Can an object maintain uniform motion without any external force?

[Silverbeam]

yes!

But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?

 

[Silverbeam]

I may have misunderstood your question earlier. I thought you were asking if you would need to step on the gas in a car to maintain speed through a turn. It is not necessary for a marble to “step on the gas” as it were.

That is what I meant.

 

[etotheipi]

But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?

sorry, I don't understand what you mean about inefficiency and fundamental physics principles

if the centre of mass of the car is accelerating at some $\ddot{\mathbf{x}} = (v^2 / \rho) \mathbf{e}_n$, then the net force on the car must be $m\ddot{\mathbf{x}} = (mv^2 / \rho)\mathbf{e}_n$. the only external force on the car in such a situation, which can provide that force, is friction.

 

[Dale]

Ok, let’s start with the basics.

You now understand the difference between velocity and speed. Acceleration is a change in velocity. Acceleration, like velocity, is a vector so it has a direction as well as a magnitude. When acceleration is parallel to the velocity then it changes the speed. When acceleration is perpendicular to the velocity then it changes the direction of the velocity.

Force is proportional to acceleration. So in order to go in circular motion you need a force that is perpendicular to the velocity. That force is required in order to turn.

When a marble turns on a smooth track the force is perpendicular to the velocity. So a marble can turn without any additional push from behind. It only needs the push from the side given by the track.

When a car turns, because of how tires work, the force is not perfectly perpendicular to the velocity. There is a little bit of force going anti-parallel to the velocity. So you need a touch of gas to counteract that. You need the push from the side but also a bit of a push from behind due to the inefficiency of turning with tires.

 

[etotheipi]

When a car turns, because of how tires work, the force is not perfectly perpendicular to the velocity. There is a little bit of force going anti-parallel to the velocity. So you need a touch of gas to counteract that. You need the push from the side but also a bit of a push from behind due to the inefficiency of turning with tires.

I think the key point to understand here is that no matter how complex the many different forces between the tyres and the road, the sum of all these forces from the road as well as of course the weight (which, neglecting the air, are the only net external forces on the car) is always proportional [parallel] to the acceleration of the centre of the mass of the car

 

[hmmm27]

If you take a pinball and shoot it directly at (the inside of) a V, it will bounce off one arm, go sideways, bounce off the other, then run back where it came from, experiencing no loss of speed at any time. If you were inside the pinball, you'd get creamed at each bounce because of the massive instantaneous change in velocity.

Now shoot it at a U ; it slides down the inside, curves around the bottom, then procedes to roll back in the opposite direction. If you were inside that one you'd be much more comfortable, since the changing velocity (ie: acceleration) is spread out over time. Like the V example, the speed doesn't change throughout the procedure.

 

[Dale]

I think the key point to understand here is that no matter how complex the many different forces between the tyres and the road, the sum of all these forces from the road as well as of course the weight (which, neglecting the air, are the only net external forces on the car) is always proportional [parallel] to the acceleration of the centre of the mass of the car

Yes agreed.

I only explain about tires because if they actually do the experiment they will find that they do slow down. That isn’t because the theory is wrong, but because cars are complicated and messy machines. The marbles are simpler and easier to analyze. I always prefer simple experiments.

 

[etotheipi]

but because cars are complicated and messy machines. The marbles are simpler and easier to analyze. I always prefer simple experiments.

Yes, exactly! Much better to build up complexity gradually, rather than starting with an extremely complex mechanism like a car! There is much to be gained by carefully understanding the dynamics of a single particle, then generalising to a system of particles, then a system of interacting particles, continuous bodies etc.

e.g. your example of the marble is a much better tool to understand the general motion of a particle than the example with the car that the op kept referring to

 

[russ_watters]

That's what I'm talking about. The ISS is accelerated in classical physics but the accelerometer shows zero. It doesn't work this way.

"Shows zero" and "sums to zero" is the same thing here. I'll explain:

I don't really know what you mean by 'the two accelerations are aligned and subtract to zero' for the ISS case. When we're thinking in terms of GR and all that stuff, if we ignore the atmosphere then there's no force at all on the ISS (apart from the tidal forces, which we can ignore on the small scales), and so no proper acceleration. Rather than 'two accelerations cancelling', probably clearer to say that there was no proper acceleration in the first place.

• A stationary or constant speed car with a 3-axis accelerometer reads 1.0g upward acceleration.
• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.
• Now the car does the same "turn" in a loop. At the top of the loop, the accelerometer reads...

 

[A.T.]

• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.

A banked turn just means that there is less/none lateral tire friction needed, because the normal force has a centripetal component. If the trajectory of the car is still the same as for the flat track, the proper acceleration will be of the same magnitude.

Or do you mean the entire circular flat track is now on an inclined plane?

 

[Delta2]

Acceleration can be resolved into tangential and normal component (check wikipedia link at bottom of this post). The tangential component has direction same as the direction of velocity, while the normal component has direction normal (or equivalently perpendicular) to the direction of velocity.

Seems like your Earth flat friend understands only tangential acceleration and completely ignores normal(or centripetal) acceleration. Tangential acceleration is what causes the velocity to change in magnitude (or simply for an object to speed up or down as you say) but normal acceleration is what causes the velocity to change in direction.

