A car is going 55 mph. There is a pebble stuck in the tire. When the pebble is at it's lowest point, when it is touching the ground, what speed is the pebble going? This is not a trick question.
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-mosdef
Physics question
- Thread starter mosdef
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Consider that the pebble is rotating opposite the direction that the car is moving. I'm really not sure if it's going back, forward, or not moving relative to a viewer on the side of the road.
-mosdef
-mosdef
What's the deal with konichiwa's post first showing up, then KameLeon's post showing up before his?
-mosdef
-mosdef
0 mph.
The pebble travels in arcs, at the bottom of the arc it has a velocity of 0, at the top it reaches it's maximum of 55 mph.
Viper GTS
The pebble travels in arcs, at the bottom of the arc it has a velocity of 0, at the top it reaches it's maximum of 55 mph.
Viper GTS
it's going 0 mph in the same direction as the car but wouldn't it be something along the lines of 55mph * pi.
I'm waiting until next semester to taky physics if my post seems to make no sense.
edit: wait you nees to know what the radius of the tire is. The size of the tire will have an effect on this.
at least i think so.
I'm waiting until next semester to taky physics if my post seems to make no sense.
edit: wait you nees to know what the radius of the tire is. The size of the tire will have an effect on this.
at least i think so.
Visualise it like this:
The wheel is attached to the car, so
the wheel as a whole must be doing 55.
Draw a horizontal line through the
center of the wheel. Any point on the
outside edge of the wheel ABOVE THE HORIZONTAL LINE
is traveling a little FASTER than the wheel as a whole,
because the point is moving FORWARD ON THE CAR as well as
forward WITH THE CAR.
Any point on the outside edge of the wheel BELOW THE HORIZONTAL LINE
is traveling a little SLOWER than the wheel as a whole,
because the point is moving BACKWARD ON THE CAR as well as
forward WITH THE CAR.
When the pebble hits the ground, it is in the latter
situation, traveling a little SLOWER than the car.
(In fact, at this position, the pebble is traveling
at it very SLOWEST rate of speed.) But it's not much
slower than the car... the exact speed depends on
the diameter of the tire.
The wheel is attached to the car, so
the wheel as a whole must be doing 55.
Draw a horizontal line through the
center of the wheel. Any point on the
outside edge of the wheel ABOVE THE HORIZONTAL LINE
is traveling a little FASTER than the wheel as a whole,
because the point is moving FORWARD ON THE CAR as well as
forward WITH THE CAR.
Any point on the outside edge of the wheel BELOW THE HORIZONTAL LINE
is traveling a little SLOWER than the wheel as a whole,
because the point is moving BACKWARD ON THE CAR as well as
forward WITH THE CAR.
When the pebble hits the ground, it is in the latter
situation, traveling a little SLOWER than the car.
(In fact, at this position, the pebble is traveling
at it very SLOWEST rate of speed.) But it's not much
slower than the car... the exact speed depends on
the diameter of the tire.
MereMortal
Golden Member
- Oct 16, 2000
- 1,919
- 2
- 81
The pebble is going 0 mph when it touches the ground.
Whenever you have combined translational motion of a center of mass and rotation about that center of mass, it is equivalent to a pure rotation about the contact point.
For example, take three points on the wheel: T is at the topmost point, C is at the center, and B is at the bottom.
1) If the motion was purely translational, the velocities at all points would be that of the center of mass (C), Vcm=55mph.
2) If the motion was purely rotational, Vc=0, Vt=wR=Vcm, Vb=-wR=-Vcm, where w=rotational velocity, and R=radius of tire.
3) Combining these two results yields Vc=Vcm=55mph, Vt=2Vcm=110mph,and Vb=0mph. This is the same result as taking a pure rotation about point B.
Whenever you have combined translational motion of a center of mass and rotation about that center of mass, it is equivalent to a pure rotation about the contact point.
For example, take three points on the wheel: T is at the topmost point, C is at the center, and B is at the bottom.
1) If the motion was purely translational, the velocities at all points would be that of the center of mass (C), Vcm=55mph.
2) If the motion was purely rotational, Vc=0, Vt=wR=Vcm, Vb=-wR=-Vcm, where w=rotational velocity, and R=radius of tire.
3) Combining these two results yields Vc=Vcm=55mph, Vt=2Vcm=110mph,and Vb=0mph. This is the same result as taking a pure rotation about point B.
The question didn't state a frame of reference.
But, assuming we use the ground/earth: 0mph.
Relative to the car: -55mph. (the negative direction would be towards the back of the car)
(edit: physics is easy; typing is hard)
But, assuming we use the ground/earth: 0mph.
Relative to the car: -55mph. (the negative direction would be towards the back of the car)
(edit: physics is easy; typing is hard)
When I drive anywhere, I do not impart a velocity to the road. The road has 0 velocity before and after I drive over it.
When the imbedded pebble comes in contact with the road, it has the velocity of the road (unless your tires are slipping).
