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Potato Gun Physics

By Amanda Rodriguez,2014-06-17 02:03
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Potato Gun Physics ...

Potato Gun Physics

    Students are told to make use of a Food Delivery Device (FDD) to deliver a potato to a

    circular compound some 30 meters distant from firing point. Students should “calibrate”

    their FDDs on the first day to determine affect of pressure, acceleration length, angle of

    launch, and potato mass on ability to hit the target. After the first day of calibration the

    “winds of fate” blow, and students are constrained on one of the firing parameters but

    must make adjustments to hit the target none the less.

Potato Gun Assembly

    Approximately 70 cm of 3 inch PVC tubing for pressure chamber

    Schrader type tire valve, available at auto parts store (short version is better).

    Cap for 3 inch PVC

    1.5 meters approximately of 2 PVC tubing

    10 cm piece of 2” PVC tubing Ball valve for 2 inch PVC

    Reducer for 3” to 2” PVC

    Cleaner and glue for PVC pipe.

    1. Drill hole for valve in 3” PVC, about 15 cm from the end, per hole size

    recommended by the valve manufacturer..

    2. Feed the Schrader valve in from the inside, and carefully using pliers, pull it

    through until the capture flange is in place.

    3. Cut about 10 cm of 2” PVC pipe to go from reducer to the ball valve.

    4. Without glue, assemble your gun, front to back and make sure all the parts fit.

    The order is: End cap, pressure chamber (with Schrader valve), reducer, 10 cm of

    2” PVC, ball valve, 1.5 meters of 2” barrel

    5. Disassemble on a long table, and clean each joint with PVC cleaner (in a well

    ventilated area). Then one at a time, put PVC solvent on the interior of each

    fitting and press in the next piece. Working from end-to-end, assemble the FDD

    one joint at a time. Ensure you hold the parts long enough to keep them straight

    during assembly.

    6. Dry for 24 hours before pressurizing or firing.

Cautionary and Helpful Notes:

    ? Take a piece of 2”PVC and using an electric sander (disc sander is ideal) sharpen

    the end to make a potato cutter. This allows students to cut the potato and mass

    it before putting it in the barrel.

    ? Load potatoes with the ball valve open, then, close the ball valve. Measure the

    length down the tube over which the potato is accelerated for later force

    calculations.

    ? Have students fire first test at less than 15 pounds of pressure and at an angle of

    greater than 65 degrees. This ensures potatoes are not fired too far.

    ? Never fire at higher than 60 pounds and don’t tell the students the rating on the

    PVC. The 3” tubing is not rated for pressure at all anyway.

    ? The dirty little secret of the whole thing is that potato seal in the barrel, and valve

    turning rate are the real keys to repeatable results.

    ? Don B. Cameron dbcameron@alumni.northwestern.edu 1 of 4

    Student Rules for Firing

    These rules are non-negotiable and part of the criteria for success. Failure to follow

    these rules (there will be NO warnings), will result in immediate removal from the

    activity and a call to the highest authorities

    ? Whether charged with air, or not, the FDD must NEVER be pointed at another

    person, building, or object, EVEN IN JEST.

    ? The pressure end of the FDD must be on the ground when fired. No shoulder

    fired, hand held, or other operation lifting the FDD off the ground is permitted.

    ? The FDD shall never be pressurized above 25 lbs/in2 unless given permission by

    the teacher.

    ? A “firing’ warning shall be issued for all launches audible to a perimeter of 40

    meters from the launch location.

    ? Loading of the potato shall be done “from the side”, never load the potato while

    standing or being otherwise located in front of the FDD muzzle.

Typical Data Table for Data Collection

Trial Angle Pressure Acceleration Potato Distance Time

    (degrees) (psi) Length Mass Δx Δt

     l(m) (kg) (m) (s) ?a

Typical Data Table for Calculations

    Trial actual model = VVAccel.-a Force (N) Max ?xi iV x2 Height (m) VV?tg?xxi= ma 22(m/s) Visin?cos?2l2cos?sin?a 2(m/s) 2g(m/s) (m/s)

Students calculate and compare model values to actual values and observe how good the

    model is (It’s actually pretty good). They also realize that science is messy and

    repeatable results can be challenging to obtain.

Assessments

    ? Lab write up including calculations, and comparing model (with out air resistance) to

    actual data (with air resistance). There is usually very good agreement regardless of

    how “bad” the firing and repeatability.

    ? Provide some dummied up data and have students calculate velocity or force from

    data provided.

    ? Discuss Sources of Error in measurement, timing, assumptions

    ? Don B. Cameron dbcameron@alumni.northwestern.edu 2 of 4

    Advanced Topics Derivations of the Equations used Above

    Vi

    Θ

    Δx

Derivation of Equations (in word form)

    1. Since Velocity is displacement over time, the velocity in the horizontal (x)

    direction must be equal to Δx/Δt.

    2. Since Velocity is a vector, then we can calculate the velocity out of the end of the

    gun by dividing by the cosΘ.

    3. Again, since velocity is a vector we can find the velocity in the vertical direction

    by multiplying the velocity out of the gun by the sinΘ.

    4. Vi-model - This derivation is a little tedious and is shown below:

A. At the peak the Velocity in the vertical direction is zero. How can this help me? You

    also know that this occurs when the time is ? of the total flight time. So, you have

    moved ? of the distance. Looking at my 2D motion equations what can I do with this

    information? Well, if you find the time of flight and the initial velocity you can use that

    12information to find the height using ?y = V sin??t - g (?t) i22 22. 1. V = V sin?- 2g(?y) y,fiVertical parts

    122. ?y = V sin??t - g (?t) i2

     3. V = V sin?-g(?t) y,fi

     4. V = V cos?= constant x,fiHorizontal parts 5. ?x = V cos??t i? Don B. Cameron dbcameron@alumni.northwestern.edu 3 of 4

     = V sin?-g(?t) and we know that V = 0 at the If I make use of equation 3 I see that Vy,fiy,f

    Visin??tpeak. So we can solve this equation for ?t and get which is true ? way ?g1through the flight. We also know the ball has gone half the distance in this amount of

    time. Using equation 5 you see that ?x = V cos??t or, half way through the flight that i

    ?x?t?x2means . So now we have two equations in terms of time and ??Vicos?12Vicos?

    can find Vi.

    ?t?xVisin??tThe two equations are: and ??g112Vicos?

    Setting these equal to each other you get:

    Visin??x= g2Vicos?

Solving the second two equations for V I get. i

    g?x V?i2cos?sin?

    5. Finding Acceleration “a”. Since the potato starts at rest, but leaves the gun at

    2Vispeed Vi, then we can use the acceleration length in the equation . This 2la

    equation is itself derived from the standard distance formula and the definition of

    acceleration equation (change in velocity over change in time) and is not shown

    here.

    6. Force Since force is just mass times acceleration they could multiply the

    acceleration by the mass (kg) to get force.

    7. Maximum height can be modeled as follows. Either use ? of the actual time, and

    put it in the height equation (and assume 9.81 for gravity) or put the velocity into

    Visin??tthis equation: and use this Δt to calculate max y. Substituting ?g1

    algebraically into the height equation, this can be done in one step using:

    22Visin?. As you see this does not make use of time, so it is definitely a model. 2g

    ? Don B. Cameron dbcameron@alumni.northwestern.edu 4 of 4

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