Science Buddies: "Ask an Expert"

HEY!

IM HOPING TO DO A PROJECT INVESTGATING HOW THE HIGHT, WIDTH AND WEIGHT OF A BODY INFLUENCES ITS PROBABILITY F TIPPING OVER ON A SLOPE.

THIS INVESTIATION I THEN WOULD LIKE TO APPLY TO MOTOR CARS, MOTORBIKES ETC. TO DETERMINE WHICH IS MOST LIKELY TO TIP,WHY AND WHEN.

SINCE THE TOPIC IS QUITE LONG I'M NOT SURE WHAT TO TYPE INTO SEARCH ENGINES WHEN LOOKING FOR INFORMATION. ANY IDEAS???

PLEASE HELP!

Hi Candice,

That sounds like a complicated topic, but I'm sure there's a lot you could do with it. Could be very interesting. There may be someone else here more knowledgeable than I, but this may help you get started.

For a simplified car-like object (say a cube with four wheels) you can get a realistic picture of how they tip over using material from a highschool level physics textbook.

An example of a well-posed problem that might provide insight: take a cube car with known dimensions. If the car is turning around a tight corner (for example, going around a circle with a radius equal to the car length), how fast would it have to be going so that the force on the inside wheel goes to zero? You can get a pretty good answer that depends only on the distance between the wheels and the height of the car's center of mass.

Or - if the cube car is going downhill on a slope and hits the front breaks, how much acceleration would you need so the force on the back wheel goes to zero? (Speeding up while going uphill is similar.)

Those sort of questions, even if you consider them qualitatively (without doing the math), may help you get a sense of what factors are important.

For motorbikes, the situation is somewhat different. Tipping over by hitting the breaks while going straight and getting thrown over the front of the bike could be treated a lot like the car example. Tipping over by turning around a corner and having the bike slip out from under you is rather different, and you'll need to know something about the friction between bike tires and various surfaces when turning.

The three wheeled case is more complicated. It's not obvious to me what would be important, but I'm sure given some time and research you could dig up something interesting.

Some keywords you may find useful: "center of mass", wheelbase, and "rollover resistance" Adding something like "nhtsa" is likely to give you real statistics, adding "physics" will get you simplified theory.

Two slightly related articles that include a lot of information about how vehicles turn and how tire-road interactions work:
car stuff (the Physics of Racing, a copylefted ebook series)
http://www.miata.net/sport/Physics/index.html
motorbike stuff:
http://www.tonyfoale.com/Articles/

Good luck,
Erik

Thanks so much for your reply Erik!

Today I am setting aside totally for research, so I thought I would ask if any science buddies had any answers for me so I can make a nice litttle compilation of explanations.

I had done my experiment now and found my results.

What I did was I used a wooden plank as my slope, and identical blocks of wood as my cars. When investigating height i made sure that the withdth remained constant (and since I did not have the materials to increase height without increasing weight slightly, I can only hope that the weight increase was negligible in this instant). I then placed a block of wood on the slope and increased the angle of the slope slowly untill the block tipped over. I then took note of the angle at which it tipped. Then I added another block of wood on top (i made a plan so that they acted as one body) thus doubling the height, and adjusted the angle of the slope until it tipped. I did this with 5 blocks of wood and investigated width, height and weight this way.

My findings were as follows:

As the weight of an object increases, the smaller the angle of the slope reached before tipping over becomes.

As the height increases, the smaller the angle of the slope becomes befor it tips over.

As the width increases, the greater the angle of the slope becomes before it tips over.

I did a fairly simple experiment, but I am hoping to give quite detailed (yet easily understandible) explanations.

I would really appreciate anyone's input in explaining my findings!

Thank you ever so much

Hi Candice,

Sounds like an interesting experiment.

Your conclusions about the effect of width and height sound reasonable.

I'm a little surprised that the weight of the object makes a difference. What are you doing to compare different weights?

You might consider finding a way to use objects that are the same shape and constructed so that each is made from uniform material - for example, a wood block, a styrofoam block, and a block of modeling clay (or plaster, cement, ice, etc) - so you can separate geometry from weight.

A few keywords that may find useful are "center of mass" or "center of gravity."

Best,
Erik

Hey!

Thanks for the reply!

With the wight what I did was I used an empyt contaner. First I used it empty, and then I gradually added more and more weights inside it. Would that not work? I was also surprised by the result though, because I thought that the downward force of weight would keep the object down more - not increase its likelihood to tip. Please explain that to me!

Regarding the height and width, what I have been able to find out so far is that the things tip because their centre of gravity exceeds their base. Thus as the object gets higher, the centre of gravity gets higher etc. Attatching a pice of string to the centre of the block proves its point, but I have yet to find anything that tells me WHY.

Why does the centre of gravity exceeding th base cause it to tip????????

As I said I am hoping to give a detailed explanation, and all I can find are basics. PLEASE HELP!

