Mass & Friction: Cart Question Answered

[oobgular]

So suppose two carts roll down a hill. One is more massive than the other, but they both have the same size. Neglecting air resistance, which one reaches the bottom first?

Without friction, I think both reach the bottom at the same time. However my first thought was that the heavier car will have a greater friction force, the lighter one will reach the bottom first. However, I'm not sure if the mass cancels from all the friction terms. Any insight?

 

[haruspex]

So suppose two carts roll down a hill. One is more massive than the other, but they both have the same size. Neglecting air resistance, which one reaches the bottom first?

Without friction, I think both reach the bottom at the same time. However my first thought was that the heavier car will have a greater friction force, the lighter one will reach the bottom first. However, I'm not sure if the mass cancels from all the friction terms. Any insight?

Why not write out the equations and find out for sure?
Another approach is dimensional analysis. Are you familiar with that?

 

[shihab-kol]

Well, let's consider the acceleration, a
F=m.a
a=f/m
So,
a ∝ 1/m
This means greater the acceleration, the lower has to be the mass ( or vice versa)
So, for a greater mass acceleration will be lower
Thus,the lighter cart reaches the ground first for the same force.

 

[haruspex]

a ∝ 1/m

Only if F is the same for both.

 

[shihab-kol]

Only if F is the same for both.

Exactly
thanks

 

[haruspex]

Exactly
thanks

But it isn't.

 

[shihab-kol]

But it isn't.

But that is not specified by oobgular

 

[haruspex]

But that is not specified by oobgular

The question says they are rolling down a hill. It does not say they are being pushed down by some unspecified force. We can safely assume the acceleration is purely a result of gravity.

 

[shihab-kol]

The question says they are rolling down a hill. It does not say they are being pushed down by some unspecified force. We can safely assume the acceleration is purely a result of gravity.

Yes
Then the acceleration is equal for both.

 

[berkeman]

So suppose two carts roll down a hill. One is more massive than the other, but they both have the same size. Neglecting air resistance, which one reaches the bottom first?

Without friction, I think both reach the bottom at the same time. However my first thought was that the heavier car will have a greater friction force, the lighter one will reach the bottom first. However, I'm not sure if the mass cancels from all the friction terms. Any insight?

@oobgular -- is this a question for schoolwork? Or just a general interest question?

If it's for schoolwork, I would expect that there would be more to the problem statement. Like, is just the body of the cart heavier, or the wheels, or both?

If it's for general interest, you probably need to give more thought to the various affects that more weight will have, in order to answer the question well.