For an object such as a roller coaster which sits on wheels which undergo rolling without slipping, does changing the total mass of the vehicle change how it accelerates down the incline? I have been studying these kind of scenarios lately and my calculations tell me that a larger mass will result in a larger acceleration but many online sources claim that this is false. I intend to test this myself when I can but until then this is the best I can do to find an answer.
Angular acceleration "α" = acceleration / radius (for the wheels).
Force of static friction on each wheel = kma where "k" is the coefficient for the moment of inertia. I got this equation from considering static friction acting at a distance "r" causing a torque which is equal to Fr = km(r^2)α and simplifying.
So nkma - MgSin(theta) = -Ma where "n" is the number of wheels and "M" is the total mass with "m" being the mass of a wheel. I took static friction as positive pointing up and made "Ma" negative to indicate the downward acceleration.
Solving for the acceleration I find that you get:
a = MgSin(theta)/(nkm + M)
I ran some calculations to see how this plays out and found that although changing the total mass will increase the acceleration, the change is quite small unless the change in total mass is quite large. I'm assuming everything else is equal of course such as number of wheels, the value of "k" and angle of incline. I'm also ignoring air resistance and other resistances such as rolling resistance.
So am I right here or have I made another mistake?