# Relationship between momentum and inertia

1. Dec 11, 2011

### samclocks

1. The problem statement, all variables and given/known data
So, let's say a car is rolling down a ramp. I have to maximize its acceleration, but I am confused about some things. I think that if I increase the car's mass, then it will have more momentum and roll down the ramp faster. But according to Newton's First Law of Motion, an object's mass is inversely proportional to its acceleration. Its saying that having more mass will slow down the car's acceleration. So to me, these two things are contradicting to each other. Should I increase the mass, or decrease the mass of the car to make it roll down the ramp faster?

2. Relevant equations

3. The attempt at a solution

2. Dec 11, 2011

### Andrew Mason

Your question is one that scientists before Galileo argued about. Galileo showed that all objects dropped from the same height take the same time to reach the ground. This means that all objects have the same acceleration due to gravity.

Newton showed that F = ma or a = F/m.

So if acceleration, a, is the same for all objects (about 9.8 m/sec^2) what does that say about the relationship between the force of gravity and mass?

AM

3. Dec 11, 2011

### samclocks

So no matter what the car's mass is, the acceleration will be always 9.8m/sec^2 when rolling down the ramp?

4. Dec 11, 2011

### Andrew Mason

No. That would be the acceleration if the car was dropped. But the acceleration down the ramp will always be the same regardless of the mass of the car, assuming that there are no other forces retarding motion down the ramp.

AM

Last edited: Dec 11, 2011
5. Dec 11, 2011

### netgypsy

Think of a ramp that's only 1 degree above vertical. Surely the car is not going to accelerate at the same rate it would if dropped vertically.

You do realize this does not take in to consideration variations in friction, different types of tires, tire inflation and so on.

6. Dec 11, 2011

### netgypsy

Here's something to think about - why will a somewhat heavier person invariably beat a light person when sledding down a snow covered hill on the same sled? But a really heavy person will be last.