i think beach balls not travelling as well when kicked is due to something else. Rebound forces, loss of kinetic energy due to the material of the object and so on. Once it's already travelling, the rate at which it slows down (horizontally) due to air resistance is actually probably somewhat similar to a soccer ball since they have a similar shape. I don't think that the mass of an object factors into drag forces. I'm not an expert in any of this though so I could be straight up wrong about some of this stuff . . .
The mass of an object wouldn't factor into drag forces, no, but it would factor into how quickly drag slows said object down. A soccer ball going at the same speed as a beach ball will be harder to slow down because it has more mass, and therefore more force (mass * velocity). Since to get an object to stop moving you have to apply the same amount of force with which the object is moving in the opposite direction, and the drag will be applying the same amount of force on both a beach ball and a soccer ball, drag will have more of an impact on the beach ball's force percentage wise, and therefore more of an impact on its speed.
I think.
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Look at what you've done. You spoiled it. You have nobody to blame but yourself. Go sit and think about your actions.
Don't be mean. Rudeness is a vicious cycle, and it has to stop somewhere. Exceptions for things that are funny. Go to the current Competition of the Finest 'Brews! It's a cool place where cool people make cool things.
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Ah yes ok you are speaking of momentum, which I hadn't really considered. So momentum is not a force per se, it's more of an object's resistance to outside forces per unit of time, sort of. So, an object launched upwards does not continue to have an upward force acting upon it, but it does have upward momentum. So the question becomes, is this a greater factor than the force of gravity in determining how quickly an object slows and then descends?
I'm pretty sure the answer is no. When problems are solved with the simplification of ignoring air resistance, objects will still begin with upward momentum. But at a given initial upward velocity an object with greater mass will return towards the ground more quickly due to the greater gravitational force. So as mass and weight increase, resistance to drag forces increases but gravity increases more.
But yeah I'm not sure about any of that, weightless objects are weird!
This is why my favorite answer to these sorts of questions is: "D&D is a role playing game, not a physics engine."
For the example comparing a weightless ball to a normal ball being launched upward let's walk through the equations and see what happens.
First, let's list out our starting assumptions.
1) The weightless ball experiences no gravitational force, but is otherwise identical to the other ball.
2) Both balls are launched upward at the same initial velocity of 10m/s, a mass of 1kg, and a cross sectional area of 1m^2.
3) This experiment is being conducted on earth, at sea level.
From that starting point both balls travel up and are acted upon by two forces, gravity and drag. Gravity acts downward and drag acts in opposition of motion through the air, which is also downward.
So for the weightless ball the force from gravity is 0 from assumption #1. For the ball with weight Fg = m*g ( Fg is the force due to gravity, m is the balls mass, and g is acceleration due to gravity). The balls mass is 1kg(assumption #2) and acceleration due to gravity is 9.81m/s^2(assumption #3). So the force due to gravity acting on the ball with weight is 1*9.81 = 9.81 Newtons.
To calculate the force from drag we use the following equation: Fd = 0.5*p*v^2*Cd*A ( Fd is the force due to drag, p is the density of the fluid being moved through, v is the objects velocity relative to the fluid, Cd is the coefficient of drag due to the objects shape, A is the cross sectional area of the object). So we know the balls cross sectional area is 1m^2 and its initial velocity is 10m/s from assumption #2. From Google I find the density of air at sea level is 1.22kg/m^3 and the coefficient of drag for a sphere is 0.5. Plug that all in and we get Fd = 0.5*1.22*(10^2)*0.5*1 = 30.5 Newtons.
So what acceleration does each ball experience the moment it is launched? Well, we know the forces acting on each ball and Newton's second law relates force, mass, and acceleration thusly: F = m*a. We can rearrange it to: a = F/m. Since each ball has mass of 1kg then the acceleration they experience in m/s^2 is the same as the net force on each ball in Newtons. So the moment the weightless ball is launched it immediately starts decelerating at 30.5m/s^2. The ball with weight on the other hand starts decelerating at 9.81 + 30.5 = 40.3m/s^2. Hopefully this is sufficient to show that in this to show that the weightless ball will spend more time traveling up and thus reach higher. You could calculate the height, forces, and velocity millisecond by millisecond for an approximation, or break out calculus, but there is a more interesting question I want to get to.
Specifically the fact that in our hypothetical we assumed the weightless ball still has mass. That seems odd, doesn't it? So, what if instead we assume the weightless ball has no mass instead being unaffected by gravity? The gravitational force experienced by the weightless ball is still 0 because 0kg * 9.81m/s^2 is 0 Newtons. The drag force equation doesn't involve mass so that is unchanged. So the ball with mass still had an initial deceleration of 40.3m/s^2. As for the ball with 0 mass we get that the deceleration it experiences equals 30.5/0. And now we have a problem.
