How can i measure the acceleration of wooden cars being rolled down a hill?

http://physics.info/acceleration/

Place tape or chalk or some kind of marker across the path of the wooden car. Get a stop watch and take note of how quickly the car travels in between the marks. Toward the top of the hill the times will be slightly higher whereas after time.. the car builds up its maximum speed and the times will even out. This will give you some idea of the acceleration because of the variation in times.

Or .. is that not what you are looking to do? lol

@NaturalMineralWater That’s what i was thinking but he mentioned some sort of formula involving the angle of the hill, and the time the car takes to go down. i would guess it also includes the weight of the car. Unfortunately he didn’t specify the formula, which is why i need help…

@iRemy_y

You can easily calculate the acceleration of the car in an ideal situation, meaning no friction or air resistance. But that doesn’t seem to be what your teacher is looking for.

@Ivan If i need to my neighbor is a high ranking boy scout leader. i could try to convince him to allow me to use a pine wood derby ramp indoors and alter anything i need to. I have a dehumidifier if that helps and I’m almost positive i can get hold of a shop room to build the wooden cars and get them accurate.

Do you have access to a ticker tape device? That can help you to calculate the acceleration.
But for what he sounds like he is asking, you will need to know the angle of the slope they are rolling down from the horizontal. If you can do that, I can help you.

@shrubbery Yes I’m pretty sure i can figure out the angle. Most I will most likely be using a standard pine wood derby ramp which look like this: http://www-cs-students.stanford.edu/~mdevine/pinewood/pinewood_derby.html unfortunately they are curved at the bottom… which is the hard part that i need help on. If it is not possible to do, or requires too much effort, i could try rolling them down my hill which i can find the angle of, or better then that, build a small wind tunnel with a fan, build the cars, place them in there, throw some color sand or drops of paint and video it. then make observations on that.

Ok, that should be fine, give me a few minutes, I’m gonna try and draw a diagram :)

So here’s the diagram
The F with what looks like an 11 next to it is The Force parallel to the slope. The F with what looks like an upside down T next to it is the Force perpendicular to the slope.
The forces acting on the car are mg (mass x gravity) and the normal force of the slope on the car Fn. The force of the trolley on the slope, F perpendicular, is equal to Fn so they cancel out. So F parallel is the thing that contributes to the car’s acceleration.
from diagram, using sin/cos/tan rules, F parallel = mgsinθ
m = mass of car
g = gravity (9.8m/s^2)
θ = angle of slope from horizontal
F = ma
therefore ma = mgsinθ
a = gsinθ
So now you have a way to calculate the acceleration.
To calculate the time taken, you need to measure the displacement (distance travelled) of your car. On the derby slope, I’d recommend measuring the displacement like this from where you car starts to the point where the ramp starts to curve.
Your car starts from rest, so the initial velocity, symbol u, is 0m/s
Your acceleration, symbol a, is what you just calculated, in m/s^2
Your displacement, symbol s, measured as in diagram, in m
Your time, symbol t, is unknown, in seconds
The equation used is s = ut + ½a(t^2)
Rearrange to make t the subject and voila, you have the time taken for the car to travel the measured distance!

I’m just thinking though, because your experiment is about “the effect of the shape of a car on the aerodynamics” you might have to go into friction… and that’s even more complicated. hrm.
If you change the mass of the car by changing the shape then you could argue that the mass is what causes difference in acceleration, not necessarily the shape, because if you change the shape but keep the mass constant, by the above formulas the acceleration of the car will be the same. This is because the formulas are assuming that you are in a frictionless vacuum, which kind of defeats the purpose of your experiment. Perhaps you should talk to your teacher again about what you need to do. Or am I reading too much into it?

@shrubbery HAHA! i feel so stupid after reading that post like seven times and not getting half of it… i think i get the basic idea but i just emailed my teacher about the wind tunnel idea… if that works then my only problem will be measuring the speed of the wind, which should be no trouble at all. hopefully the idea goes thruogh. if not i’ll show him the post to see if that’s what he wanted. thanks!

The best way to fix differing masses is simply to add mass to make sure they are the same. I used to do this when I made pinewood derby cars back in the day. I used lead (though that may not be terribly safe) and melted it down and poured it into holes drilled in the car in order to maintain the maximum weight. Lead is toxic so I don’t recommend trying this by yourself. There may be a non-toxic alternative however using a wind tunnel test would eliminate the differing mass problem.

I’m an aerospace engineering major and I can tell you that the best way to determine how the shape of a car will effect its performance is by doing a wind tunnel test. Most wind tunnels will allow you to measure both lift and drag on a model. The drag would indicate the amount of force opposing the motion of the model at a certain wind speed (which you would select) and the lift would indicate how much normal force would be applied to the model due to the aerodynamics. The normal force would have some effect on the frictional forces so this cannot be fully neglected. You may find that the force is very small, but you can’t really know until you test.

I had a nearby university in junior high that allowed me to use its wind tunnel for a few minutes to collect some data for a science project of mine. It’s definitely worth looking into, the experience is definitely worth it.

@Shuttle128 I think I’m going to end up building the wind tunnel. Then its just a matter of building the car models, getting the tunnel together, and reading up on lift and drag. anything you can tell me that would help me study them? Or could you tell me how to measure them?

@iRemy_y don’t feel stupid, I have trouble grasping it and I’m doing 12th grade physics. Sorry I couldn’t make it any easier for you to understand.
I reckon from the sounds of it the wind tunnel is the way to go :P
@Shuttle128, wow, I want to do aerospace engineering next year!

I think your adviser is leading you to learning how forces change on an inclined plane which is a good thing to learn. I’m trying to help my 11th grade daughter with the same thing right now and I know how difficult it is. I have to agree with some of the above, if you want to do a good job measuring air drag based on different shapes, then a wind tunnel is the way to go if you can get to one. If a near by university has one, it’s a great way to see and learn way more than your experiment will teach you. If none is available I’d suggest the following:
Build a simple wind tunnel. I’d get a refrigerator box and with duct tape build a square tunnel about one foot square and 4 feet long. Put a large box fan at one end. Cut out trapezoid shaped pieces of card board and tape them together to match the fan size down to the tunnel. The trapezoid section is called a plenum and the tunnel is called a duct. Build a small table in the middle of the tunnel that you can place your car on. Adding a door you can close will help. When the fan is on, a FORCE will be exerted on the shape. You can measure this force by tying a string to the car, running the string over a pulley and seeing how much weight can be placed on the end of string to balance the force of air. This would be when the car does not move. see figure 1 in this link for an idea on how this might be set up.

http://en.wikibooks.org/wiki/How_To_Build_a_Pinewood_Derby_Car/Physics

skip all the stuff before it as it’s pretty complex, just get the idea from the drawing.
To be accurate, measure the friction of the car wheels by this method with the fan off, subtract that from what you get with the fan on. Don’t wory about measuring the air speed, you’re looking for the effect of shape on drag. In this case you want the air speed to be the same for each measurement.

If you are still thinking of measuring acceleration using a track, here is what I’d suggest.
You’ll need a cam corder that can display time to at least a tenth of a second or video editing software that shows time.
Mark off the track with clearly visible stickers every foot. Video record runs of different shaped cars. Determine the time it takes to go through each one foot section. Calculate the average speed in each section, speed = distance/time
plot the speed against time. If you do this you should see a straight line with different slopes for each shape. ACCELERATION is the change in SPEED over a period of time.
or (Velocity at time2 – Velocity at time1)/ (time 2— time1)
Acceleration will also be the slope of the line.
CAREFUL this is getting you dangerously close to Calculus! Once you go down that road, wonderful things are learned!