The physics of flywheel launchers (like tennis ball shooters)

[cardboard_box]

Yes, you are correct.
Certain amount of energy flows from the launcher to the projectile.
If the launcher is not fed with replenishing energy (like from an electric motor), and keeps giving impulse to several projectiles consecutively, it will simultaneously slow down more, and more and will deliver weaker and weaker torque, after each launch.

but how can I measure this flow of energy/impulse without just looking at the finished results? and most importantly how exactly does it apply a torque while free spinning? objects with momentum must have the ability to exert a force by themselves to cause an impulse, so if we have 2 objects which we know the momentum of how do we find what force they will exert on one another during collision without knowing the end momentum of each object?
Also, wouldn't a faster spinning flywheel result in less time in the shooter and therefore lesser impulse? seems contradicting

 

[cardboard_box]

an updated question: does momentum exert a force? in the shooter the wheel has momentum but no active force on it, it interacts with the wheel via friction but friction is a "reactive" force, is friction effected by velocity or momentum the objects?
if we for example take 2 cubes, 1 is just standing in space and the other is moving towards it, when they impact there is an impulse and momentum change, so there must be a force. does it make sense the force is the reaction of friction and the atoms pushing back due to electric charge and resisting, and if so how can we measure the force an object will exert on another due to its momentum?

 

[Baluncore]

I do not think momentum will help you here. The ball is free until it is grabbed by the wheels and accelerated as a part of the wheels. It is then released at the final velocity of the wheels.

The acceleration impulse takes a finite time, while friction is slipping, until the ball is held against the wheels without slip. That may last a few milliseconds, it is not an instant. The friction and the acceleration happen, but the detail of the clutch is best ignored.

You know the mass of the ball, the RPM and the energy in the flywheels. Solve for the exit velocity of the ball, which will equal the final velocity of the wheels. That will be an energy balance equation. You can ignore the loss of energy to friction, unless you notice the ball gets hot when it is launched.

You can initially assume that two wheels, on the same shaft, form a cylindrical roller. Deeper analysis will show that the wheels do not contact the ball at its outer diameter, but closer to the ball's axis. That will not be important for two shafts with four identical wheels, two on each shaft. It will become important for a one-sided thrower, where one side of the ball is held against the hood.

 

[cardboard_box]

I do not think momentum will help you here. The ball is free until it is grabbed by the wheels and accelerated as a part of the wheels. It is then released at the final velocity of the wheels.

The acceleration impulse takes a finite time, while friction is slipping, until the ball is held against the wheels without slip. That may last a few milliseconds, it is not an instant. The friction and the acceleration happen, but the detail of the clutch is best ignored.

You know the mass of the ball, the RPM and the energy in the flywheels. Solve for the exit velocity of the ball, which will equal the final velocity of the wheels. That will be an energy balance equation. You can ignore the loss of energy to friction, unless you notice the ball gets hot when it is launched.

You can initially assume that two wheels, on the same shaft, form a cylindrical roller. Deeper analysis will show that the wheels do not contact the ball at its outer diameter, but closer to the ball's axis. That will not be important for two shafts with four identical wheels, two on each shaft. It will become important for a one-sided thrower, where one side of the ball is held against the hood.

but if the ball simply accelerates to the surface velocity of the wheel after a couple moments wouldn't it break the definition of energy as distance*force? because if the ball is in contact with the wheel for a distance of 5m or 5km it will still just be the surface velocity of the wheel, and then adding more wheels like a series would also not increase its velocity.

why would the ball start with kinetic friction that will then transform to static friction if it didn't start sliding on the wheel?

I am not sure what you mean in your final paragraph either.

 

[Baluncore]

but if the ball simply accelerates to the surface velocity of the wheel after a couple moments wouldn't it break the definition of energy as distance*force?

Once the ball is grabbed and reaches the speed of the wheels, the force becomes zero and there is no relative movement. Work is being done by the wheels on the ball, only while kinetic friction is operating.

A force without movement in the direction of the force, or a movement without a collinear force, does not constitute work being done. The pinching force, that holds the ball, is perpendicular to the movement, so does no work.

The acceleration and energy exchange is done, immediately the ball is locked to the wheels.

why would the ball start with kinetic friction that will then transform to static friction if it didn't start sliding on the wheel?

It will start sliding on the wheels, that kinetic friction will pull the ball further into the wheels, resulting in the ball being grabbed by the wheels.

I am not sure what you mean in your final paragraph either.

The final paragraph can be ignored for now. It is a subtlety that will mess up the numbers by throwing the ball faster than expected, from a one-sided thrower with a hood.