You mensioned something about its geometry... would that be a point of investigation? Please elaborate

Thanks a million!

Candice:

Here are a few sites that discuss and show center of gravity diagrams with explinations.

http://www.grc.nasa.gov/WWW/K-12/airplane/cg.html

http://www.exploratorium.edu/snacks/cen ... avity.html

http://en.wikipedia.org/wiki/Center_of_gravity

http://theory.uwinnipeg.ca/physics/rot/node4.html

http://www.phy.ntnu.edu.tw/java/block/block.html

http://142.26.194.131/aerodynamics1/Basics/Page2.html

http://physics.bu.edu/~duffy/py105/Rotationalkin.html

Matt Mulanax

Hi Candice,

Check out the links Matthew posted for some tips on how to explain what you've observed. For more detail, you might try browsing through a highschool physics textbook. (I'm sure the physics teacher at your school would be happy to lend you a good one.)

The problem with taking an empty container and adding weights to it is that you're actually changing the height at the same time you're changing the weight. Even though the height of the rim of the box doesn't change, the center of mass (which you can think of as the average height of everything in your block) does.

You could try taking the same box and filling it up to the top using weights made of stuff with different densities. (wood, sand, water, pennies, etc). The results might be more in line with what you expect.

Of course offering an explanation for why you initially got surprising results could be a good idea too.


>Why does the centre of gravity exceeding th base cause it to tip????????

You'll need to spend some time thinking about the forces that act on the object to see what's going on there. This probably isn't enough detail to get you all the way there, but hopefully will get you started. Try a few google searching for things like "physics introduction forces gravity" for background.

Effectively, gravity is pulling down on the object in a line going straight down from it's center of mass. The table is pushing up on the object in a direction going straight up from the bottom of the object. As long as the center of mass is located above the base, the two forces are lined up and pointing directly at each other, and the object doesn't rotate. (Like two people facing each other and trying to push a big box into each other: nothing moves.)

But, once the table is tipped enough that the line from the center of mass doesn't go through the base of the object, things change. Now the gravitational force is offset by some distance from the force from the table, and that causes the object to rotate. (Imagine both people pushing the box continue pushing in the same direction, but each person takes a step to their left. Now the box spins.)

>You mensioned something about its geometry... would that be a point of investigation? Please elaborate

Sorry for being unclear. I just meant that if your differently weighted objects are also different heights, then you may be confusing two different effects.
Good luck,
Erik

Thank you so much Erik and Matt for your replies! I think I'm finally getting somewhere!

After plotting the graphs for angle versus height, and angle versus width, I seem to be finding a directly proportional relationship. Is that realistic?

However the weight measurements are still worrying me. What should I be expecting? I am about to re- do the weight investigation as you advised - so as not to change the height, but I have a hunch the probability of tipping over will still increase as the weight increases. Is that wrong? How is that possible?

I just re-plotted the graphs, and it turns out I made a mistake - the height versus angle graph is INVERSELY PROPORTIONAL whilst the width versus angles is DIRECTLY PROPORTIONAL. Why on earth is the height graph inversely proportional??? Please explain how and why that is possible

Thanks again

Hi Candice,

I just re-plotted the graphs, and it turns out I made a mistake - the height versus angle graph is INVERSELY PROPORTIONAL whilst the width versus angles is DIRECTLY PROPORTIONAL. Why on earth is the height graph inversely proportional??? Please explain how and why that is possible

That sounds pretty reasonable. Think about how hard it is to push over boxes of different shapes. As the box gets taller, it gets easier to tip it over. That's related to the statement that your model tips over at a smaller angle as it gets taller.

As the box gets wider, it gets harder to tip it over, which is similar to saying that the angle at which the object tips gets bigger.

Consider how much easier it is to tip over a cereal box when it's standing upright than when it's laying flat on it's back.

(Pushing the box over isn't exactly the same as tipping it using a slope, but it should give you some intuition for which way things should go.)

It's not obvious whether or not the angle is exactly porportional (or exactly inversly porportional) to the angle. You'd have to do some geometry to figure that out. There may be some trig functions in there somewhere. For small angles, you probably wouldn't notice the difference.

Best,
Erik

Hey!

I handed in my project last week so I just wanted to thank everyone that helped me to understand my investigation!

Regarding the plotting, I realised it was a good thing that my one graph was inversely proportional and that my other was directly proportional, as it made perfect sence as to what I had noticed. The inverse graph explained that as the one went down, the other went up - which was true! And for the directly prop ones as the one increased, the other did too.

My teacher was actually the one to realise why my weight results were so strange - because in effect, although I was keeping the other vaiables constant, the weight was situated at the top - thus portraying the characteristics of somwthing that is 'top heavy'. If I had siuated the weight below the base my findings would have been opposite.

So anyway, thanks again

Hi Candice,

Glad to hear it, and thanks for the update.

Best,
Erik