If we accept an additional assumption that mass is strictly positive then we can make some sense of this as then the equation a = F/m approaches infinity as m approaches 0. Thus the ball without mass would immediately stop once released and not travel anywhere.
If we accept that mass can be negative then the limit of a = F/m doesn't converge to a single value when you take the limit. It approaches infinity when coming from the positive side of 0 but it also approaches negative infinity when coming from the negative side of zero. So without a value for deceleration the behavior of the ball without mass is undefined.
For the two scenarios where we could actually solve the equations the weightless ball comes to rest in mid-air. Gravity exerted no force on the weightless ball and once it stops moving relative to the air, drag no longer exerts any force on the ball. And an object experiencing no net force continues its motion unchanged, which for the weightless ball is no motion at all.
And do you really want to do all of this in the middle of a session?
The magic ball has no weight but the creature inside still has full mass and weight. Thus a magic ball around a 100kg human would would weigh 100kg in total.
If a giant is kicking the ball its essentially just kicking the person and after a few punts around the forest the magic ball will be smeared red inside and what is left of the human would be feed for pigs.
The magic ball has no weight but the creature inside still has full mass and weight. Thus a magic ball around a 100kg human would would weigh 100kg in total.
If a giant is kicking the ball its essentially just kicking the person and after a few punts around the forest the magic ball will be smeared red inside and what is left of the human would be feed for pigs.
If you believe that the sphere doesn't prevent fall damage, that is. If it does, then a giant could have an amazing game of pinball, baseball, bowling, or whatever they wish with an entrapped wizard for the duration of the spell.
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Look at what you've done. You spoiled it. You have nobody to blame but yourself. Go sit and think about your actions.
Don't be mean. Rudeness is a vicious cycle, and it has to stop somewhere. Exceptions for things that are funny. Go to the current Competition of the Finest 'Brews! It's a cool place where cool people make cool things.
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Fangeye, thanks for the breakdown! I think that all of that agreed with what I wrote, just more precisely and confidently. For this hypothetical I think that your assumption #1 is important, that the weightless object still has mass. Because without mass you really don't have the object any more. Or, at best instead of a tangible ball we'd be talking about a ball of energy. I don't think that forces can be applied to balls of energy in the Newtonian sense pretty much because of the problem with the math that you ran into.
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The mass of an object wouldn't factor into drag forces, no, but it would factor into how quickly drag slows said object down. A soccer ball going at the same speed as a beach ball will be harder to slow down because it has more mass, and therefore more force (mass * velocity). Since to get an object to stop moving you have to apply the same amount of force with which the object is moving in the opposite direction, and the drag will be applying the same amount of force on both a beach ball and a soccer ball, drag will have more of an impact on the beach ball's force percentage wise, and therefore more of an impact on its speed.
I think.
Look at what you've done. You spoiled it. You have nobody to blame but yourself. Go sit and think about your actions.
Don't be mean. Rudeness is a vicious cycle, and it has to stop somewhere. Exceptions for things that are funny.
Go to the current Competition of the Finest 'Brews! It's a cool place where cool people make cool things.
How I'm posting based on text formatting: Mod Hat Off - Mod Hat Also Off (I'm not a mod)
Its a human hamster ball.
https://www.ebay.com/itm/363823004614?var=0&mkevt=1&mkcid=1&mkrid=711-53200-19255-0&campid=5338590836&toolid=10044&customid=d71df345436619476be597cafeef65d9
Treat it as such in the game.
https://www.ebay.com/sch/i.html?_nkw=human hamster ball&norover=1&mkevt=1&mkrid=711-34001-13078-0&mkcid=2&mkscid=102&keyword=human hamster ball&crlp=_2-1300-0-1-1&MT_ID=&geo_id=&rlsatarget=kwd-76553705418815:loc-190&adpos=&device=c&mktype=&loc=99916&poi=&abcId=&cmpgn=418333415&sitelnk=&adgroupid=1224856189842320&network=s&matchtype=e&msclkid=8d4538f87ad1161b13695c77c4e3708a
Ah yes ok you are speaking of momentum, which I hadn't really considered. So momentum is not a force per se, it's more of an object's resistance to outside forces per unit of time, sort of. So, an object launched upwards does not continue to have an upward force acting upon it, but it does have upward momentum. So the question becomes, is this a greater factor than the force of gravity in determining how quickly an object slows and then descends?
I'm pretty sure the answer is no. When problems are solved with the simplification of ignoring air resistance, objects will still begin with upward momentum. But at a given initial upward velocity an object with greater mass will return towards the ground more quickly due to the greater gravitational force. So as mass and weight increase, resistance to drag forces increases but gravity increases more.
But yeah I'm not sure about any of that, weightless objects are weird!
This is why my favorite answer to these sorts of questions is: "D&D is a role playing game, not a physics engine."
For the example comparing a weightless ball to a normal ball being launched upward let's walk through the equations and see what happens.
