ie. mass of earth and radius of earth + elevation)Water PistolAmount of water in the water pistolSubstance be fired from the water pistol (water)Elevation of water pistolAngle of water pistolAir densityFlow of air around experiment (Do indoors where there is lesswind)

Velocity of frame of reference (earth)Altitude of ground (flat surface)Elevation of water pistol (vertical height)Force on trigger

Apparatus:

Procedure:1. Fix the water pistolat an angle of 0 to the horizontal, at a constant elevation.2. Place a ruler along the line of action of the water pistol, placing 0 directly below the water

pistol muzzle, keeping the ruler horizontal.3. Fire the waterpistol, by slowly applying a constant force on the trigger.4. Measure the approximate average distance (x) the water traveled.5. Repeat step 3 and 4 multiple times. Each time keep the things in the same/constant column

the same.6. Record results.7. Calculate average.

Ground

Water Pistol

Stream of water

Elevation

(y)

Distance (x)


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Data Recorded/Data:F ireNumber Distance(m) x E levat ion (m) y Initial Velocity (ms- )

1 2.28 0.455 7.482

2 2.99 0.455 9.812

3 1.63 0.455 5.349

4 2.44 0.455 8.007

5 2.56 0.455 8.401

6 1.95 0.455 6.399

7 2.26 0.455 7.417

8 2.67 0.455 8.762

9 2.01 0.455 6.596

10 1.84 0.455 6.038

The graph below shows the results that I collected.

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1

Distance (m) x

Calculations:Process

Use yauv yyy $#" 222

to findy

v (y

u = 0, a= 9.8, y$ = elevation)

Then use atuv #" to find t( yvv" , 0"u , 8.9"a )

Then use tux x"$ to find xu ( "$x horizontal distance)

xu will equal)

u because the water is launched horizontally, thus there is no vertical motion at the

beginning. The direction of xu will always be along the line of action of the water pistol.

Actual Calculations

!1

482.7455.06.19

8.928.2

6.19

8.9 %"

1

1"

1

1" ms

y

xu

"1

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xu

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xu

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TheFunctionThe relationship between horizontal distance, vertical height, and initial velocity can be determined,and is given by:

y

xu

+,

-./

0

2"2

5

5

7 O R

y

xu

1

1"

6.19

8.9

Where,u= initial velocityx= horizontal distance

= vertical height

The graph of this relationship is shown below, (where zaxis is u)


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Statistical Analysisof DataAverage horizontal distance: 2.263 m

Range horizontal distance: 1.36 m

Average initial velocity: 7.4263ms-1

Initial Velocity Standard Deviation: 1.294

Discussion of Reliability and Conclusion:Using this method and these calculations eliminates the need for measuring time, which would be

impractical and unreliable, especially as it is a stream of water not a single object, and given that the

time of flight is relatively short.

Also the lower the height then the less horizontal distance traveled, and thus less affected by air

resistance (as my formula used do not account for air resistance), and thus a more accurate velocity,

however the greater the horizontal distance, the more accurate your measurements are. But also if

the height is too high then the water will reach its terminal velocity and thus the results would be less

reliable. Also different values of height result in different values of g. So this should be taken intoaccount and gshould be calculated. However even if you change your height 100m the value of gwill only change by 0.0003.

The reliability of this experiment was also decreased because the trigger of the water pistol was

controlled by a human, this leads to the problem that a human cannot apply the same amount of

force on the trigger every time.

There are flaws in my method and thus this experiment is less reliable. This can be explained with

the diagram below.

As you can see above, when the water pistol is fired, the water initially follows one line and stays

stuck together, however after just falling slightly in height, the water disperses, and once it lands on

the ground there are many different droplets in different places. In order to correctly fulfill the aim of

the experiment, I would need to measure the distance from the position of every one of those

droplets landed at, to the wall directly underneath the water pistol muzzle. Then take the averageofall those distances. However there are far too many droplets for this to be done. Not to mention the

Clump ofwater

droplets


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there were multiple drops that landed in that position, as this would affect the average.

The standard deviation of the data was quite high, so this means that the experiment is not veryreliable.

The ratio of elevation to average distance was 455:2263. So the distance was quite long compared tothe height. This is bad in terms of experiment reliability because the long distance means that there ismore dispersion of the water droplets, and the water is more affected by air resistance. The reasonfor the dispersion error is shown in the figure below. As you can see the further the water went, themore it spread out.

The only way to compensate of this is to increase the height. However as mention previously, thisalso has adverse effects, unless in a vacuum.

As with any experiment, it could have repeated it more times to get a more accurate result.

Another factor that could have affected the reliability of my experiment was air currents (wind). Thisis a problem because non zero air currents are not taken into account in the formula that were used.

This can be controlled to a certain extent by conducting the experiment indoors, without the fans on.

A problem also arose by trying to apply a constant force to the trigger, for the duration of the firing,and also each time the water pistol is fired. This could be controlled using a spring balance attachedto the trigger. But this method has a factor of human error, so it could be automated with a robot.

Conclusion:The average muzzle velocity of my water pistol was 7.4263ms

-1, in the direction that the water pistol

was oriented.


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.-%'$ 4/6'/5 #-(+.'-,# !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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*'*('-D4)%"& !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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*'*('-D4)%"& !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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9-4C+()F3).) #"//. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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9-4C+()F3).) #"//. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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9-4C+()F3).) #"//. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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