Is a car moving up a hill at a constant velocity accelerating?

[byee614]

This is not a homework problem, I just got into an argument with my friend about a very basic physics problem that I hope you can help us settle.

A car is moving up a hill at a constant velocity. Is the car accelerating?

I know it's simple, but I argued for an hour about this.

 

[Doc Al]

What do you think? (Give a reason for your opinion.)

Note that many arguments are really disagreements about the meanings of words. In physics, terms like velocity and acceleration have precise meanings.

 

[Hootenanny]

constant velocity.

No constant velocity = no acceleration.

-Hoot

 

[byee614]

I think the acceleration is zero. The velocity is constant. Acceleration by definition is the rate of change of velocity with respect to time. If the velocity is not changing, the acceleration is zero.

My friend argues that the car must be accelerating to counteract the force of gravity. He says that the force applied on the car when you press the gas pedal implies acceleration because F=ma.

I countered this argument by saying you have to encorporate every force acting on the car when you use F=ma. There are 3 forces acting on the car. Gravity, the ground pushing on the car perpendicular to the ground, and the force when you press the gas pedal. The NET FORCE is zero. Thus F=ma means that 0=m(0) and acceleration is zero.

But he won't listen.

 

[Doc Al]

You are correct; your friend is not.

 

[Hootenanny]

I countered this argument by saying you have to encorporate every force acting on the car when you use F=ma. There are 3 forces acting on the car. Gravity, the ground pushing on the car perpendicular to the ground, and the force when you press the gas pedal. The NET FORCE is zero. Thus F=ma means that 0=m(0) and acceleration is zero.

In my opinion you are correct on your argument, it is the net that will accelerate a body. The car is still exerting a force, but this force is equal and opposite to the sum of the gravitational force and any frictional forces acting.

-Hoot

[Edit] Doc Al is still faster than me

 

[vanesch]

No constant velocity = no acceleration.

And to be pedantic and confusing:

In *Newtonian* physics, this is correct (if we consider the reference frame with which the velocity is defined, is considered sufficiently inertial).
In *General relativity*, the car is "accelerating away" from its geodesic with about the Earth's gravity acceleration, g... as does a car that is standing still, btw.

I'm saying this because it might be THIS which was at the origin of the discussion ; that using the equivalence principle, that a car at constant velocity (whether it is going uphill or downhill or on a flat road) is undergoing the force of gravity, which is equivalent to AS IF IT WERE ACCELERATING (and "pulling 1 g")

 

[russ_watters]

He says that the force applied on the car when you press the gas pedal implies acceleration because F=ma.

To help him understand why he is wrong, ask him if a book sitting on a table is accelerating. The table is exerting an upward force on it...

 

[Doc Al]

What counts is the net force acting on the car, which is zero. The fact that the car also exerts forces on the road surface (contact force/friction) and on the Earth (gravity) is not immediately relevant to the acceleration of the car.

 

[byee614]

And to be pedantic and confusing:

In *Newtonian* physics, this is correct (if we consider the reference frame with which the velocity is defined, is considered sufficiently inertial).
In *General relativity*, the car is "accelerating away" from its geodesic with about the Earth's gravity acceleration, g... as does a car that is standing still, btw.

I'm saying this because it might be THIS which was at the origin of the discussion ; that using the equivalence principle, that a car at constant velocity (whether it is going uphill or downhill or on a flat road) is undergoing the force of gravity, which is equivalent to AS IF IT WERE ACCELERATING (and "pulling 1 g")

Ok, I showed my friend this thread and he says that this statement about "general relativity" is what he's trying to argue. Which I think is BS because there was no mention of relativity or frame of reference when we first started arguing about it. It was a problem given on a Physics 101 college midterm.

 

[ZapperZ]

Ok, I showed my friend this thread and he says that this statement about "general relativity" is what he's trying to argue. Which I think is BS because there was no mention of relativity or frame of reference when we first started arguing about it. It was a problem given on a Physics 101 college midterm.

YOu are right. Your friend is giving you a bunch of BS.