First, let's list out our starting assumptions.
1) The weightless ball experiences no gravitational force, but is otherwise identical to the other ball.
2) Both balls are launched upward at the same initial velocity of 10m/s, a mass of 1kg, and a cross sectional area of 1m^2.
3) This experiment is being conducted on earth, at sea level.
From that starting point both balls travel up and are acted upon by two forces, gravity and drag. Gravity acts downward and drag acts in opposition of motion through the air, which is also downward.
So for the weightless ball the force from gravity is 0 from assumption #1. For the ball with weight Fg = m*g ( Fg is the force due to gravity, m is the balls mass, and g is acceleration due to gravity). The balls mass is 1kg(assumption #2) and acceleration due to gravity is 9.81m/s^2(assumption #3). So the force due to gravity acting on the ball with weight is 1*9.81 = 9.81 Newtons.
To calculate the force from drag we use the following equation: Fd = 0.5*p*v^2*Cd*A ( Fd is the force due to drag, p is the density of the fluid being moved through, v is the objects velocity relative to the fluid, Cd is the coefficient of drag due to the objects shape, A is the cross sectional area of the object). So we know the balls cross sectional area is 1m^2 and its initial velocity is 10m/s from assumption #2. From Google I find the density of air at sea level is 1.22kg/m^3 and the coefficient of drag for a sphere is 0.5. Plug that all in and we get Fd = 0.5*1.22*(10^2)*0.5*1 = 30.5 Newtons.
So what acceleration does each ball experience the moment it is launched? Well, we know the forces acting on each ball and Newton's second law relates force, mass, and acceleration thusly: F = m*a. We can rearrange it to: a = F/m. Since each ball has mass of 1kg then the acceleration they experience in m/s^2 is the same as the net force on each ball in Newtons. So the moment the weightless ball is launched it immediately starts decelerating at 30.5m/s^2. The ball with weight on the other hand starts decelerating at 9.81 + 30.5 = 40.3m/s^2. Hopefully this is sufficient to show that in this to show that the weightless ball will spend more time traveling up and thus reach higher. You could calculate the height, forces, and velocity millisecond by millisecond for an approximation, or break out calculus, but there is a more interesting question I want to get to.
Specifically the fact that in our hypothetical we assumed the weightless ball still has mass. That seems odd, doesn't it? So, what if instead we assume the weightless ball has no mass instead being unaffected by gravity? The gravitational force experienced by the weightless ball is still 0 because 0kg * 9.81m/s^2 is 0 Newtons. The drag force equation doesn't involve mass so that is unchanged. So the ball with mass still had an initial deceleration of 40.3m/s^2. As for the ball with 0 mass we get that the deceleration it experiences equals 30.5/0. And now we have a problem.
If we accept an additional assumption that mass is strictly positive then we can make some sense of this as then the equation a = F/m approaches infinity as m approaches 0. Thus the ball without mass would immediately stop once released and not travel anywhere.
If we accept that mass can be negative then the limit of a = F/m doesn't converge to a single value when you take the limit. It approaches infinity when coming from the positive side of 0 but it also approaches negative infinity when coming from the negative side of zero. So without a value for deceleration the behavior of the ball without mass is undefined.
For the two scenarios where we could actually solve the equations the weightless ball comes to rest in mid-air. Gravity exerted no force on the weightless ball and once it stops moving relative to the air, drag no longer exerts any force on the ball. And an object experiencing no net force continues its motion unchanged, which for the weightless ball is no motion at all.
And do you really want to do all of this in the middle of a session?
I would treat it thus/
The magic ball has no weight but the creature inside still has full mass and weight. Thus a magic ball around a 100kg human would would weigh 100kg in total.
If a giant is kicking the ball its essentially just kicking the person and after a few punts around the forest the magic ball will be smeared red inside and what is left of the human would be feed for pigs.
If you believe that the sphere doesn't prevent fall damage, that is. If it does, then a giant could have an amazing game of pinball, baseball, bowling, or whatever they wish with an entrapped wizard for the duration of the spell.
Look at what you've done. You spoiled it. You have nobody to blame but yourself. Go sit and think about your actions.
Don't be mean. Rudeness is a vicious cycle, and it has to stop somewhere. Exceptions for things that are funny.
Go to the current Competition of the Finest 'Brews! It's a cool place where cool people make cool things.
How I'm posting based on text formatting: Mod Hat Off - Mod Hat Also Off (I'm not a mod)
Fangeye, thanks for the breakdown! I think that all of that agreed with what I wrote, just more precisely and confidently. For this hypothetical I think that your assumption #1 is important, that the weightless object still has mass. Because without mass you really don't have the object any more. Or, at best instead of a tangible ball we'd be talking about a ball of energy. I don't think that forces can be applied to balls of energy in the Newtonian sense pretty much because of the problem with the math that you ran into.