# Homework Help: Does mass affect acceleration on a slope?

1. Mar 18, 2015

### goonking

1. The problem statement, all variables and given/known data
A cart goes down a ramp with an incline of 10 degrees with acceleration A. Would adding mass on that cart change the acceleration?

2. Relevant equations
F = ma

3. 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.

2. Mar 18, 2015

### Orodruin

Staff Emeritus
Did you try applying Newton's second law?

3. Mar 18, 2015

### 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:

4. Mar 18, 2015

### goonking

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?

5. Mar 18, 2015

### Orodruin

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

6. Mar 18, 2015

### goonking

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

7. Mar 18, 2015

### Orodruin

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

8. Mar 18, 2015

### goonking

gravitational force = m g

normal = m g

frictional force= coefficient of friction x Fnormal

9. Mar 18, 2015

### Staff: Mentor

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

10. Mar 18, 2015

### goonking

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: Mar 18, 2015
11. Mar 18, 2015

### Orodruin

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