What is the role of mass in understanding inertia and its effect on motion?

[sgstudent]

Hi guys, I read about inertia on various websites and my textbook but I don't quite understand it. I just don't get the general understanding of it. I read that mass is the only variable, however since F=ma, and a=0 so won't there be no variables? My teacher gave us this question: you push an object on the moon and the Earth which is harder to move. I thought it was Earth as friction is greater. But the answer was the same as inertia is dependant only on mass.

I hope you guys can clear out any misconceptions and help me understand thus. Thanks so much for all the help!

 

[Ken G]

The teacher should have also said you are pushing the object horizontally over a frictionless surface! That is the way to isolate on the issue of inertia. If you are pushing the object upward, then gravity complicates things, and if you are pushing it against friction, then friction complicates things. But if you have no friction, and no gravity to worry about, then F=ma implies a=F/m, so F produces a but the a will be less if m is greater. That's what inertia means-- how much a you get for a given F, and you get less a from the same F if inertia (m) is higher.

 

[sgstudent]

The teacher should have also said you are pushing the object horizontally over a frictionless surface! That is the way to isolate on the issue of inertia. If you are pushing the object upward, then gravity complicates things, and if you are pushing it against friction, then friction complicates things. But if you have no friction, and no gravity to worry about, then F=ma implies a=F/m, so F produces a but the a will be less if m is greater. That's what inertia means-- how much a you get for a given F, and you get less a from the same F if inertia (m) is higher.

Oh, so there is acceleration when dealing with inertia? Then for a car case, when we brake and get lashed forward how do we apply inertia? Thanks for the help!

 

[haruspex]

Inertia is the tendency of objects to keep moving at the same speed in the same straight line. It requires a force to change this, and the more mass the higher the force needed for the same rate of change (acceleration).
Note that acceleration doesn't just mean going faster. That's only when some of the acceleration is in the same direction as the movement. Acceleration in the reverse direction is what is more commonly called deceleration, while acceleration at right angles will make the object change course.

 

[jay.yoon314]

Oh, so there is acceleration when dealing with inertia? Then for a car case, when we brake and get lashed forward how do we apply inertia? Thanks for the help!

A useful way of thinking about it is breaking up that process into two phases, the first being after you brake and then get lashed forward until immediately before the seat belt becomes taut, and the second beginning where the first ends.

In the first phase, you're still going forward because you have mass, and hence inertia. The fact that you pressed the brakes, at least directly, does nothing to slow you down personally, as the brake force acts on the car, and not you. So some other force must slow you down, preferably before you hit the windshield.

But during the second phase, where your belt becomes taut and the "force" of its tightness "pulls" you back into your seat so that both you and the car that you're in come to a stop, the reason that the pulling force is even necessary to stop you from continuing to move forward is because you have mass, which is inertia.

So inertia is "responsible" for both the fact that you lurch forward after you press the brakes, and the fact that you are pulled back when and only when your seat belt becomes taut.

The former is an example of inertia as a property of matter in general. What I mean by "in general" is that any nonzero mass would keep going at the speed that it was going (the speed of the car before you pressed the brakes) before. More specifically, regardless of whether you weighed 50 kg or 500 kg, you would continue to move at 30 mph if you were moving at that speed prior to slamming the brakes. This observation that matter keeps moving if it is not subject to any net external force is thus a general property of all objects with mass, no matter what numerical quantity that mass may be. During the lurch forward, no force is being exerted on you; the fact that you slammed the brakes only means that a force has been exerted on the car, and you and your car are, again, two different objects!

In the latter case, when you are pulled back by the seat belt, a force is being exerted on you. Now, since we're dealing with a nonzero force, it actually matters what the mass is, as both of these variables, jointly, will determine the acceleration.

So in essence, if the force exerted on an object is nonexistent, then all masses, no matter how small or large, will respond in the same way - nothing changes. For that reason, it is not necessary to know what the mass of that object happens to be, although it certainly doesn't hurt (it would just happen to be extraneous information). If the force exerted on an object is nonzero, then knowing the mass of that object becomes absolutely essential to "predict" its future - that is, to know the instantaneous acceleration it will undergo.

In a world without forces, it doesn't matter what your mass is. Everything either moves in a straight line at the same speed or is perpetually stationary. But a world without forces would have to be a world without masses (because of gravity).

Hope this helps.

 

[AbsoluteZer0]

Inertia is the resistance to force. The more mass an object has, the more inertia. The more inertia an object has, the more force is needed to produce acceleration.

