Does mass affect acceleration on a slope?

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Homework Help Overview

The discussion revolves around the effect of mass on the acceleration of a cart descending a ramp inclined at 10 degrees. Participants explore the relationship between mass, force, and acceleration, referencing Newton's second law and empirical observations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss empirical observations from lab tests and question how to mathematically prove that mass does not affect acceleration. There are inquiries about applying Newton's second law and modeling the forces acting on the cart, including gravitational, normal, and frictional forces.

Discussion Status

The discussion is active, with participants offering guidance on applying Newton's second law and modeling the forces involved. There is an ongoing exploration of how different forces relate to mass and acceleration, but no consensus has been reached.

Contextual Notes

Participants reference specific experiments and observations, such as the feather and marble drop in a vacuum, and discuss the implications of friction and gravitational forces in relation to mass. There is mention of the need for diagrams to clarify the forces acting on the cart.

goonking
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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.
 
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Did you try applying Newton's second law?
 
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:
 
Orodruin said:
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?
 
goonking said:
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?
 
Orodruin said:
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?
 
So how does gravitational force, the normal force, and friction force depend on the mass?
 
Orodruin said:
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
 
goonking said:
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?
 
  • #10
NascentOxygen said:
You haven't drawn the diagram, have you, showing a mass sliding down a slope?
udSFB02.png


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
 
Last edited:
  • #11
So since all of the forces are proportional to the mass, what can you say about the acceleration through Newton's second law?
 

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