I am interested to find out if anyone has checked out this little idea.
A pendulum, B curved ramp with the same profile of the pendulum,
C a ramp with a drop slop and D with a parabolic up ramp.
A. The little idea is a pendulum almost returns to the same height from one side of the swing to the other.
B. Like wise a ramp with the same profile does the same, but both do not make it for the usual reasons.
As we know the speed built up during the down movement is used to drive the ball up the other side.
However an arc is not the optimum profile to get the maximum speed.
C. So by changing the profile in the first half we cause the ball to have more speed.
This of cause will cause the ball to move further up the second half of the ramp.
D. If the shape of the curve can effect the speed on the way down then the shape of the curve can effect the final height on the way up.
Black and White of Curves
Moderator: scott
No it won't! All three balls roll at the same speed at the bottom. (Galileo discovered this.) All three balls will roll up to the same height at the far end, but they will take different amounts of time to reach the bottom and the end position. The pendulum will also swing up to the same height, but it will swing faster than the rolling ball. This is because gravity must make the balls roll in addition to following their respective curved paths. Moving objects have two types of inertia. One is linear inertia while the other is rotational inertia. The force of gravity gets split between the two types of inertia.agor95 wrote:This of cause will cause the ball to move further up the second half of the ramp.
re: Black and White of Curves
I agree the ball will arrive at the bottom of the ramp with the same speed for most paths. Also the delay in movement in fig B is caused by rotational inertia.
Further the potential energy present in the initial position, will be equal to the linear and rotational momentum present at the bottom of the ramp. This being a logical statement without including entropy.
By restricting to the down ramp of fig B. We can see the arc averages to a straight line between start and end positions. For this dialogue the arc path is preferred as the linear momentum is horizontal at the end position.
An optimum profile that results in a speed greater than the arc or straight line would mean the system has increased in energy.
There are three classes of paths that can be followed. Did Galileo check all of them before his departure in 1642?
Further the potential energy present in the initial position, will be equal to the linear and rotational momentum present at the bottom of the ramp. This being a logical statement without including entropy.
By restricting to the down ramp of fig B. We can see the arc averages to a straight line between start and end positions. For this dialogue the arc path is preferred as the linear momentum is horizontal at the end position.
An optimum profile that results in a speed greater than the arc or straight line would mean the system has increased in energy.
There are three classes of paths that can be followed. Did Galileo check all of them before his departure in 1642?
re: Black and White of Curves
These are the two laws that were declared by Galileo and the test equipment described to have been used by him to disprove Aristotle.
The first law tells us that freely failing bodies accelerate at a constant speed, regardless of their weight, and that the distance they cover is proportional to the square of the time elapsed during their fall.
The second identifies the trajectory of projectiles as a parabola and rests on the realization that horizontal and vertical motions can be combined without interfering with one another.
Galileo revolutionized basic scientific principles which were posited by Aristotle and held firmly by scholars of the High Middle Ages and Renaissance. One of his most important experiments was the inclined plane experiment. Galileo used his inclined plane, a simple board with a groove down which he rolled a small metal ball, to examine Aristotelian ideas about motion. Galileo's inclined plane experiment radically changed these ideas by concentrating on acceleration, a stage of motion ignored by Aristotle and most of his followers.
A piece of wooden moulding or scantling, about 12 cubits [about 7 m] long, half a cubit [about 30 cm] wide and three finger-breadths [about 5 cm] thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball.
However although these laws are without question correct. The equipment is restrictive.
You can see in the equipment he was using a hard ball on a straight inclined plane.
Galileo was disproving Aristotle as his prime target and using every method he could use.
That he did with Euclidean Geometry and the system of reasoning it
supplied.
In his two inclined planes experiment he assumed the ball was under a constant force.
That of cause was gravity, but on an inclined plane it would be, however a ball following different paths would experience a variation in force.
Where a path exists that increases the force acting to push the ball against the track the ball will increase in speed.
That variation is cause by centrifugal force.
There is more ...
The first law tells us that freely failing bodies accelerate at a constant speed, regardless of their weight, and that the distance they cover is proportional to the square of the time elapsed during their fall.
The second identifies the trajectory of projectiles as a parabola and rests on the realization that horizontal and vertical motions can be combined without interfering with one another.
Galileo revolutionized basic scientific principles which were posited by Aristotle and held firmly by scholars of the High Middle Ages and Renaissance. One of his most important experiments was the inclined plane experiment. Galileo used his inclined plane, a simple board with a groove down which he rolled a small metal ball, to examine Aristotelian ideas about motion. Galileo's inclined plane experiment radically changed these ideas by concentrating on acceleration, a stage of motion ignored by Aristotle and most of his followers.