To sum it up: Velocity is a vector it has both magnitude and direction. Tangential acceleration changes its magnitude, normal acceleration changes its direction. Simple as that, tell that to your friend and let me know what he thinks about.

https://en.wikipedia.org/wiki/Acceleration#Tangential_and_centripetal_acceleration

 

[PeroK]

But Dale says the only additional force I need to turn a corner in my car with constant speed is due to inefficiency, not a fundamental physical principle. Why doesn't the same additional force need to be required for the car as for the Moon?

Your basic mistake here is to try to understand the relative complexity of moving on a surface using an engine, rubber tires and friction on the surface - where accelerating, braking and turning are not trivial mechanical processes.

This is why physics is usually begun by studying Kinematics - studying motion without reference to the causes of motion. A good example is, of course, uniform circular motion. You learn about velocity and acceleration vectors, kinetic energy etc.

There is an interesting parallel here between your struggles and why it look until 1687 for someone (Isaac Newton) to formulate the laws of motion. No one previously had seen through the complexities of everyday motion to realize that there were basic fundamental laws governing all motion. And that there was a relationship between the motion of objects on Earth, and the motion of the planets around the Sun. For example, if we look at Newton's first law:

An object will remain at rest or move with constant speed in a straight line, unless acted upon by an unbalanced force.

This flew in the face of previous "Aristolelian" wisdom, which asserted that objects naturally slow down and need a force to keep them moving. And so, the hand of God was needed to keep the planets moving through the heavens, as it were.

Newton was the first to realize that any slowing down is the result of external forces. And, although we cannot avoid these forces on Earth, the movement of the planets do not slow because there are no dissipative forces like air resistance and friction. To quote Newton himself:

Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motion, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.

May I offer a personal view here that it is a tragedy that you, a 21st Century science student, are ignorant of this.

Note that I've underlined where Newton also pointed out that uniform circular motion (in the example of a top - which is an old-fashioned spinning toy) carries on indefinitely unless slowed by the air.

In short, you are making the same mistake as Aristotle and his disciples that energy is needed to maintain circular motion. But, Newton said otherwise in 1687. Note that:

a) A car, as explained above, is relatively inefficient at turning and will slow down relatively quickly.

b) A spinning top may continue for a few minutes perhaps, but air resistance gradually slows it down.

c) The Moon, having neither friction not air resistance to contend with, may continue its orbit about the Earth almost indefinitely.

This is very much the starting point for modern science.

 

[etotheipi]

• A stationary or constant speed car with a 3-axis accelerometer reads 1.0g upward acceleration.
• This car has excellent tires. It turns a hard circle to the left, at 1g. The accelerometer reads 1.0g up and 1.0g to the left, for a sum of 1.4g, at a 45 degree angle from vertical.
• Now the car does the same turn on a 45 degree banked track. To be clear: I mean the same turn, in the plane of the turn, not in the horizontal (Earth's surface) plane. Now we have the upwards acceleration of 1g and a downward and to the left acceleration of 1g at the top of the turn; add them together and you get a resultant 0.7g. Note: the accelerometer doesn't read them as 1g in each axis here because they are starting to oppose each other.
• Now the car does the same "turn" in a loop. At the top of the loop, the accelerometer reads...

I don't quite see what you're getting at here. To compute the proper acceleration in classical physics, you can just sum all of the forces except weight, and divide by the mass.

- The car stationary on the Earth's surface reads 1.0g upward acceleration since there's only an upward normal force on it
- When it does the hard turn, it has an upward normal force on it, and an inward frictional force on it, so the proper acceleration is, say, 1.4g at 45 degrees to the horizontal.
- If it does the turn on a frictionless banked track, it has a normal force with both an upward and horizontal component (this time the horizontal component is provided by the normal force, and not friction), and once again the proper acceleration is, say, 1.4g at 45 degrees to the horizontal
- At the top of the loop the loop, the normal force depends on how fast the car's going, and the proper acceleration will point downward toward the ground with some as of yet unknown magnitude.
- For the ISS, there's no forces at all, and its proper acceleration is zero.

 

[DrStupid]

"Shows zero" and "sums to zero" is the same thing here.

Of course it is. The wording is irrelevant. The centripetal acceleration of the ISS cannot be measured with an accelerometer - no matter how you phrase it.

 

[etotheipi]

Well I didn't mean to start an argument, I was just bringing up the obvious fact that I can write the number 69 as 69 + 8 - 8 if I wanted to, and just add random stuff and subtract it again, but that's detracting from the point.

for the ISS it's not a case of 'two accelerations cancelling', it's a case of there being no proper accelerations at all in the first place. that seems pretty conceptually clear to me?

 

[Herman Trivilino]

To make his point he asked what a car driving around and around in a circle would do if it were accelerating. He says it must speed up.

You're arguing semantics. Acceleration is not equal to the rate of change of speed. It's equal to the rate of change of velocity.

Ask your friend if he can drive his car in a circle on wet ice with bald tires. You need a force of friction between the tires and the road surface to move in a circle.

 

[kinsler33]

Acceleration is a change in the speed and/or the direction of an object. Both a change in speed or a change in direction require an external force. Ask your friend if there's any way to change the speed or direction of an automobile without applying an external force--either the force of friction from the front tires on a turn, or by gunning the engine to make the car go faster.