Why does mass not affect sliding speed down an inclined plane?

[MeesaWorldWide]

Homework Statement

Two kids of different masses are having a toboggan race down a frictionless hill. Which kid reaches the bottom first: the one with less mass or the one with more?

Relevant Equations

F = ma

I think that both kids experience the same acceleration (irrespective of mass) since the only force pushing them downwards is acceleration due to gravity, which is the same for both of them. Thus, since they start sliding down the hill at the same time (assumption), and are accelerating at the exact same rate, they should both reach the bottom at the same time. However, if F = ma and a is the same for both, then the one with more mass will experience a greater total force, which seems like it would make him reach the bottom first... but how is that possible if they both experience the exact same acceleration?

 

[I_Try_Math]

I'm not sure I understand your question. The larger mass requires a larger force to move it down the incline. This is not inconsistent with it reaching it the bottom of the incline at the same time as the smaller mass.

 

[Orodruin]

F = ma, but gravitational force is also proportional to mass.

 

[kuruman]

See Galileo's tower of Pisa experiment.

 

[hutchphd]

What do you mean by why ?