A piece of wooden moulding or scantling, about 12 cubits [about 7 m] long, half a cubit [about 30 cm] wide and three finger-breadths [about 5 cm] thick, was taken; on its edge was cut a channel a little more than one finger in breadth; having made this groove very straight, smooth, and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball.
However although these laws are without question correct. The equipment is restrictive.
You can see in the equipment he was using a hard ball on a straight inclined plane.
Galileo was disproving Aristotle as his prime target and using every method he could use.
That he did with Euclidean Geometry and the system of reasoning it
supplied.
In his two inclined planes experiment he assumed the ball was under a constant force.
That of cause was gravity, but on an inclined plane it would be, however a ball following different paths would experience a variation in force.
Where a path exists that increases the force acting to push the ball against the track the ball will increase in speed.
That variation is cause by centrifugal force.
There is more ...
re: Black and White of Curves
dawnzky05
You are correct, but the text of Galileo finding would be nice to have here on this thread.
on the 14th Jan I explained
In cases were the curve is an arc of a circle connected to the start and end points the centrifugal force does exist. However its effects are averaged out along the slope
So the optimum curve is not an arc connected to the start and end.
Also it is not a incline plain as both of these paths are well tested.
I believe Bessler found a principle that brings momentum into a system from outside the system. This conserves momentum so everyone is happy.
Regards Agor95
You are correct, but the text of Galileo finding would be nice to have here on this thread.
on the 14th Jan I explained
By restricting to the down ramp of fig B. We can see the arc averages to a straight line between start and end positions.
In cases were the curve is an arc of a circle connected to the start and end points the centrifugal force does exist. However its effects are averaged out along the slope
So the optimum curve is not an arc connected to the start and end.
Also it is not a incline plain as both of these paths are well tested.
I believe Bessler found a principle that brings momentum into a system from outside the system. This conserves momentum so everyone is happy.
Regards Agor95
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bluesgtr44
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re: Black and White of Curves
When I think of the rolling sphere designs, I have pondered the idea that maybe the sphere shape needs to be manipulated. So far, I have been proven wrong, but I thought that if I could invert the sphere, so to speak, It would react differently. What I found was that I started manipulating the track inversley to line up with my reverse sphere, so it was tit for tat.
I thought I could get it to accelerate faster and then shift tracks as to where it was driving on the fatter portion and that my "supposed" increase in velocity would get me a bit higher than the point in which I started.....have had no success with this yet, I do still think about it though.
Steve
I thought I could get it to accelerate faster and then shift tracks as to where it was driving on the fatter portion and that my "supposed" increase in velocity would get me a bit higher than the point in which I started.....have had no success with this yet, I do still think about it though.
Steve
Finding the right solution...is usually a function of asking the right questions. -A. Einstein
re: Black and White of Curves
I have a question that would be nice to know.
The question is based of the above;
Three slopes a. inclined plain, b. a parabola [the natural path] , c. a parabola adjusted [This has a slight increase in angle along the path] and
d. parabola adjusted [This has a slight decrease in angle along the path]
If the ball has an initial linear momentum of 45 degrees from the horizontal and an appropriate rotational momentum.
Does the ball finish at the same hight for each cases.
Agor95
D. If the shape of the curve can effect the speed on the way down then the shape of the curve can effect the final height on the way up.
The question is based of the above;
Three slopes a. inclined plain, b. a parabola [the natural path] , c. a parabola adjusted [This has a slight increase in angle along the path] and
d. parabola adjusted [This has a slight decrease in angle along the path]
If the ball has an initial linear momentum of 45 degrees from the horizontal and an appropriate rotational momentum.
Does the ball finish at the same hight for each cases.
Agor95
re: Black and White of Curves
http://www.newadvent.org/cathen/06342b.htmYou are correct, but the text of Galileo finding would be nice to have here on this thread.
http://inventors.about.com/od/gstartinv ... alilei.htm
http://www.answers.com/topic/galileo-galilei
"the distances covered in natural motion are proportional to the squares of the number of time intervals, and therefore, the distances covered in equal times are as the odd numbers beginning from one." By natural motion, Galileo meant the unimpeded fall of a body, and what he proposed was the law of free fall, later written as s = 1/2 (gt2), where s is distance, t is time, and g is the acceleration due to gravity at sea level.
re: Black and White of Curves
Ralph
It is good to get some educational links into the thread.
The first link has some points
The first quote shows one should be diplomatic but it seems Galileo, Newton and Bessler has one thing in common.
The image below shows the first stage:-
This is the pre-jump and its purpose is to convert linear momentum into increased spin and potential energy in hight.
As Jim stated the ball needs to spin up when it hits the ramp.
