How far behind the front wheels is the center of mass located?

[superjen]

To determine the location of the center of mass of a car, the car is driven over a scale. When the front wheels are over the scale, the weight recorded by the scale is 5.70 x 10³ N. When the rear wheels are over the scale, the scale reads 6.30 x 10³ N. The distance between the front and rear wheels is 3.32 m. How far behind the front wheels is the center of mass located?


The equation i was using was

X = m1x1 + m2x2 / (m1+m2)
m1 = 5.70 x 10³ N = 581.039kg
m2 = 6.30 x 10³ N = 642.202kg
X = ?
x1 = 3.32
x2 = 3.32 - x

i don't understand how to fill in the rest. maybe I've gotten something done wrong here! Help will be awesome :)

 

[Dr.D]

Draw a FBD of the car with the reactions that support it. When it is on the scale, one of the reactions id provided by the scale. See if that will get you going.

 

[superjen]

i've tried this, but i still get nowhere.

 

[jack b]

It looks like you are trying to work out the centre of mass treating the car like it is two separate weights, placed at the front and back wheels. I don't think that will work very well. Here is how I would approach the problem, assuming you have learned about moments. If you haven't learned about moments, ignore this post.

When the front wheel is on the scale, you can consider the moments arround the back wheel, as the car is not rotating, the clockwise and anticlockwise moments are equal:
moment due to mass = moment due to force on scale
Mass x g x (3.32-L) = force1 x 3.32

You can do the same when the back wheel is on the scale:
moment due to mass = moment due to force on scale
Mass x g x L = force2 x 3.32

You should then be able to work out L, even withought knowing the mass (or g for that matter)

Hope this helps
Jack

PS: This is my first attempt at answereing questions in this forum. I'm trying to give hints without giving answers. Mods and experienced members feel free to critise.

 

[superjen]

so. say if this was the way i went

Mass x g x (3.32-L) = force1 x 3.32

what would my mass and g be?

 

[jack b]

You don't need to know (unless the question asks for them?). It is possible to work out L by using the two equations I gave together.

g is the accelaration due to gravity is 9.81ms^-2, Mass is unknown, but could also be found from the two equations I gave.