Physics question

[poop]

The answer is 0, sure enough. Simple explanation:

at the bottom, the rock is moving 55 mph backwards
the car is moving 55 mph forwards

55-55 = 0

Relative to the road, that is.

 

[poop]

BECAUSE, at the top of the tire, the pebble is going 110 mph.

The average speed is 55 mph.

 

[Handle]

Artemedes... the tire will rotate at different ANGULAR speeds (radians per second) for different radii, but they will maintain the same speed (metres per second). Example... to travel 2PI m/s you need a tire with radius 1m to travel at 1 rev/s or 2PI radians/sec. But if the radius drops to 0.5m, you need to travel at 2 rev/s or 4PI radians/sec to travel at 2Pi m/s. In the question given though, the constant is the 55mph. Since the speed, not the angular speed is constant, there is enough information to answer his question.

 

[raptor13]

Relative to road: 0 mph.

Relative to car: -55 mph.

Relative to top of wheel: -110 mph.



That is all scientific FACT which you'd be stupid to contradict. If I have to explain it, I will, but please don't make me.

 

[Capn]

Sohcrates, speed is a scalar quantity. Velocity must have magnitude and direction.

I really don't think you need much math to prove the slowest speed of the pebble is 0mph. Think about this: The point at which your tire hits the road the tire does not slip. Now assuming the road is not moving, at any instantaneous point in time the part of the tire in contact with the road (since there is no slip) must have the same velocity of the road (0mph). The pebble at some point in time will also be in contact with the road and have slip, therefore the minimum speed is 0mph.

 

[emjem]

Youall talking about the micro view. Cosmically, the pebble is traveling at the rotational speed of the earth, plus the speed of the earth traveling around the sun, compounded by the rate of expansion of the universe plus the unknown speed, if any, of the universe traveling through the void.

Since we do not know the location of the pebble on the surface of the earth, nor the speed at which the universe travels through the void, the answer can not be calculated.

 

[artemedes]

okay, couldn't sleep cause of this damn problem...

This makes sense to me:

relative to the tire it is embedded in 0 mph - it hasn't moved in relation to the tire

relative to the road = 55mph it is moving down the road just like the car (Handle's horizontal speed)

If speed is the measure of the rate of motion then how can the physics lexicon describe something rotating around an object (lets assume constant speed of rotation) as not moving (0mph)especiall when this object is moving along something like a road as in this scenario.

This is why I maintain that we need to know more. The question is so general you do not know what information is really desired here.


Please don't get bent out of shape of you don't agree with this I am just having fun thinking though this problem.

 

[UG]

<...When the pebble is at it's lowest point, when it is touching the ground, what speed is the pebble going?..>

Come on, folks. Think.

The pebble is moving at least 18 miles per second -- Earth's orbital velocity around the sun, not counting Earth's rotational velocity at the tire's latitude, and the sun's orbital velocity around the galaxy's center.

Sheesh.

 

[GoldenBear]

My God look at the original date of this thread..hmm.

 

[Handle]

artemedes... great to see that this interests you. Genuine interest is truly refreshing! Genuine interest may tend to drop off when you take university classes (with lots of math) dealing with questions like this (actually, this would be considered quite easy compared to some of the stuff they make us do).

Relative to the CENTRE of the tire: the speed is equal to 55mph at all times. The velocity is equal to 55mph in the direction tangent to the tire. This is quite a trivial answer because the answer is somewhat obvious.

Relative to an inertial observer on Earth: this is more complicated. You must add the velocity vector of the pebble relative to the centre of the tire to the velocity vector of the centre of the tire relative to the inertial observer. If you think about what I just wrote, it makes intuitive sense. Velocity of pebble relative to centre of tire + velocity of centre of tire relative to observer yields velocity of pebble relative to observer.

The only time the speed of the pebble is zero is when it is contacting the road. This may seem intuitively incorrect, possibly because the pebble is accelerating at this point. Just think about it like throwing a ball in the air. When the ball goes up, it must come down, which means that at some point, the speed of the ball is zero. The acceleration is always constant (9.8 m/s^2 down), but since it is a continuous function, the speed is zero at a point.

 

[emjem]

Old is good!

