Does Distance Affect Speed?

In an effort to get Matthew more invested in his work, I assigned him to find several science labs that he could do with his brothers.  There were a few rules:

1. Do not blow up the house.
2. Do not launch your brothers into outer space.
3. Do not make me take anybody to the emergency room.

After the gleam in his eye, I added a codicil: Do not do anything that you will need to explain to an insurance adjuster.

He pulled out a few books and started looking through them. The book gave him ideas and general instructions, but I assigned that he needed to write me a full lab report.  After he gave me his "finished" report, we had a discussion of what my idea of a "final report" is vs. his.  We have a bit to go on reconciling expectations, but we'll get there.

The first experiment he chose was from the physics section.  Jackpot!  Luke is doing physics as well, so we swapped out brothers; instead of Jude and Damien for lab partners, Matthew had Luke and Jude.  Once the data was collected, Matthew got to do the easier calculations, while Luke got the more technical ones.  Both boys were right, but for different reasons.

Does Distance Affect Speed?

Hypothesis: If the height from one end to the other is higher, then the water will flow through faster.


Materials: 

short hose (about 4')
a friend
two bowls with quart markings
stairs
water
stop-watch
a way to prime the small hose, if necessary (we used our regular garden hose)

Procedure:

1. Fill up one bowl with water and place it on the top step.  Put the empty one on the bottom step/landing. 
2. Prime the small hose, if necessary.  (If all the water ran out of it while moving it, you'll need to prime it.)  Fill it with water  - we held it end-to-end with a garden hose, turned on the tap until water came out the far end of the short piece - then turn a kink in an end to maintain the vacuum.
   
   
   
   
   
   
3. Put each end in each bowl, straightening the kinked end once the "wet" end of the hose is submerged.
4. Time how long it takes to fill get the bowl at the bottom of the steps to the two-quart line. 
5.  Kink an end to keep the hose primed to repeat the experiment.  
6.  Refill the bowl at the top of the stairs with the contents of the bottom bowl, and move the filled bowl to a lower step.
7. Repeat steps 2-4.
8. Empty bowls and put materials away.

Data/Calculations:

Matthew, calculating water speed:

Distance traveled: Ideally, you'd measure each step to get accurate readings.  If you want to do that, you'll need a tape measure.  Since the "junk drawer" swallowed ours, we just went with standard construction measurements. (Not something you want to do if you're trying to find runoff rates, etc., but for academic purposes, it was good enough.) The standard "run" of a stair step is 11.5 inches, so to find out the total distance traveled, multiply (11.5 x the number of steps traveled), then convert it to meters.  Do this for each round of experiment.

We know how long it took for each one, because we used a stop watch.

To calculate speed, divide the displacement, or the total distance traveled in meters,  by the seconds required to travel said displacement. 

When the bowls were five steps apart, the water took 14 seconds to travel from one bowl to the other. By multiplying the standard length by the five step difference, we get a total distance of 57.5 inches, or 1.46 meters.  Since speed is equal to the displacement per second, we divide 1.46 meters by 14 seconds, which gives us approximately 0.1 meters/second that the water traveled. 

When the bowls were three steps apart, the water took 90 seconds to travel between bowls. If we again take the standard length and again multiply it by the three step difference,  we get a distance of 34.5 inches, or approximately 0.87 meters. By dividing 0.87 meters by 90 seconds and rounding, we get approximately 0.01 meters per second. 


Luke, calculating the slope of the hose:

The slope of the hose affects how fast the water will come out.  The steeper the slope, the more gravity will affect the water, and it will come out faster.  If the slope is more flat, gravity will have less of an effect.

Slope is calculated by dividing the rise over the run.  Using standardized figures, the rise of each step was 7.75 inches, while the run was 11.5 inches.

Normally, the slope can be easily altered by adjusting the height or the length. However, the standardized stair size remains constant, and the 90° angle made by the the stair flight stays constant as well.  While the flight size itself changes, as long as the angle made by the stair in comparison to the ground remains the same, the measurements of the corresponding sides of both triangles will be proportional. So, if you find the slope of one stair, you have found the slope of the whole flight as well. Calculating slope to be rise over run, or 0.19685 meters divided by 0.2921 meters, we get a slope of approximately 0.02 meters. 

While the slopes remain constant, the velocity will not.  We know from Matthew's calculations that the speed of water in the second experiment was significantly slower.  The slope is the same, so the speed should be, right?  Or, it should be less time for the lower steps, because the water isn't traveling for as long a distance between the top of the stairs and the bottom. Here's part of why it isn't:  the distance the hose is traveling changes, but not the distance the water is traveling.

In addition, the hose has a definite length, so as the distance over the shortens, the hose coils up. The water is still traveling through the same length of hose as before, but now has to go against gravity in some parts in order to continue to travel through the hose.  Since gravity has a major effect on speed, a coil will causing the water to take longer to travel the same distance as before.  Velocity = mass x acceleration , but gravity increases acceleration proportionally to the distance fallen.  If you look at a playground slide, a corkscrew slide looks like you will go faster, and the ride be more intense, because of its rotation.  However (assuming the sliders are of equal mass, and the actual length of the slides are equal), a straight slide is going to run "faster" because gravity has a greater effect when there is no lateral motion to impede it.


Conclusion:

Our  hypothesis was correct because when the bowl was 5 steps higher than the empty bowl it went faster. 

Matthew: Yes, distance does affect speed of the water.
Luke: Distance affects speed, but what affects it more is how vertical that distance is.




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