By using the separating rails method the ball will have the rotational spin to connect the slope correctly even after its speed has increased due to gravity. The pre-jump also caused the parabolic path to be more vertical.
In the first drawing the expected path is a parabola were the ball move far away from the drop slope.
The ball connects the slope correctly when the ball is rolling equal to or faster than its speed in relation to the slope.
Agor95
It is good to get some educational links into the thread.
The first link has some points
Moreover, he wielded an exceedingly able pen, and unsparingly ridiculed and exasperated his opponents. Undoubtedly he thus did much to bring upon himself the troubles for which he is now chiefly remembered. As Sir David Brewster (Martyrs of Science) says, "The boldness, may we not say the recklessness, with which Galileo insisted on making proselytes of his enemies, served but to alienate them from the truth."
He studied the properties of the cycloid and attempted the problem of its quadrature
The first quote shows one should be diplomatic but it seems Galileo, Newton and Bessler has one thing in common.
The image below shows the first stage:-
This is the pre-jump and its purpose is to convert linear momentum into increased spin and potential energy in hight.
As Jim stated the ball needs to spin up when it hits the ramp.
By using the separating rails method the ball will have the rotational spin to connect the slope correctly even after its speed has increased due to gravity. The pre-jump also caused the parabolic path to be more vertical.
In the first drawing the expected path is a parabola were the ball move far away from the drop slope.
The ball connects the slope correctly when the ball is rolling equal to or faster than its speed in relation to the slope.
Agor95
re: Black and White of Curves
This is a link to a previous thread that explains Jim's point on this topic.
http://www.besslerwheel.com/forum/viewt ... =7110#7110
At the end of the thread we can see an image of a metal ball on a metal track. Also a velocity graph.
This shows simply the ball will arrive with the same speed but at different times.
So the ball used in MT124 could not have been metal and it's mechanical properties change when placed in direct midday sunlight.
Agor95
http://www.besslerwheel.com/forum/viewt ... =7110#7110
At the end of the thread we can see an image of a metal ball on a metal track. Also a velocity graph.
This shows simply the ball will arrive with the same speed but at different times.
So the ball used in MT124 could not have been metal and it's mechanical properties change when placed in direct midday sunlight.
Agor95
re: Black and White of Curves
When the ball drops down to the bottom of the slop it's speed will be redirected horizontally.
If both the ball and ramp were solid then the speed into the bottom curved section would be approximately the same on the way out as on the way in.
If the ball was rubber then the ball would be compressed as it goes around the curve.
When it is on the way out the ball will come out of compression, bounce, as will as having the speed described above.
The question on my mind is the speed of the ball on the way out.
Is it the same for a ball that is solid to one that is made of rubber?
If both the ball and ramp were solid then the speed into the bottom curved section would be approximately the same on the way out as on the way in.
If the ball was rubber then the ball would be compressed as it goes around the curve.
When it is on the way out the ball will come out of compression, bounce, as will as having the speed described above.
The question on my mind is the speed of the ball on the way out.
Is it the same for a ball that is solid to one that is made of rubber?
re: Black and White of Curves
Hello DrWhat
The thing that gets me is the final momentum?
If a solid ball drops down the curve and exits with the momentum it has built up, but it has been converted to a horizontal vector.
Then a rubber ball will do the same; However the centrifugal force will be stored in the ball and released on the exit from the curve.
So the ball will have the momentum of the solid ball. Also it will rise up due to the bounce.
The bounce is extra momentum; Therefore as that is impossible the horizontal speed needs to be less than the solid ball to keep things orthodox.
The thing that gets me is the final momentum?
If a solid ball drops down the curve and exits with the momentum it has built up, but it has been converted to a horizontal vector.
Then a rubber ball will do the same; However the centrifugal force will be stored in the ball and released on the exit from the curve.
So the ball will have the momentum of the solid ball. Also it will rise up due to the bounce.
The bounce is extra momentum; Therefore as that is impossible the horizontal speed needs to be less than the solid ball to keep things orthodox.
re: Black and White of Curves
When the ball rolls around the bottom curve the CF compression should reduce the effective diameter. Therefore it will rotate faster and have less linear momentum.
If the curve is correct the CF is released slowly. This will allow the diameter to return to normal and transfer the faster rotation to linear with friction on the track.
So were does this get us anyway?
Has anyone watched how a ball bounces when it is dropped vertically onto a level surface.
Then again dropped with it spinning around its horizontal axis?
If the curve is correct the CF is released slowly. This will allow the diameter to return to normal and transfer the faster rotation to linear with friction on the track.
So were does this get us anyway?
Has anyone watched how a ball bounces when it is dropped vertically onto a level surface.
Then again dropped with it spinning around its horizontal axis?