Which Physics Principles Govern a Car's Impact on a Statue?

[Carolina Girl]

I am trying to set up a forensic scenario and might have gotten in a little over my head on physics portion of the "crime".

Scenario is a car rolled down a hill and knocked over a big rock statue. I want students to both model the crash and use some math to calculate how heavy a car would have to be to knock over the statue due to acceleartion caused by gravity alone. (I'm using a car and weight set for the model of the vehicle)

I started off thinking this would be a simple F=ma type formula, and students would calculate a=g sinθ so that students would see that the mass didn't affect the acceleration, but only the force with which the car would hit the "statue" (for the model it is a piece of 2x4).
I realize now it can't be that simple since those 2 formulas in no way take into account how far along the incline the car had to have traveled prior to striking the barracade, and therefore the speed at which the vehicle was traveling when it hit the barricade.

HELP!

Thanks in advance.

 

[Simon Bridge]

Yes - you need to know how far the car traveled and how fast it was going when it hit the incline. You need to know it's acceleration down the incline as well - the formula you used would be the best case scenario because you neglected energy losses in the car.

You may want to push a real car down an incline - the students will like that.

Where was the point of impact with the statue - did the statue fall on the car or get pushed over (compare center of mass of statue). Pushing the statue over is a torque problem.

You could do this by conservation of energy too.

This would actually be a neat extended investigation.
I take it you'd rather just make a point about mass and gravity?

 

[Carolina Girl]

We are saying the car started at rest. The ramp model is 18 inches. Once I hve the model set I plan to just scale up to what the "actual scene" was.

(I think pushing a real car might put me over budget for the lab- but if you have a car to donate...)

While the model car hits below the center of mass of the "statue" it typically falls over (away from the car) but I have had once when it fell back towards the car.

I kind of don't *care* what equation physics concept ends up being applicable to this. My goal is to integrate more physics into forensics, which should be an integraded science class, in a way that isn't just bullet trajectories.

I'm game for the studetns having to figure out what is going on, but I need to know myself before I send them on that quest!

 

[Simon Bridge]

I've done this sort of thing with real cars - it does not have to hurt them (just don't do the crashing part).

So your physics is conservation of energy, and you'll need torques for the way the statue falls. It sounds like the statue get slid along a bit and when the car+statue stops, then the statue topples (the base stops moving but the com still carries inertia). Thus the car is not moving fast enough to topple the statue :)

There is a lot of auto crash forensics physics online.

I saw a nice demo where a first approximation for a vehicles speed was obtained, for eg, by driving a similar car at a legal speed and slamming on the breaks, then comparing the resultant skid marks with those in the crash.

Students could let a similar car roll down a similar slope and measure the speed at different distances.

I'm game for the students having to figure out what is going on, but I need to know myself before I send them on that quest!

:) chicken ;)

I like giving students something to do where I don't know what they will find out (though the first time I did this it was very scary - so I don't blame you). Just make sure the science is reasonable for their level. It's great: they end up doing the lesson for you.

Whatever you do, you are looking at an open-ended lesson so the students will be learning all kinds of things, not all of them on plan or in the curriculum. That would be the main prep for you.

Back to your simple model:
you have a car rolls down a slope and hits a statue, comes to rest, statue falls over away from the car.

you have F-f=ma (f=friction) and kinematics as you suspected
you need torque for the collision with the statue
conservation of momentum (and more friction) for the post-collision
and law of inertia to topple the statue.

use a real slope and car (no statue)
how does the car really accelerate down the slope
how long would it normally take to come to rest when it hits the flat
(how far did it push the statue - a couple of feet or so?)

Should be both informative and empowering xD

 

[PJC01]

I would first like to commend you on your creativity and effort in setting up a forensic scenario for your students. It is always great to see educators finding innovative ways to engage their students in the subject of physics.

In this particular scenario, the concept of force and collision both play a role in understanding the impact of the car on the statue. The force formula, F=ma, is indeed a good starting point to calculate the force of the car hitting the statue. However, as you have correctly pointed out, the speed of the car and the distance it traveled on the incline before hitting the statue also need to be taken into consideration.

To accurately model the crash, you can use the formula for kinetic energy, KE=1/2mv^2, where m is the mass of the car and v is its velocity. This formula takes into account both the mass and speed of the car, giving you a better understanding of the energy of the car before it collided with the statue.

Additionally, the concept of momentum can also be useful in this scenario. The momentum of the car before the collision can be calculated using the formula p=mv, where p is the momentum, m is the mass, and v is the velocity. This can help in understanding the force of the impact on the statue.

In conclusion, the force and collision formulas both have a role to play in understanding the physics behind this scenario. It is important to consider all the relevant factors, such as mass, velocity, distance, and momentum, in order to accurately model the crash and calculate the required force to knock over the statue. I hope this helps and good luck with your forensic scenario!