I appreciate these questions are trivia and everyone knows how a ball bounces. However the simple common place toys may be were some effects exist.
You never know it could spark some one to see things a little different.
The first question of the ball dropped vertically onto a level surface.
When the ball drops it accelerates and makes contact. The momentum is converted into deformation of the ball until it stops. Then the energy is released to send the ball into the air.
The ratio of final height over initial height is use to describe how effective a ball is at storing and releasing energy.
There is a finite period of time the ball is in contact with the surface.
The time the ball is in contact is important.
IMO this period of time may be relative stable compared to the speed the ball can hit the surface. A slow speed hit results in less deformation, at quicker speeds the deformation is more, but the return speed is also quicker.
There are limits to the speed range were the ball splits or is to light a contact to measure.
How can we cause the ball to have a final height greater than the initial height?
Black and White of Curves
Moderator: scott
re: Black and White of Curves
A steel ball dropped onto a cold steel plate will bounce higher than its starting height, IIRC - but of course you are putting energy into the system by super cooling the plate, IINM.
re: Black and White of Curves
Drop two balls. Before the balls reach the bottom transfer the speed of the first ball to the second ball (this being the hard part to solve). Conservation of Momentum Law indicates that this should be possible. This leaves the first ball not moving and the second ball moving twice as fast. A ball moving twice as fast will rise four times as high. After the ball reaches the highest point and has started moving back down let is raise the first weight back up. Both balls should end up somewhere higher than their original start position and lower than twice the first drop height.agor95 wrote:How can we cause the ball to have a final height greater than the initial height?
At least in theory this seems possible. The sticker is how to cause one ball to slow down and one to speed up such that all or most of the momentum gets transferred from the decelerating ball to the accelerating ball.
If you can find a mechanism that causes momentum to naturally move from a slower object to a faster object then such a mechanism might be labeled a Mechanical Maxwell's Demon.
re: Black and White of Curves
The trouble is that momentum is a subjective property, unlike angular momentum which is an objective property.
Momentum (and kinetic energy) is subjective because velocity is subjective. There is no fixed frame of reference for velocity. It depends on where the observer is standing in relation to the moving object.
This is not true of angular momentum.
Momentum (and kinetic energy) is subjective because velocity is subjective. There is no fixed frame of reference for velocity. It depends on where the observer is standing in relation to the moving object.
This is not true of angular momentum.
Who is she that cometh forth as the morning rising, fair as the moon, bright as the sun, terribilis ut castrorum acies ordinata?
re: Black and White of Curves
How can we cause the ball to have a final height greater than the initial height?
I started with the simple answer and that also used external energy.
However not as cool as the super cold steel plate; Interesting idea.
Every thing is relative to a frame of reference. We can fix it to the surface. fix it to the ball or between the two.
If the ball was resting on the surface it would have weight, on earth.
If the ball was doing the same in space in a room, that was accelerating, it would have weight.
When the ball is dropped onto the surface fixed F.O.R. it decelerates.
This is equivalent to the surface accelerating into the ball.
The ball behaves as if its weight has increased; in the short term.
The simple answer is during the contact phase accelerate the surface into the ball. This will increase the deformation of the ball. Then stop after the ball is no longer in contact and return the surface back to its original position. Yes I have just invented a bat ;-)
This of cause will need energy, except if you can cause the surface to accelerate into the ball without moving. What a strange idea.
The next section is :- A ball dropped with it spinning around its horizontal axis?
Then we will get back to the strange idea. Also you may see a solution to the transferal of momentum in the two ball problem.
I started with the simple answer and that also used external energy.
However not as cool as the super cold steel plate; Interesting idea.
Every thing is relative to a frame of reference. We can fix it to the surface. fix it to the ball or between the two.
If the ball was resting on the surface it would have weight, on earth.
If the ball was doing the same in space in a room, that was accelerating, it would have weight.
When the ball is dropped onto the surface fixed F.O.R. it decelerates.
This is equivalent to the surface accelerating into the ball.
The ball behaves as if its weight has increased; in the short term.
The simple answer is during the contact phase accelerate the surface into the ball. This will increase the deformation of the ball. Then stop after the ball is no longer in contact and return the surface back to its original position. Yes I have just invented a bat ;-)
This of cause will need energy, except if you can cause the surface to accelerate into the ball without moving. What a strange idea.