 

[Handle]

UG... don't forget about the velocity of the galaxy. That isn't constant though, as researchers now believe that not only is the universe expanding, but it is accelerating outward.

That's why everything should be taken in relation to an inertial observer on Earth. Makes everything simpler.

 

[UG]

Handle,

Don't forget the Universe is also rotating.

So many vectors, so little appreciation.

 

[spidey07]

Is not velocity relative as well? I equate speed with velocity (mind you I haven't been in school for a while). Your vector would be measured at a constant rotational velocity of (do the math...circumference of tire/time as measured from the center of the tire).

My point is you cannot measure speed given a single instance in time like &quot;pebble is at the bottom&quot;. But you have already given reference by saying car is traveling 55 mph (humans assume this means traveling down a road in a straight line)

This is way too much like the &quot;your traveling down the road at 120 MPH. You drop an apple out the window, what is the speed of the apple?&quot; C'mon...this is all basic relativity. And has everything to do with the observer. The speed of the apple is 120 MPH...the speed of the apple is 0 MPH. The speed of the appleis 15000 mph relative to the center of the universe. The speed of the apple is xxx relative to the observer.

Somebody do an Einstein train/lightning analogy...I'm going to bed.

 

[Handle]

<< My point is you cannot measure speed given a single instance in time like &quot;pebble is at the bottom&quot;. >>



Yes you can. Even if it was accelerating, you can measure the speed at a single instant of time. That is one of the entire concepts behind calculus, measuring things at an instant. The instantaneous speed is: v=ds/dt where ds is an infinitesimal change in position and dt is an infinitesimal period of time. You measure instants by taking the limit as things approach zero. You'll learn about it in calculus (you may learn to hate it in calculus )

 

[UG]

<... The instantaneous speed is: v=ds/dt where ds is an infinitesimal change in position and dt is an infinitesimal period of time...>

Locally, perhaps. But the universe is comprised of perhaps infinite localities.

Where you are likely is quite different from where everyone/everything else is. Your absolute truth is not someone else's.

Calculus is reductionist. The universe, by nature, cannot be reduced by reason. It is what it is. Calculus is less.

 

[spidey07]

yeah, haven't been in school for 10 years. forgot about integrals and their tremendous power.

Never really did get calc until I finished it (got straight As...just didn't know what it meant). It was only until 4th year hardcore physics/statics/dynamics/chemistry that I truly understood the power.

By the way, your talking calculus to you must understand that you have bounds on your integrals (zero, variable, inf)? If you only have the singular reference in time then you have zero bounds=zero=velocity of the pebble.

 

[Capn]

Graphs for your own enjoyment
Graphs Here, for sale cheap

The first plot is a parametric plot of position of the tire (x vs. y) for the first 5 seconds of the pebble motion. Assuming y is normal to the supposed plane of the earth and x is the direction of the car (for 16&quot; tire). The units on the first graph are feet vs. feet.

The second graph is X position vs. time. Time being the independent variable and X position being the dependent variable. As you can see from the second plot there are places where the slope of the curve (indicating velocity) is zero. So we can conclude that at some point in time the pebble has no velocity in the x direction.

The third graph is similar to the second but instead of X vs. time it is Y (or height of the pebble vs. time) In a similar manner as before we can conclude based upon the fact that there are points on the graph with zero slope (ergo zero velocity) that the pebble at these times has no vertical or Y velocity. Now, if we look at graphs 2 and 3 the points at which there is no X and no Y velocity do coincide when Y=0. Thus we can say that the minimum speed (or the magnitude of the velocity) is definately zero.

 

[MereMortal]

Handle, you misunderstood what point C was in my explanation. It is the point at the center of the tire (where the pebble never resides).

Anyway, my explanation was relative to the road. If this was a HS or undergrad level problem, there would be little chance it was something else. After grading 10 billion problems like this I just assume that they have no effects that make them difficult (and interesting) to solve. Although I do think that some here are adhering to the proverb, &quot;If you can't impress them with intelligence, baffle them with bullshit!&quot;

 

[Handle]

MereMortal: Oops... you're right. Now that I think back, I don't know how I misunderstood that. Sorry.

 

[GreenBeret]

Listen to handle. (and anyone who answers similarly)