# Center of mass of a vehicle

#### Altairs

ah … because then I can add the two weights to give me the total weight of the vehicle.

(I know you want to add the weights of all the components … but I think my way is simpler! )
I will weigh the whole car on the platform.

Surely the weight on the platform is the reaction?
But those reactions changes with the position of tyres over the platform. And consequently the COM calculated would change.

#### tiny-tim

Homework Helper
But those reactions changes with the position of tyres over the platform. And consequently the COM calculated would change.
But the COM does change if the car is tilted, and the reactions change accordingly, and the weights on the platform equal those reactions.

#### Altairs

I wasn't talking about the tilting operation. The other one, where you said that simply putting the tyres over the platform would give the reactions. What I am saying is that, those reactions will change with the position of tyres over the platform and those reactions would therefor be dependent on the position of the tyres and wouldn't be 'absolute'.

Gold Member

#### tiny-tim

Homework Helper
What I am saying is that, those reactions will change with the position of tyres over the platform and those reactions would therefor be dependent on the position of the tyres and wouldn't be 'absolute'.
Hi Altairs!

I'm wondering whether we're talking about the same thing.

What do you mean by "the position of tyres over the platform"?

I've never used one of these platforms, but I was assuming that it didn't matter which part of the platform the tyre was on.

Am I missing the point you're making?

#### Altairs

Okay. I'll explain what I perceived from your posts.

That you said that what I need to do in order to find reactions at the tyres is simply to put the front two tyres and get their reactions and repeat this for the back two tyres. My point here is that the reading on the scales wouldn't be the 'real' or 'absolute' reaction of the tyres as the reading would change with the amount of portion of car over the platform with even only two tyres over it. So, the readings would change if we move the car around.

#### tiny-tim

Homework Helper
My point here is that the reading on the scales wouldn't be the 'real' or 'absolute' reaction of the tyres as the reading would change with the amount of portion of car over the platform with even only two tyres over it. So, the readings would change if we move the car around.
Hi Altairs!

The reading doesn't change with the amount of portion of car over the platform, it only depends on which tyres are on the platform (and on the angle, of course).

If we put the front two tyres on the edge of the platform, and the rest of the car over solid level ground, the weight shown will be exactly the same as if we move the car forward so that the rear two tyres are almost on the platform.

#### Altairs

Then all I need to do is to weigh the front two tyres and divide it by two (assuming that they support equal weight) and do the same for the back two tyres.

#### tiny-tim

Homework Helper
Then all I need to do is to weigh the front two tyres and divide it by two (assuming that they support equal weight) and do the same for the back two tyres.
Yup!

(except why bother to divide by two … you only need the ratio … )

#### Altairs

When I'll take side view and front view than I'll only be considering the two tyres in view then won't I be assuming that the whole weight of the car is supported by those two tyres ?

#### tiny-tim

Homework Helper
Hi Altairs!
When I'll take side view and front view than I'll only be considering the two tyres in view then won't I be assuming that the whole weight of the car is supported by those two tyres ?
(I assume that by "view" you mean "on the platform")

Nooo … the total weight of the car is still supported by all four tyres.

You are measuring how much is supported by those two (and the rest of the total weight of course is supported by the other two, and you take the ratio).

(oh … but why take "side view" at all, if the c.o.m. is in the middle?)

#### Altairs

No with side view I mean the real side view. With the doors in view. By taking moment along one tyre and as I would know the reaction and the total mass of the whole car won't I be able to find the centre of mass in one axis ?

Doing the same for the front view (the windscreen) one I can find the COM in another axis ?

Is this feasible ?

#### tiny-tim

Homework Helper
No with side view I mean the real side view. With the doors in view. By taking moment along one tyre and as I would know the reaction and the total mass of the whole car won't I be able to find the centre of mass in one axis ?

Doing the same for the front view (the windscreen) one I can find the COM in another axis ?

Is this feasible ?
Yes, that's right … if you know the total weight, then you can find the x-coordinate of the c.o.m. by weighing the front tyres on the flat, the y-coordinate of the c.o.m. by weighing one set of side tyres on the flat, and the z-coordinate of the c.o.m. by weighing any pair of tyres on a slope.

#### Altairs

Right. Let's say that in the side view the tyres are T1 and T2. And in front view the tyres are T1 and T4. For calculating the coordinate in the side view I'll only need one of T1 and T2 and in the same way for calculating the coordinate in the front view I only need one of T1 and T4. I hope that I am right here.

