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Puzzle 4
- Thread starter zekeman
- Start date
ChrisDuncan
Mechanical
It's impossible to start the pendulum without friction. How do you push mass up the slope/arc of the pendulum, against gravity, if you don't have anything to push against? A rocket motor works in vacuum because it pushing against the exhaust gasses it's propelling out, just like you could propel yourself through a vacuum if you threw baseballs in the other direction.
- Thread starter
- #82
"yes, there are horizontal components of force that can, and do act, on a pendulum. The external force acting is that of gravity, and the horizontal reaction forces transmitted through the pivot point of the pendulum (the reaction force is equal and opposite to the force that the kid exerts to move his legs to-and-fro)"
Trueblood,
So you are saying that a rope attached to the bob can sustain a horizontal component of force at the pivot point.
Think again. The only forces on the rope are tensile.
The so-called reaction force you mention is internal and moves the legs and remainder of the body in opposite directions such that the CM must remain at the rest position.
Trueblood,
So you are saying that a rope attached to the bob can sustain a horizontal component of force at the pivot point.
Think again. The only forces on the rope are tensile.
The so-called reaction force you mention is internal and moves the legs and remainder of the body in opposite directions such that the CM must remain at the rest position.
Still no-one has answered where the horizontal reaction comes from, except by ignoring Newton's first Law of Motion.
Let's summarise what's agreed:
Everyone agrees that with a rigid rod it's possible to generate horizontal movement. A bicycle operates in a similar way in principle.
Everyone agrees that a real child on a real swing can set it in motion from rest, although it's considerably more difficult than starting with a small amount of movement.
The question where people still differ is what happens on an idealised swing in a vacuum with a frictionless rope of zero flexural rigidity.
For those people who say that the reaction force comes from the momentum of the kids moving their centre of mass, how do the kids move their centre of mass with no reaction force to start with?
Doug Jenkins
Interactive Design Services
Let's summarise what's agreed:
Everyone agrees that with a rigid rod it's possible to generate horizontal movement. A bicycle operates in a similar way in principle.
Everyone agrees that a real child on a real swing can set it in motion from rest, although it's considerably more difficult than starting with a small amount of movement.
The question where people still differ is what happens on an idealised swing in a vacuum with a frictionless rope of zero flexural rigidity.
For those people who say that the reaction force comes from the momentum of the kids moving their centre of mass, how do the kids move their centre of mass with no reaction force to start with?
Doug Jenkins
Interactive Design Services
GregLocock
Automotive
Imagine two masses displaced horizontally. Attach the chain to one of them. push the other one away.
The chain now has an angle, and the cg has raised.
Now exploit that geometrical non linearity somehow.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
The chain now has an angle, and the cg has raised.
Now exploit that geometrical non linearity somehow.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
ChrisDuncan
Mechanical
"no-one has answered where the horizontal reaction comes from"
yes they did, pushing against friction of the pivot and possible air resistance
"Everyone agrees that with a rigid rod it's possible to generate horizontal movement. A bicycle operates in a similar way in principle."
a bicycle would be like pushing off the ground on a swing, you are fixed to the pivot in all axis and pushing the pedal/swing. Not touching ground on a swing you are only fixed in the vertical axis.
""The question where people still differ is what happens on an idealized swing in a vacuum with a frictionless rope of zero flexural rigidity.""
My instinct says you can't start the pendulum.
"" how do the kids move their centre of mass with no reaction force to start with?""
they don't
yes they did, pushing against friction of the pivot and possible air resistance
"Everyone agrees that with a rigid rod it's possible to generate horizontal movement. A bicycle operates in a similar way in principle."
a bicycle would be like pushing off the ground on a swing, you are fixed to the pivot in all axis and pushing the pedal/swing. Not touching ground on a swing you are only fixed in the vertical axis.
""The question where people still differ is what happens on an idealized swing in a vacuum with a frictionless rope of zero flexural rigidity.""
My instinct says you can't start the pendulum.
"" how do the kids move their centre of mass with no reaction force to start with?""
they don't
- Thread starter
- #86
OK, if you still believe you can get a net reaction force by extending the legs, consider this next case.
You're sitting in the middle of a frozen lake. Now this is a special frozen lake. It is frictionless.( not a new problem) and you have to get to the shore.
Tell me that you can move by extending your legs.
Seems to be very much the same problem of the swing starting from rest.
(I know the other ways but they are not allowed for this exercise)
You're sitting in the middle of a frozen lake. Now this is a special frozen lake. It is frictionless.( not a new problem) and you have to get to the shore.
Tell me that you can move by extending your legs.
Seems to be very much the same problem of the swing starting from rest.
(I know the other ways but they are not allowed for this exercise)
GregLocock
Automotive
Not similar enough, because the chain is only attached to one of the two masses, and by moving the masses apart you have change the geometry of the chain. Draw it out.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
- Thread starter
- #88
Well, let's add the ball and chain instead of feet to the guy on the lake.
Does he now get to the shore. I don't think so.
He pushes (impulse Fdt) the ball, m2, achieving velocity v2 and the guy , m1,goes opposite with velocity v1.System Momentum=0 before push. System momentum just after
initial push =0. After the chain becomes taut both masses are stopped internal impulse same as before, final system momentum=0. Final position of the, CM of 2 mass system is at the starting point. Poor guy is stuck!
Does he now get to the shore. I don't think so.
He pushes (impulse Fdt) the ball, m2, achieving velocity v2 and the guy , m1,goes opposite with velocity v1.System Momentum=0 before push. System momentum just after
initial push =0. After the chain becomes taut both masses are stopped internal impulse same as before, final system momentum=0. Final position of the, CM of 2 mass system is at the starting point. Poor guy is stuck!