Therefore the answer would have to be 0.
When the imbedded pebble comes in contact with the road, it has the velocity of the road (unless your tires are slipping).
Therefore the answer would have to be 0.
The answer is Nil.
The time frame that is being recorded is when the pebble is at the lowest point(on the road). Assuming this is a perfectly round tire with no distortion of the tire due to car weight. The pebble can only be on the ground at one instant.
So if it is only on the ground for one instant there is no way to messure the speed of the pebble as there is no reference point.
This is all of course conjecture. This what I've deducted from reading many Michio Kaku books.
The time frame that is being recorded is when the pebble is at the lowest point(on the road). Assuming this is a perfectly round tire with no distortion of the tire due to car weight. The pebble can only be on the ground at one instant.
So if it is only on the ground for one instant there is no way to messure the speed of the pebble as there is no reference point.
This is all of course conjecture. This what I've deducted from reading many Michio Kaku books.
Are you looking for a vector (magnitude and direction) Better yet, do you want the radial velocity or linear velocity?
I believe MereMortal has the right answer and explanation for the most part. But when the pebble is at the centre of the vertical (y) height of the wheel, the speed would not be 55mph. Its HORIZONTAL (x) speed component would be 55mph, but its actual speed at that point would be 55mph in the x-direction and 55mph in the y-direction, which yields a speed of (55^2 + 55^2)^(1/2), 45 degrees from horizontal.
The motion of the pebble is that of a cycloid, hence, this motion is described as cycloidal motion. When doing a question like this, it is useful to consider two frames of reference. One is totally fixed (not moving) and the other one is centered in the middle of the tire. The second frame of reference has a speed of 55mph relative to the first frame. The pebble has a speed about the second frame of reference which can be described with a simple circle. Adding the vectors allows you to calculate the total speed.
Now, if this question were more complicated (i.e. car is accelerating uniformly from 0 to 50mph. If it takes 30 seconds to reach 50 mph, what is the speed of the pebble after 8 seconds?) Then you need other correction terms, and the problem gets more complicated (like when Coriolis acceleration enters the picture).
Ah... don't you love first year university courses in dynamics.
The motion of the pebble is that of a cycloid, hence, this motion is described as cycloidal motion. When doing a question like this, it is useful to consider two frames of reference. One is totally fixed (not moving) and the other one is centered in the middle of the tire. The second frame of reference has a speed of 55mph relative to the first frame. The pebble has a speed about the second frame of reference which can be described with a simple circle. Adding the vectors allows you to calculate the total speed.
Now, if this question were more complicated (i.e. car is accelerating uniformly from 0 to 50mph. If it takes 30 seconds to reach 50 mph, what is the speed of the pebble after 8 seconds?) Then you need other correction terms, and the problem gets more complicated (like when Coriolis acceleration enters the picture).
Ah... don't you love first year university courses in dynamics.
HomeBrewerDude
Lifer
- Jan 18, 2001
- 14,465
- 1
- 0
Assuming the car has zero acceleration, the pebble would have a constant rotational speed regardless of where it is in the rotational cycle. This speed depends on the radius of the tire.
If you assume the question is asking for a translational velocity, then the pebble is going 0 mph relative to the road (otherwise the tire is slipping over the surface of the road and it is impossible to know the speed of the pebble b/c you don't know the rotation rate of the tire). Therefore, the pebble is moving -55 mph relative to the car.
If you assume the question is asking for a translational velocity, then the pebble is going 0 mph relative to the road (otherwise the tire is slipping over the surface of the road and it is impossible to know the speed of the pebble b/c you don't know the rotation rate of the tire). Therefore, the pebble is moving -55 mph relative to the car.
troglodytis
Golden Member
- Nov 29, 2000
- 1,061
- 3
- 76
zero zero
but it sure is accelerating!
and MereMortal has got a nice simple reason...and true too!
friction friction ra ra ra
but it sure is accelerating!
and MereMortal has got a nice simple reason...and true too!
friction friction ra ra ra
Sorry, not enough info to answer your question.
The only thing we know is that pebble is moving around a tire, on a car that is going 55mph. Speed is a measure of motion, so I don't see how 0mph works. Even if it is in relation to the road, saying it is 0mph is like saying it is not moving. It doesn't adequately describe the motion of the object in question.
Do you want to know the speed (rpm) the pebble rotates around the axle? Wouldn't you need to know the radius of the tire to figure that? Tires of different sizes (height) will rotate at different speeds to maintain the same vehicle at 55mph.
The only thing we know is that pebble is moving around a tire, on a car that is going 55mph. Speed is a measure of motion, so I don't see how 0mph works. Even if it is in relation to the road, saying it is 0mph is like saying it is not moving. It doesn't adequately describe the motion of the object in question.
Do you want to know the speed (rpm) the pebble rotates around the axle? Wouldn't you need to know the radius of the tire to figure that? Tires of different sizes (height) will rotate at different speeds to maintain the same vehicle at 55mph.
actually...i do believe the answer lies in the rotation of the tire and its speed. IE Actual RPM.
