Undergrad Do objects of different mass but same size/shape accelerate the same?

[greypilgrim]

Hi.

I remember having learnt in school that if you'd like to verify that bodies of different mass accelerate the same in free fall, but don't have a vacuum available, the bodies should be of same size and shape (e.g. spheres).

This made sense to me back then because drag should be the same then. But if I write down Newton's 2nd law with gravitational forces and drag and divide by the mass, mass doesn't go away completely, but is still there in "drag/mass", giving rise to different accelerations.

Am I doing something wrong, or do you really need objects of different size (or shape) for them to accelerate the same?

 

[PeroK]

Hi.

I remember having learnt in school that if you'd like to verify that bodies of different mass accelerate the same in free fall, but don't have a vacuum available, the bodies should be of same size and shape (e.g. spheres).

You may be misremembering. When air resistance is taken into account, bodies of the same mass only fall at the same rate if they are the same size and shape.

This made sense to me back then because drag should be the same then. But if I write down Newton's 2nd law with gravitational forces and drag and divide by the mass, mass doesn't go away completely, but is still there in "drag/mass", giving rise to different accelerations.

Exactly. You would need more drag force on the object with the greater mass.

Am I doing something wrong, or do you really need objects of different size (or shape) for them to accelerate the same?

When air resistance is taken into account, objects generally do not fall at the same rate. The drag force per per unit mass is the variable in the equation.