One example is when skydiving. Let's say there is skydiver A and skydiver B. Skydiver A weighs 80 kg and Skydiver B weighs 90 kg. Skydiver B will fall a greater distance before reaching terminal velocity than Skydiver A. (Terminal velocity is reached when an object in free fall stops accelerating. This occurs when the acceleration due to gravity is canceled out by air resistance.) Because Skydiver B weighs 10KG more than Skydiver A, he has a greater resistance to air resistance and is able to fall farther because he has more mass.

There are two formulas for finding acceleration.

1) A = ΔV/T, where A is Acceleration, ΔV is change in velocity, and T is the time interval
2) A = F/M, where A is acceleration, F is the net force, and M is the mass.

For A = F/M, when you increase the value of M, the acceleration produced decreases. When you decrease the value of M, the acceleration produced increases.

 

[Ken G]

Inertia is the resistance to force. The more inertia an object has, the more force is needed to move it.

Be careful-- it is important to say this correctly: the more inertia (mass) an object has, the more force is needed to get a given acceleration (not to "move" it).

For example, it is much easier to pickup a 5lb rock than it is to pick up a 50lb boulder.

That is potentially confusing. In Einstein's model of gravity (general relativity), your statement is indeed a reflection of inertia, but most people know Newton's model of gravity instead, and in that model, it is not. In Newton's model, gravity is a force, so an object with more mass experiences a larger gravitational force. Thus, to lift the object at all (even with very tiny acceleration), you need more force on the more massive object, to balance gravity. But these are balanced forces, so have nothing to do with inertia (which relates to how much acceleration you get when the forces are unbalanced). So if the OPer is thinking in terms of Newton's model of gravity, then your answer will get them very confused about what inertia is. Of course, Einstein's model includes the "equivalence principle", and in that situation, your description is indeed equivalent to inertia, so it's not formally wrong, but I fear it will confuse the OPer.

Important Note: The difference between velocity and acceleration is that velocity is vector while acceleration is scalar.

No, acceleration is also a vector (as are ΔV/t and F/m), see haruspex's post above.

 

[Bob S]

Inertia is the tendency of objects to keep moving at the same speed in the same straight line. It requires a force to change this, and the more mass the higher the force needed.......

This is essentially Newton's definition of inertia, and my college textbook (Becker, Intro. to Theoretical Mechanics) actually states that the "quantitative measure of inertia is mass. "

However, photons have momentum, and a force is required to change the direction of a photon beam. So if mass is the criteria for having inertia, then stating that "Inertia is the tendency of objects to keep moving at the same speed in the same straight line. It requires a force to change this..." is insufficient to exclude massless photons.

 

[AbsoluteZer0]

Be careful-- it is important to say this correctly: the more inertia (mass) an object has, the more force is needed to get a given acceleration (not to "move" it).
That is potentially confusing. In Einstein's model of gravity (general relativity), your statement is indeed a reflection of inertia, but most people know Newton's model of gravity instead, and in that model, it is not. In Newton's model, gravity is a force, so an object with more mass experiences a larger gravitational force. Thus, to lift the object at all (even with very tiny acceleration), you need more force on the more massive object, to balance gravity. But these are balanced forces, so have nothing to do with inertia (which relates to how much acceleration you get when the forces are unbalanced). So if the OPer is thinking in terms of Newton's model of gravity, then your answer will get them very confused about what inertia is. Of course, Einstein's model includes the "equivalence principle", and in that situation, your description is indeed equivalent to inertia, so it's not formally wrong, but I fear it will confuse the OPer.
No, acceleration is also a vector (as are ΔV/t and F/m), see haruspex's post above.

All right, thanks mate.
It looks like i'll have to do a bit of studying as well.
So with Newton's model, the more inertia an object has the more gravity acts upon it? And when the force of gravity is greater, the force needed to balance gravity is also greater?

Thanks,

 

[Ken G]

So with Newton's model, the more inertia an object has the more gravity acts upon it? And when the force of gravity is greater, the force needed to balance gravity is also greater?

Exactly. The connection between inertia and the force of gravity is just a coincidence in Newton's picture, which was the big weakness that Einstein corrected (when he came up with the idea that having a force of gravity is equivalent to being in an accelerating reference frame and not noticing it).

 

[sgstudent]

Oh, so inertia is the resistance to accelerate. So when I brake in the car, I am decelerating but because of inertia I continue to move forward which is the process of slowing me down? Is this correct? Thanks for all the help guys!

 

[stacybyars]

Inertia is the tendency of objects to keep moving at the same speed in the same straight line. It requires a force to change this, and the more mass the higher the force needed for the same rate of change (acceleration).
Note that acceleration doesn't just mean going faster. That's only when some of the acceleration is in the same direction as the movement. Acceleration in the reverse direction is what is more commonly called deceleration, while acceleration at right angles will make the object change course.

I agree, great answer