# Thought Experiment: same objects different mass but same acceleration due to friction

I was just thinking about inertia and i understand that smaller masses accelerate faster under the same force. Then I thought about an objects acceleration under the frictional force.
Now say there were two objects of the same material, same volume but different masses. They are in contact with the same surface (so the coefficients of friction are equal). Now theoretically these objects should have the same acceleration if friction is the only force present.

Fg = Fn = mg
Ff = (mu)Fn = (mu)mg
Fnet = (mu)mg

Fnet = ma
a= F/m
a= (mu)mg/m ------> mass cancel
a = (mu)g

So by this equation we can say that since mass cancel, it is irrelevant in determining the acceleration of any two objects. So this makes sense to me calculation wise but I have trouble grasping that in real life an object of say 5 kg and 50 kg even though they are of the same material will slow down at the same rate. Does this make any sense?

The thing I want to know is how two objects can be made of the same material and have the same volume, but have different masses. To me, that's impossible.

One could be more dense. The thing that doesn't matter. They could also be different volumes and their force of friction would remain the same because it depends on mass not volume.

Hmm, so its hard imaging that a 1kg weight will slow down as fast as a 100kg weight when sliding across the same surface in real life. Yeah, I can see why that wouldn't make sense intuitively. Perhaps it would help to consider how external forces influence these. It would take 100x as much force to keep the 100kg weight moving at a constant velocity than to keep a 1kg weight moving at a constant velocity. So while the 1kg weight will slow down just as fast as the 100kg weight, it will be a 100 times easier to push again and keep going. Also in real life there can be traction, which can complicate things.

Hopefully that helps, I'm new.. So.. yeah!

Thanks.

In your example it is just coincidence that the mass "cancels" out. Not even coincidence, you specifically engineered the problem in order to have the mass cancel out. However, in real life rarely does that happen. You have to take both mass and friction into account when determining a motion of an object, and therefore neither is irrelevant. In fact the mass (and force) is of fundamental importance for how fast the object will accelerate. The friction merely modifies the motive force, but as you well know the equation F=ma still needs to be used.

It shouldn't be hard to grasp how a lighter object can be harder to accelerate than a heavier one, though. Just yesterday I was moving a large dresser across the floor, and it was quite hard to push (although I did it ). A boulder of the same weight set tightly on the ground, however, might as well be impossible to move for a person. Yet, a car an order of magnitude heavier can be relatively easy to push due to the fact that it's on wheels.