The next section is :- A ball dropped with it spinning around its horizontal axis?
Then we will get back to the strange idea. Also you may see a solution to the transferal of momentum in the two ball problem.
re: Black and White of Curves
A ball dropped with it spinning around its horizontal axis?
This description needs to be done so we can link it back to the previous description and forwards to Jims request for momentum transfer.
A ball is dropped spinning anti-clockwise [just to fit the last diagram]. The ball will loose some slight amount of spin to air resistance and it should drift to the right slightly, but this is not the focus of the text.
The ball [subjective property] is to be almost weightless as it is in near free fall.
The air resistance is causing the ball's fall rate to be less than maximum.
The surface will appear to accelerate towards the ball and first contact is made. At this point the outer layered of the ball, after an initial slippage will cause traction. However there will be internal twisting within, the same way a rubber band can be twisted.
The process previously stated is also happening and the ball is going into compression. This is equivalent to the ball gaining weight, in the short term. This compression stage takes a finite period of time and during that time the outer layers of the ball have rotated. Therefore the compressed sector of the ball instead of being aligned vertically is now at an angle. The ball will go into the bounce stage with this angle compression in place.
The internal twisting will also have reversed and will be propagating back from the center to the outer layers.
This also take a finite length of time in the same way the bounce and will have a relatively stable time period. The time period being compare with the spin rates.
So selecting the correct spin rate will result in the ball bouncing away with a reversed rotation.
The main focus is the angled push by the ball and the effect that the ball acts like it's weight increased during impact.
How does a ball react against a curved [circular] surface compared to an spiral curve?
Note a rubber ball reaction allows us to see how all impact must happen at some level. Reactions between impacting objects are not instantaneous.
Mathematical representations keep away from these points in time for that is were infinities lurk. IMO that is were we should be looking for effects.
This description needs to be done so we can link it back to the previous description and forwards to Jims request for momentum transfer.
A ball is dropped spinning anti-clockwise [just to fit the last diagram]. The ball will loose some slight amount of spin to air resistance and it should drift to the right slightly, but this is not the focus of the text.
The ball [subjective property] is to be almost weightless as it is in near free fall.
The air resistance is causing the ball's fall rate to be less than maximum.
The surface will appear to accelerate towards the ball and first contact is made. At this point the outer layered of the ball, after an initial slippage will cause traction. However there will be internal twisting within, the same way a rubber band can be twisted.
The process previously stated is also happening and the ball is going into compression. This is equivalent to the ball gaining weight, in the short term. This compression stage takes a finite period of time and during that time the outer layers of the ball have rotated. Therefore the compressed sector of the ball instead of being aligned vertically is now at an angle. The ball will go into the bounce stage with this angle compression in place.
The internal twisting will also have reversed and will be propagating back from the center to the outer layers.
This also take a finite length of time in the same way the bounce and will have a relatively stable time period. The time period being compare with the spin rates.
So selecting the correct spin rate will result in the ball bouncing away with a reversed rotation.
The main focus is the angled push by the ball and the effect that the ball acts like it's weight increased during impact.
How does a ball react against a curved [circular] surface compared to an spiral curve?
Note a rubber ball reaction allows us to see how all impact must happen at some level. Reactions between impacting objects are not instantaneous.
Mathematical representations keep away from these points in time for that is were infinities lurk. IMO that is were we should be looking for effects.
re: Black and White of Curves
Hi All
This was an early design where a rubber ball is dropped and directed so that it bounces at, say, 45 degrees. The up ramp has a curve that follows it's natural trajectory with an added upward angle of 1 degree.
The other option of this is to put in inside a fixed rotating wheel.
P.S. As recommended to Raj.
Regards
This was an early design where a rubber ball is dropped and directed so that it bounces at, say, 45 degrees. The up ramp has a curve that follows it's natural trajectory with an added upward angle of 1 degree.
The other option of this is to put in inside a fixed rotating wheel.
P.S. As recommended to Raj.
Regards
[MP] Mobiles that perpetuate - external energy allowed
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Last edited by agor95 on Sat Dec 02, 2023 11:22 am, edited 3 times in total.
[MP] Mobiles that perpetuate - external energy allowed