Constant velocity does not mean there aren't any forces acting on an object. It just means that the vectorial SUM of all these forces produces a net force of ZERO, thus, no acceleration. The car must produce some force to counteract the force of gravity. The presence of such forces does not automatically imply an acceleration.

If he wants to argue about the equivalence of "gravity" and "acceleration", tell him he should at the very least WAIT till he actually understands basic Newtonian kinematics before jumping rear-end first into general relativity.

Zz.

 

[cepheid]

You guys didn't ask him if the hill was curved. If it were, wouldn't that mean his velocity vector would be changing in direction, if not magnitude?

Edit: nevermind. He specified that the velocity was constant from the very beginning of the thread. So I guess the hill is a ramp, by assumption.

 

[Bart001]

I was just about to mention curvature of a hill...
If the hill is a ramp, with Constant slope, then for the time that the car is moving on a ramp with a constant slope then the acceleration is zero..
But if the hill doesn't have a constant slope, or if you are thinking of before the car starts on the hill, till the time its on the ramp, the car had to accelerate when changing its slope...

and don't worry about curvature of Earth or anything. cause as long as the slope is constant, then the cars path is constantly straight in the universe...
basically
constant slope = constant velocity
variable slope = variable velocity ->accerelation

 

[berkeman]

So what you guys are saying is that if I spin a weight around on the end of a string in a circle, the weight is not accelerating? Let's see, what's that term again? Centri-something acceleration...

 

[Hootenanny]

Centri-something acceleration...

That made me giggle. Just to defend myself the OP did state constant velocity, and in circular motion velocity isn't constant.

-Hoot

 

[berkeman]

That made me giggle. Just to defend myself the OP did state constant velocity, and in circular motion velocity isn't constant.

-Hoot

Good point. So that means the OP's friend wins the bet after all, since it's pretty hard to make a car that can sustain a constant velocity of 24,000 mph westward...

 

[russ_watters]

Good point. So that means the OP's friend wins the bet after all, since it's pretty hard to make a car that can sustain a constant velocity of 24,000 mph westward...

Sorry, you're still wrong. If the problem defines a constant velocity, then the velocity is constant. Period.

Besides, in this case, all a constant velocity assumption requries is the assumption of an earth-based reference frame - and that is not only reasonable, it is necessary for the problem to be clear and meaningful.

 

[PatPwnt]

If... gravity is warped space time. Then, are we not accelerating through it as we stand at rest with the ground?

 

[vanesch]

If... gravity is warped space time. Then, are we not accelerating through it as we stand at rest with the ground?

That was the point I tried to make, but admittedly when talking about a car and a hill and so on, one can take it that it is seen in the framework of Newtonian gravity and not in general relativity...

Again, in the Newtonian framework, gravity is a FORCE, and space is Euclidean. As such, no matter what is going on, if the problem states that VELOCITY IS CONSTANT, then, acceleration being the derivative of velocity, and the derivative of a constant being zero, acceleration is zero.
And if you're now talking about "in which frame", well, I think it is fair to say IN THE SAME FRAME AS THE ONE WHERE THE VELOCITY WAS DEFINED.

So there's no discussion: in Newtonian physics, if velocity (in frame A - whatever it is, inertial or not!) is constant, then acceleration (in the same frame A, inertial or not) is zero.

Even if frame A is a non-inertial frame, btw. There will be "inertial forces" and all that working upon the object, but that's not the point. The point is:
acceleration = derivative of velocity

Always.

The link with forces is something else.

Now, in general relativity, things are different. Gravity is not a force, but a curvature of spacetime, and as such, the notion of "derivative" becomes a bit more involved. And then it is fair to say that the best "geometrical" way to define acceleration is by its "deviation from a geodesic", which would, for a car in said situation, correspond to about the acceleration of gravity.

However, such a car would not have "constant velocity as a geometrical object" either! At most one could talk about "constant derivatives of spatial coordinates wrt to the time coordinate in a specific reference frame". And in as much as THIS is accepted as a definition of "velocity", then we're back to the original statement: if we now take it that "acceleration" is the second derivatives of the spatial coordinates wrt the time coordinate in a specific reference frame", then, for the same reason as before: if the FIRST derivative is constant, then the SECOND derivative is zero.