#### tiny-tim

Homework Helper
Right. Let's say that in the side view the tyres are T1 and T2. And in front view the tyres are T1 and T4. For calculating the coordinate in the side view I'll only need one of T1 and T2 and in the same way for calculating the coordinate in the front view I only need one of T1 and T4. I hope that I am right here.
I'm confused … are you saying that you only need to put one tyre on the platform each time?

i] You can't put one tyre on, and then just double the weight;

ii] it's physically much easier to put two tyres on anyway, isn't it?

#### Altairs

I will be weighing two tyres at once.

My confusion still exists. I'll explain.

If there are two tyres over the platform (let's say front two) then changing the position of the car over the platform in such a way that rear two tyres are still on the ground should change the reading on the meter because the more the portion of the car is over the platform the more the reading will be. Is this the case ? You have already said both yes and no in previous posts.

#### Altairs

If there is the whole car on the platform and we lift it up at an agle such that it is just enough to put the rear two tyres in air and then take the reading. Then repeat this by tipping it on the back tyres then will the two readings equal the weight ?

#### tiny-tim

Homework Helper
If there are two tyres over the platform (let's say front two) then changing the position of the car over the platform in such a way that rear two tyres are still on the ground should change the reading on the meter because the more the portion of the car is over the platform the more the reading will be. Is this the case ? You have already said both yes and no in previous posts.
It's definitely no … the reading depends only on which tyres are on the platform (and the angle of the car), not on the "overlap".

I didn't intend to say "yes" … where do you think I did?
If there is the whole car on the platform and we lift it up at an agle such that it is just enough to put the rear two tyres in air and then take the reading. Then repeat this by tipping it on the back tyres then will the two readings equal the weight ?
Do you mean lifting the rear tyres just an inch off the ground, or do you mean "balancing the car on its front legs"?

#### Altairs

Do you mean lifting the rear tyres just an inch off the ground, or do you mean "balancing the car on its front legs"?
Just an inch. BTW what's the difference?

#### Altairs

It's definitely no … the reading depends only on which tyres are on the platform (and the angle of the car), not on the "overlap".
It means that while the front two tyres are over the platform the reading will remain constant and it will shoot to the maximum value (weight) only when the previous two tyres are also over the platform. And in this duration (i.e. just before the rear two tyre are on the platform and just after the front two tyres are over platform) the reading won't change ?

#### tiny-tim

Homework Helper
Just an inch. BTW what's the difference?
Well, if you lift the rear tyres an inch off the ground, then that means that you are now supporting the same weight that the ground was supporting … so the platform reading (from the front tyres) will be the same.

But if the car is balanced (so that if you let it go, it would stay there), then all the car's weight is supported by the front tyres, and so the platform reading will show the whole weight.

#### Altairs

Here it is.

But the problem is that lets say at one time only 1/4 th of the car is on the weighing platform with the front wheels.

Next time, half of the car is over the platform but still only the front two tires are over the platform. Won't the readings change ?
Yes you can … if you put one or two tyres on the scale, and the others on the ground, then the scale will measure the weight that the scale is supporting.

By Newton's third law, that's equal and opposite to the (vertical component of the) reaction at that point!

#### tiny-tim

Homework Helper
It means that while the front two tyres are over the platform the reading will remain constant and it will shoot to the maximum value (weight) only when the previous two tyres are also over the platform.
Yes, that's right … drive the car slowly forward,and the platform reading will stay the same right until the rear tyres reach the platform.

#### Altairs

Well, if you lift the rear tyres an inch off the ground, then that means that you are now supporting the same weight that the ground was supporting … so the platform reading (from the front tyres) will be the same.

But if the car is balanced (so that if you let it go, it would stay there), then all the car's weight is supported by the front tyres, and so the platform reading will show the whole weight.
The idea is that the whole car will be over the platform. Then the car will be lifted from it back by men or something so that they will be standing on the ground. My point was that there is no difference in this and simply putting front two tyres over and rear two tyres off the platform but my friends wouldn't agree. Second point is that will this procedure (the tipping one) when performed for both the front and the rear tyres equal the weight ?

#### tiny-tim

Homework Helper
Here it is.
Altairs said:
But the problem is that lets say at one time only 1/4 th of the car is on the weighing platform with the front wheels.

Next time, half of the car is over the platform but still only the front two tires are over the platform. Won't the readings change ?
Ah … now I see …

No, when you said 1/4 th of the car, I thought you meant that only one tyre was on the platform

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