 

[cardboard_box]

Once the ball is grabbed and reaches the speed of the wheels, the force becomes zero and there is no relative movement. Work is being done by the wheels on the ball, only while kinetic friction is operating.

A force without movement in the direction of the force, or a movement without a collinear force, does not constitute work being done. The pinching force, that holds the ball, is perpendicular to the movement, so does no work.

The acceleration and energy exchange is done, immediately the ball is locked to the wheels.


It will start sliding on the wheels, that kinetic friction will pull the ball further into the wheels, resulting in the ball being grabbed by the wheels.


The final paragraph can be ignored for now. It is a subtlety that will mess up the numbers by throwing the ball faster than expected, from a one-sided thrower with a hood.

okay a couple of questions:
1. why does the ball start with kinetic and not static friction? that seems really dependent on the set up, since if it touches tangentially it should start rolling against the hood.

2. could you expand on relative velocity and why it makes the force turn to 0? I just am still not really sure what the source of the force is, it seems to be due to momentum since if for example 2 objects collide in a vacuum there is still a force exerted in the impulse, so does momentum exert a force during collision and how?

3. isn't a force without movement in the direction of the force paradoxical? since force causes acceleration there must be some sort of movement in the system.

4. if the ball is rolling, which in a lot of the mechanism I saw it those, then that should mean there is static and not kinetic friction.

 

[Baluncore]

1. why does the ball start with kinetic and not static friction?

Because there is a differential velocity throughout the period of acceleration. The relative movement of surfaces during acceleration must be kinetic, not static.

2. could you expand on relative velocity and why it makes the force turn to 0? I just am still not really sure what the source of the force is, it seems to be due to momentum since if for example 2 objects collide in a vacuum there is still a force exerted in the impulse, so does momentum exert a force during collision and how?

For this project, you must forget about the momentum of objects colliding in a vacuum. It is irrelevant here. Any initial ball momentum is lost because the ball is trapped for a finite time, trapped by the wheels spinning on a fixed axis. The ball is not free to preserve momentum. To preserve momentum, the ball and thrower would need to be floating free in space throughout their contact.

3. isn't a force without movement in the direction of the force paradoxical? since force causes acceleration there must be some sort of movement in the system.

When you rest a block on the table, gravity holds it on the table, but there is no movement, so no work is being done.

4. if the ball is rolling, which in a lot of the mechanism I saw it those, then that should mean there is static and not kinetic friction.

The ball may roll into the thrower, but then it is dynamically drawn in, accelerated, before being gripped by static friction. A one-sided thrower, accelerates the ball with kinetic friction, then employs static friction to roll the ball between the wheel and the hood. A ball rolls, with static friction, into a two-sided thrower, kinetic friction accelerates the ball, then static friction grips the ball between the wheels.

 

[cardboard_box]

Because there is a differential velocity throughout the period of acceleration. The relative movement of surfaces during acceleration must be kinetic, not static.


For this project, you must forget about the momentum of objects colliding in a vacuum. It is irrelevant here. Any initial ball momentum is lost because the ball is trapped for a finite time, trapped by the wheels spinning on a fixed axis. The ball is not free to preserve momentum. To preserve momentum, the ball and thrower would need to be floating free in space throughout their contact.


When you rest a block on the table, gravity holds it on the table, but there is no movement, so no work is being done.


The ball may roll into the thrower, but then it is dynamically drawn in, accelerated, before being gripped by static friction. A one-sided thrower, accelerates the ball with kinetic friction, then employs static friction to roll the ball between the wheel and the hood. A ball rolls, with static friction, into a two-sided thrower, kinetic friction accelerates the ball, then static friction grips the ball between the wheels.

I'm sorry but I don't really understand some of what you said, firstly assuming you mean that since the objects don't start with the same velocity but rather accelerate to it there must be some slippage to begin with, but I don't understand why it shouldn't be possible that it starts with static friction and roll against the hood of the flywheel, otherwise how exactly do you measure the speed it takes it to become static friction and be the same velocity of the wheel.

secondly, the ball can start with zero momentum on its own, but even if we fully ignore momentum and just use KE there still must be a force exerted by the wheel on the ball, what is the source of it?

thirdly, when I rest an object on the table it doesn't move because the table is also pushing back against the force of gravity and the object with the normal force, so there is a net force of zero.

and fourthly, I am not sure what you mean in the 3rd paragraph with switching between the 2 types of friction and what they do, isn't it impossible for an object to be experiencing both kinetic and static friction at the same time? and if they do switch that would mean the ball doesn't actually starts to roll until a certain point, which I'm not sure about.