Additional Math Pages & Resources

Friday, January 8, 2010

Center of Gravity

My last few posts have dealt with concepts known as vertical, horizontal and diagonal. Because vertical is defined as the direction of the pull of gravity, it raises the question, On what does the gravity pull? Or where? We had to invent a concept called the center of gravity.

For the purposes of calculation, we define this as a point where the mass of the item is concentrated This is NOT necessarily the geometric center of the item.

For example, this photo clearly shows that the center of gravity on this car that was NOT in the center of the hoist!

Can we use math to find out what went wrong? I think we can. First we need some facts.

This is a Lotus Elise.

The car weighs 1700 lbs.
The length is 150 lbs.
The wheelbase is 90 inches.
About 32 inches of overhang on the front, and 28 on the back.
The front wheels carry 590 lbs of weight (empty gas tank).
The back wheels carry 1060 lbs of weight.

OK, that should be enough.

Here's an outline of the car, with a big black blob showing the location of the heavy engine. Two-thirds of the weight of the car is on the rear wheels when it is unladen (no people, little gas).

The red spots show where the car is lifted by a jack when you have a flat tire.
The orange in the back shows the alternative lift point when you have to raise the entire car. Notice how much farther back it is on the car, underneath the engine.

I've simplified the drawing by taking out the car and using a wedge instead. This is an estimate to show how the weight is distributed. It allows you to see the vertical red line (center of the car, and center point of the flat tire lifting points). The vertical orange line shows the center of gravity, the point about which the weight is equally balanced.

To raise this car safely, you need to position the rear lift on the orange position.

Or as the shop found out, when you take off a front wheel the car falls off the hoist.

Or a wall may fall down.

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