# Car Power/Torque to Weight — non linear?

( Hello, my first question ... )

Assume two cars, each with exactly the same body, but one a scaled down version of the other (hence, aerodynamics approach equality):

"junior car" - has an engine that delivers 200 ft-lbs of torque and weighs 3000 pounds

"base car" - has an engine that delivers 400 ft-lbs of torque and weighs 6000 pounds

My question is this: isn't the effect of "mass" non-linear? Doesn't the junior engine have less than half the work to do to accelerate than the base car because momentum, friction, drive train length, drive train mass, turbo charger mass, gearing all drain power in a non-linear way; the larger a vehicle you make? I've done the G-search thing and haven't found any answer to this type of "real world" condition.

(Or, asking the same thing in a different way: would the two vehicles above accelerate with identical track times?)

Thanks for responding.

.R.

• I agree with Harlemme's answer, but you say isn't the effect of "mass" non-linear. Just on that point, if you take $a = F/m$ and then double both the force and the mass, I would think about whether that would be linear. It's not directly applicable to ordinary cars, because the force part is hard to work out directly, but it would be applicable if you had two toy cars, one twice the mass of the other, that you push started. How much more force you would need to give the heavier car, to get the same acceleration for both? – user108787 Dec 11 '16 at 2:42