Science Buddies: "Ask an Expert"

Hi,

My son and his friend are performing the experiment listed in the "subject" of this post. We don't know how to use a scientific calculator and trig is a bit beyond most fifth graders. We need to know how to enter the data into the scientific calculator and how the answer to the formula relates to the experiment itself.

So far, we tried forming a right triangle by using the drop height for one side of the triangle and the measurement from the center of the spatter to the outermost droplet of water as the bottom side of the right angle. Then we stretched a measuring tape across the angle to make the longest side of the right triangle and used a protractor to measure the outermost acute angle. At a drop height of 46", we get an average of about 33 dgrees each time we've tested. We're not sure if this is the angle we want to be measuring or what this even proves.

Help, please? Thank you!

Hello and welcome to the Science Buddies forums! I found the experiment you are working on, and I see how it can be very confusing. Let's look at two things - what we're measuring in the experiment, and how to use a scientific calculator to solve the equations.

I find this experiment confusing - it seems like it suggests measuring one thing, and then measures another, so I'm going to recast this experiment as one that makes sense to me.

One could measure several things with the splatter of the dropped balloon. This experiment suggests measuring the time of the drop and calculating the final velocity of impact. This part looks good and should work. Did it?

Next the experiment suggests measuring the "angle of impact". The angle of impact is the angle (with respect the ground) that the balloon impacted the ground. If you're dropping these balloons from a ladder, this angle should always be almost 90 degrees. The experiment shows 2 diagrams for measuring the angle of impact. The first one, figure 2, does not make any sense to me. The measurement seems to be from the center of the "splat" to the beginning of the outermost splatter. Huh? I don't get that. However, if we look at figure 3, it looks like the measurements are of the main, largest splat, and are the width (the smaller size) divided by the length (the larger dimension). This seems like a good measurement to try, and it might give you a measure of the angle of impact. Do you have this information? I would think that most of your trials should end up around 90 degrees.

A more interesting measurement might be to measure the furthest spot which is wet after each drop. There should be some correlation between this number and the height the balloon is dropped. This is more "forensic science" related, as you could use this information to make a guess as to how far a body fell. What I'm suggesting is to change the table in the experiment so that instead of the "angle" column, you have a "ratio" column. This column would be the ratio of "the length from the center of the initial impact to the outermost spatter" to the height the balloon was dropped from. One could use this ratio to estimate distances balloons were dropped by measuring the size of the splatter. You could make an interesting plot of this data. If it's linear (sorry, I don't know if it is) then you can measure the slope of the line and come up with a constant to predict new data. (You might have to use a logarithmic plot, if so, write back and we can discuss how to do that).

Finally, to answer your scientific calculator question, here is how to get "sin-1(c ∕ a)". Enter c / a, press = . Then press the "2nd" button and the "sin-1" button. This should give you the answer (the 2nd button is required on the TI calculator I used as reference. Your calculator may be different). I hope this helps - let us know if you have any questions.

Keith

Good afternoon, rdhdbrnis!

I am sorry to see that you're encountering some challenges with this Science Buddies experiment! In addition to kgudger's great advice, I would like to add a couple of things.

First off, I am not entirely sure what the angle measurement with regards to the "outermost spatter" is supposed to represent. I might hypothesize that as the drop height increases, you would see the size (diameter) of the spatter pattern increase. In addition, the outermost spatter may become more and more elliptical (stretched out) in shape. However, how one might use this to actually predict anything is rather curious - especially if you attempt to repeat this experiment on a variety of surfaces. (In bloodstain pattern analysis, the material which the blood strikes plays an important role.)

Ordinarily, in order to calculate the approximate angle of impact of blood, width and length measurements are taken of one of the stains (as shown in figure 3 of the project guide (https://www.sciencebuddies.org/science- ... o&from=TSW) - and excluding the "tail"), with the smaller measurement being divided by the larger one. As the project guide and kgudger explained, the inverse sine of this number is then calculated using the trig function on your calculator, and this provides an estimate as to the angle of impact for that specific drop. (Although not asked for, nor needed, for this experiment, the *directionality* of the bloodstain is very important, and can be determined by an examination of the features present in the stain. You will notice in figure 3 that the drop has a tail (to the right of the droplet). This tail points in the direction that the stain is *heading*. In fact, at a certain angle, the tail will also have a separate dot at the end of it - which looks sort of like an exclamation point "!")

In practice (that is, when this is performed out in the field at crime scenes), this estimated angle of impact then allows for a piece of string (or other suitable material) to be taped at one end of the drop (pattern) and then extended out (at the measured angle) and anchored - this then provides the analyst with an approximate origin of that particular drop of blood. Does that make sense? Multiple droplets are then similarly measured which, depending on the nature of the bloodshedding event, will all return to an "area of origin", in three dimensions. This is one of the critical parts of crime scene reconstruction!

In order to provide some sort of idea as to whether or not the estimated angle calculation has any worth, a simple experiment can be set up. This can be done by angling the 'floor' rather than attempting to angle the blood drop - which can be rather tricky! Taking something that can produce drops (an eye dropper, pipette, etc.), and secure this to an immobile surface (hand tremors can introduce error). Then, simply allow the first drop to strike the 'floor' at 90 degrees (that is, with the 'floor' perpendicular to the dropper). This should produce an approximately circular drop. If you measure this, it might measure, say, 1 cm x 1 cm. Consequently, the inverse sine of 1/1 (=1) is 90 - that is, 90 degrees. If you then angle your 'floor' to, say, 45 degrees (using a protractor to measure this accurately), and then repeat the procedure, this should produce a droplet that, when measured, provides width and length measurements which calculate to approx. 45 degrees. You will find, however, that this approximation gets more challenging the closer you approach vertical (i.e. 90 degrees), but it still produces some great data. Simply repeat this experiment at 10 degree intervals and measure the widths and lengths of the drops at each recorded angle - and see how they compare. (I would also suggest performing multiple tests at each angle so as to allow for potential variation.) If you use some food coloring in the water and white cardboard, this would also produce some terrific displays!

Also, I think the reason why (in figure 2) that the measurement is being taken from the center of the impact pattern to the *start* of the outermost droplet, is because this is how far the droplet was cast *before* it struck the ground. Again, why this is critical is rather confusing, I'm afraid.

Anyway, I hope this helps (a little!), and please be sure to post back if you need more clarification or if you have any other questions.

Best wishes, and good luck!
Geoff.