Not what point its at on the arc, and not how fast your car is moving, but rather the speed of the rotation of the tire itself.
Reason why its not 0, because the tire is still in motion and thus not actually zero. Thats like taking a picture of a car going 150mph in 1/10,000 of a second and asking whats the exact speed its going at the time. Of course its zero, but if you have thousands and thousands of those pictures in a row and compile them, (IE film) then you would answer 150mph.
Thus it depends on the diameter of the wheel + tire and on the actual rpm of that circumfrence.
-M.T.O
Not what point its at on the arc, and not how fast your car is moving, but rather the speed of the rotation of the tire itself.
Reason why its not 0, because the tire is still in motion and thus not actually zero. Thats like taking a picture of a car going 150mph in 1/10,000 of a second and asking whats the exact speed its going at the time. Of course its zero, but if you have thousands and thousands of those pictures in a row and compile them, (IE film) then you would answer 150mph.
Thus it depends on the diameter of the wheel + tire and on the actual rpm of that circumfrence.
-M.T.O
dude...relativity. (sp?)
Who is the observer in the measurement of velocity? If you are talking the singular instance in time when the pebble hits the ground then there is no delta T, meaning you can't measure velocity nor accelaration.
0 M/s
Who is the observer in the measurement of velocity? If you are talking the singular instance in time when the pebble hits the ground then there is no delta T, meaning you can't measure velocity nor accelaration.
0 M/s
Yah buddhist, but I think that if you knew the radius of the tire you could also determine the RPM and the mph (assuming that it was rolling along the ground and not rotating in a stationary place).
If you knew the radius, you could computer the perimeter, and thus know how many revolutions it would take to go a certain distance. Then you could translate that to speed of the car.
Well goodnight, I don't feel like doing anyone elses homework tonight.
If you knew the radius, you could computer the perimeter, and thus know how many revolutions it would take to go a certain distance. Then you could translate that to speed of the car.
Well goodnight, I don't feel like doing anyone elses homework tonight.
isnt' speed dependent on BOTH velocity AND direction? that would mean that since the pebble is constantly changing direction, it is therefore constantly changing speed
if this is true, then do you want velocity or do you want speed?
if this is true, then do you want velocity or do you want speed?
artemedes and Buddhist: No, it does not matter what the radius of the tire is. If the centre of the tire is translating forward at a rate of 55mph, then the pebble is traveling in a circle around the centre of the tire at 55mph. When the pebble is at the top of the tire, it is moving at 110mph in the x-direction (horizontal). When it is at the bottom, it is moving at 0 mph in the x-direction. When it is in the centre of the wheel, the centre of the tire translates at 55mph in the x-direction and is moving at 55mph in the y-direction. The speed is given by v^2=v_x^2+v_y^2.
You have to remember that the pebble is moving around the centre of the tire at 55mph. Period. The tire centre is moving forward at 55mph. Period. Using simple trigonometry and basic calculus, you can calculate the exact speed at which the pebble is moving at any point on the circle (say, at a height of 6/7 of the height of the tire). You will get two different vectors for the two position that the pebble could be in, but they will be the same speed (scalar).
When asked for a velocity, normally we are referring to the velocity relative to a stationary observer on Earth for a question like this (unless you really want to centre the observer in the centre of the galaxy, then take the motion of the sun and the planets into account... trust me, you don't want to).
You have to remember that the pebble is moving around the centre of the tire at 55mph. Period. The tire centre is moving forward at 55mph. Period. Using simple trigonometry and basic calculus, you can calculate the exact speed at which the pebble is moving at any point on the circle (say, at a height of 6/7 of the height of the tire). You will get two different vectors for the two position that the pebble could be in, but they will be the same speed (scalar).
When asked for a velocity, normally we are referring to the velocity relative to a stationary observer on Earth for a question like this (unless you really want to centre the observer in the centre of the galaxy, then take the motion of the sun and the planets into account... trust me, you don't want to).
okay last post before bed.
Spydy07: relative to the road? Ok, the road is a long thin expanse of pavement. One revolution....the pebble touches the road...next revolution...the pebble touches the road X distance away...
On a moving vehicle the pebble rotating around the wheel will touch the pavement at a set distance each time. It is moving down the road and touching in equal distances along it. How can the pebble be going 0 mph if it makes it from one point on the road to another in a certain amount of time. If it moves down the road it has to have speed greater than 0.
Spydy07: relative to the road? Ok, the road is a long thin expanse of pavement. One revolution....the pebble touches the road...next revolution...the pebble touches the road X distance away...
On a moving vehicle the pebble rotating around the wheel will touch the pavement at a set distance each time. It is moving down the road and touching in equal distances along it. How can the pebble be going 0 mph if it makes it from one point on the road to another in a certain amount of time. If it moves down the road it has to have speed greater than 0.
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