Does mass affect acceleration on a slope?

[goonking]

Homework Statement

A cart goes down a ramp with an incline of 10 degrees with acceleration A. Would adding mass on that cart change the acceleration?

Homework Equations

F = ma

The Attempt at a Solution

so I tested this in lab and no, the added weight didn't affect the acceleration of the cart. It went down at the same rate. How can I mathematically prove this?

I remember an experiment where a feather and a marble dropped at the same rate inside a vacuum so mass didn't affect acceleration in that case.

 

[Orodruin]

Did you try applying Newton's second law?

 

[Simon Bridge]

You cannot prove an empirical truth mathematically.

But you can use F=ma to find that the acceleration predicted by Newton's Law is consistent with observation.
You can also reason by logic that it makes sense.

The most famous version of the feather drop demonstration was done on the Moon:

 

[goonking]

Did you try applying Newton's second law?

how would you apply F=ma in this situation?

if a was the same for both (with and without the added weight)
then m should be proportional to F

but what is F in that case?

 

[Orodruin]

how would you apply F=ma in this situation?

if a was the same for both (with and without the added weight)
then m should be proportional to F

but what is F in that case?

This is whatyou have to model. What forces are acting and what are their directions and magnitude?

 

[goonking]

This is whatyou have to model. What forces are acting and what are their directions and magnitude?

we have friction and Fg x. and Fnormal. is that correct?

 

[Orodruin]

So how does gravitational force, the normal force, and friction force depend on the mass?

 

[goonking]

So how does gravitational force, the normal force, and friction force depend on the mass?

gravitational force = m g

normal = m g

frictional force= coefficient of friction x Fnormal

 

[NascentOxygen]

gravitational force = m g

normal = m g

frictional force= coefficient of friction x Fnormal

You haven't drawn the diagram, have you, showing a mass sliding down a slope?

 

[goonking]

You haven't drawn the diagram, have you, showing a mass sliding down a slope?

oops, Fnormal = Fg y

Fgx is the acceleration of which it goes down the ramp.

F g x = sin theta x Fg

F g y = cos theta x Fg

 

[Orodruin]

So since all of the forces are proportional to the mass, what can you say about the acceleration through Newton's second law?