Why Don't Inertia Forces Cancel Out the Accelerating Force in a Moving Car?

[paul_harris77]

I was told today in a lecture that there is such a thing called an inertia force that occurs only when an object is accelerated by a force. I was also told it is equal in magnitude and opposite in direction to the force accelerating the object.
Obviously you can feel this in a car - when you suddenly accelerate forwards, you feel a force pushing you into your seat. But if the force accelerating you and the car is equal and opposite (direction) to the inertia force pushing you into your seat, why don't these forces on your body cancel out?!

Obviously they don't as you are still ultimately accelerating forwards with the car, but why is it that they don't cancel each other out?

 

[Doc Al]

Obviously they don't as you are still ultimately accelerating forwards with the car, but why is it that they don't cancel each other out?

The inertial force only appears when you view things from an accelerating frame of reference. And those forces do cancel each other out! Viewed from the accelerating frame you are at rest, thus the net force (including the inertial forces) is zero.

Of course, viewed from the ordinary inertial frame there is only one "real" force on you--thus you accelerate.

 

[paul_harris77]

Thanks for your reply.

I am finding it really hard to get my head around the reference frames.

Please could you explain the reference frames and the forces present in each a bit more and also why it is that you feel that you are pushed into your seat if there is only one "real" force?

Many thanks

Regards

Paul

 

[Doc Al]

I'll give you a link to get you started; read the section titled "Acceleration in a straight line": http://en.wikipedia.org/wiki/Fictitious_force#Acceleration_in_a_straight_line" (Inertial forces are also called "fictitious" forces.)

 

[paul_harris77]

Thanks for the link.

I think that has made it a bit easier to understand.

Thanks for all your help.

Paul

 

[Cleonis]

I was told today in a lecture that there is such a thing called an inertia force that occurs only when an object is accelerated by a force. I was also told it is equal in magnitude and opposite in direction to the force accelerating the object.
Obviously you can feel this in a car - when you suddenly accelerate forwards, you feel a force pushing you into your seat. But if the force accelerating you and the car is equal and opposite (direction) to the inertia force pushing you into your seat, why don't these forces on your body cancel out?!

Obviously they don't as you are still ultimately accelerating forwards with the car, but why is it that they don't cancel each other out?

Inertia is quite remarkable. How can it be that inertia opposes change of velocity, without preventing change of velocity?

It may be tempting to think of inertia as a kind of friction, a kind of resistance, but there is a crucial difference with friction-like effects. Friction is proportional to velocity. So if you have a constant force, and friction, then you will reach a top velocity. At that top velocity there is so much friction that you cannot accelerate further; all force is spent in overcoming friction. But the opposition from inertia is not proportional to velocity; the opposition from inertia is proportional to the second derivative: acceleration.

So maybe you can think of the opposition from inertia as something that responds and jumps into action when there is change of velocity. That would make it a self-regulating process. If inertia would prevent change of motion if would cut off the very thing that elicits the response.

Well, I haven't told you anything that you don't know already.
We have no theory that addresses the question what the inertia response is. When it comes to inertial all we can do is describe our observations, and try to infer laws of motion from those observations.

Cleonis

 

[Cleonis]

I am finding it really hard to get my head around the reference frames.
Paul

Then don't bother with the reference frames.

For instance, the expression "you are in an accelerating frame of reference". That is just a convoluted and arduous way of saying: "You are being accelerated by a force."

When a force makes your motion deviate from inertial motion then you experience the opposition of inertia to change of velocity.

Always and everywhere inertia is the reference of motion.



An example of that is inertial guidance systems. The navigational system in a car has also an inertial guidance system. The primary reference of a car's navigational system is the GPS-receiver, but the car won't lose track in a kilometers long tunnel with lots of bends.

Highly sensative instruments measure the car's acceleration in any direction, and rotation of the car when it follows a curve in the road. Starting from a known location, with a known velocity and direction of velocity, the computer accumulates data. Having accurate accelerometer data the computer can reconstruct second by second what the instantaneous velocity is. Starting from known location and velocity the computer calculates the current position.

If you have entered a kilometers long tunnel, then on exit the car's navigation unit won't indicate a jump from the tunnel's entrance to the tunnel's exit: the navigation unit will have filled in that part of the journey. That illustrates how inertia can readily be employed to find you current position, starting from a known position, moving with known velocity.

In that sense it's safe to say that inertia is the reference of motion.

Cleonis

 

[Andy Resnick]

I was told today in a lecture that there is such a thing called an inertia force that occurs only when an object is accelerated by a force. I was also told it is equal in magnitude and opposite in direction to the force accelerating the object.
Obviously you can feel this in a car - when you suddenly accelerate forwards, you feel a force pushing you into your seat. But if the force accelerating you and the car is equal and opposite (direction) to the inertia force pushing you into your seat, why don't these forces on your body cancel out?!

Obviously they don't as you are still ultimately accelerating forwards with the car, but why is it that they don't cancel each other out?

"Inertia" is kind of an archaic term. The original use of the term more closely resembled "mass", in that inertia refers to the property of an object to remain at rest, unless disturbed. So 'inertia' is also kind of like 'momentum' (the inertia of a body resists an impressed force).

The usual origin of confusion of 'equal and opposite forces' comes from considering different forces on different objects: here, you referred to one force 'accelerating you and the car', and a second force "pushing you into your seat". Forget the car- all there is, is you and the seat. The seat pushes you forward. The seat accelerates forward at (say) 10 m/s^2. If you do not fall through the seat, then you are also being accelerated at 10 m/s^2. That is the origin of the force you feel (ma = F). The seat, on the other hand, feels you pushing on it with a certain force: if the seat is flimsy, it will break. It is this 'contact force' that is equal and oppositely directed.

 

[Doc Al]

The usual origin of confusion of 'equal and opposite forces' comes from considering different forces on different objects: here, you referred to one force 'accelerating you and the car', and a second force "pushing you into your seat". Forget the car- all there is, is you and the seat. The seat pushes you forward. The seat accelerates forward at (say) 10 m/s^2. If you do not fall through the seat, then you are also being accelerated at 10 m/s^2. That is the origin of the force you feel (ma = F). The seat, on the other hand, feels you pushing on it with a certain force: if the seat is flimsy, it will break. It is this 'contact force' that is equal and oppositely directed.

It sounds like we're talking about different things. I interpreted the first post as asking about "inertial forces" that appear when analyzing things from accelerated reference frames. (I think that a lecturer who introduces such concepts prematurely is doing a disservice to the students. So I may have interpreted that post incorrectly. )

In any case, when you are in an accelerating car and choose to analyze things from that accelerating frame, then the fictitious inertial force that acts on you is equal and opposite to the force of the seat acting on you. Those "forces" are equal and opposite, but they act on the same object--they have nothing to do with Newton's 3rd law. (The seat pushing you forward and you pushing the seat backward are third-law pairs. Nothing "fictitious" about these forces. And they certainly don't "cancel out".)