Relationship between momentum and inertia

[samclocks]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[Andrew Mason]

Homework Statement

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?

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

 

[samclocks]

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

 

[Andrew Mason]

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

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

 

[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 into consideration variations in friction, different types of tires, tire inflation and so on.

 

[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.