No argument with that, but some are arguing (I now think correctly) that you don't need friction and/or air resistance.
OK, the bicycle analogy was a bit of a stretch, but the point I was making was that there is a fundamental difference between working on a rigid rod (to which you can apply a torque) and a chain or rope.
This is the question I wanted answered, and I think that Greg has now answered it.
With the no friction/ no air/ flexible chain and no initial movement, whatever you do the centre of mass of swing + rider will stay exactly where it started; under the top pivot, but the bottom end of the rope will not necessarily stay under the pivot, and as soon as you have some inclination in the rope you have a source of a horizontal reaction, and the ability to move your centre of mass.
I was arguing (to myself) that any offest between the bottom of the rope and the centre of mass will result in a rotation, and this will keep the bottom of the rope below the top, and above the centre of mass. What I missed was that will take time, so if some part of the swinger is moved sufficiently quickly, this will generate the required inclination of the rope, even though the centre of mass doesn't initially move.
Doug Jenkins
Interactive Design Services
The difference between the swing question and the moving on frictionless ice question is that the ice remains frictionless regardless of the angle of whatever is connecting you to the ice, whereas with the swing any inclination of the rope generates a horizontal force, which will affect the position of your centre of mass.
If you had a swing with a frictionless pivot and rope, in a vacuum, supported on a perfectly frictionless surface, starting from perfect rest, I don't think you could get that swinging.
Could you?
Doug Jenkins
Interactive Design Services
If you had a swing with a frictionless pivot and rope, in a vacuum, supported on a perfectly frictionless surface, starting from perfect rest, I don't think you could get that swinging.
Could you?
Doug Jenkins
Interactive Design Services
![[wink]](/data/assets/smilies/wink.gif "[wink] [wink]")
GregLocock
Automotive
I've just drawn a sketch with the swing seat supported by two angled wires, and the body and legs of equal mass, originally coincident. Then push the legs out horizontally. Then the main run of the chain doesn't move. Dang.
Did anyone actually try and read that paper I posted? I didn't.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
Did anyone actually try and read that paper I posted? I didn't.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
ChrisDuncan
Mechanical
"" but the bottom end of the rope will not necessarily stay under the pivot, and as soon as you have some inclination in the rope you have a source of a horizontal reaction, and the ability to move your centre of mass.""
""any offest between the bottom of the rope and the centre of mass will result in a rotation,...that will take time, so if some part of the swinger is moved sufficiently quickly, this will generate the required inclination of the rope, even though the centre of mass doesn't initially move.""
dang, what you just said made me flash on it. With a flexible rope you create a second pendulum by grabbing the rope above you, just like the model. Now you are anchored in all axis to a pendulum pivot that you can push off of. You raise your weight up one side of the arc, let gravity swing it back and you have your horizontal force.
good thread...lots of brainstorming
""any offest between the bottom of the rope and the centre of mass will result in a rotation,...that will take time, so if some part of the swinger is moved sufficiently quickly, this will generate the required inclination of the rope, even though the centre of mass doesn't initially move.""
dang, what you just said made me flash on it. With a flexible rope you create a second pendulum by grabbing the rope above you, just like the model. Now you are anchored in all axis to a pendulum pivot that you can push off of. You raise your weight up one side of the arc, let gravity swing it back and you have your horizontal force.
good thread...lots of brainstorming
may i suggest that you guys go donw to a nearby playground and play. hopefully you won't get arrested. you'll quickly see how a swing works. but then i guess this is a "thought experiment" and the real world is not allowed.
draw a free body diagram of the pendulum, it's something you probably did in school. the pivot point reacts radial load (zero bending stiffness in the cable), weight acts down, the horizontal component of the cable load is balanced be inertia force (the body in motion) or by a restraining force (if the body is at rest away from the neutral position).
draw a free body diagram of the pendulum, it's something you probably did in school. the pivot point reacts radial load (zero bending stiffness in the cable), weight acts down, the horizontal component of the cable load is balanced be inertia force (the body in motion) or by a restraining force (if the body is at rest away from the neutral position).
- Thread starter
- #97
My take is that in a vacuum with and without friction there is no net reaction force and no starting the swing.
In air, as others have said, pushing against air will yield an external force and thus be capable of moving the swing and, taking advantage of resonance, it could make the swing work as designed. It also could help that fellow on the frozen lake.
However,friction cannot help for a rope swing since you cannot transmit the friction torque through the rope. The rod swing may be another story but my inclination is that it can't help but can only slow things down.
In air, as others have said, pushing against air will yield an external force and thus be capable of moving the swing and, taking advantage of resonance, it could make the swing work as designed. It also could help that fellow on the frozen lake.
However,friction cannot help for a rope swing since you cannot transmit the friction torque through the rope. The rod swing may be another story but my inclination is that it can't help but can only slow things down.
i think that in a vaccuum and without friction you can start the swing ... push with the legs, pull with the arms, no net force but you've added energy to the system. consider that if you pull the swing off center and release it, then in this ideal lossless environment it would continue to swing.
consider you put a small rocket on the swing. thrust from the rocket is tangential about the pivot. the reaction is inertia, the motion is circular about the pivot. consider you pulse the rocket adding an increment of thrust each time it crosses under the pivot.
really, this is a wind up (no pun intended), isn't it ?
consider you put a small rocket on the swing. thrust from the rocket is tangential about the pivot. the reaction is inertia, the motion is circular about the pivot. consider you pulse the rocket adding an increment of thrust each time it crosses under the pivot.
really, this is a wind up (no pun intended), isn't it ?
hmm. I drew a quick FBD. I can see that using only the tension in the chain it is possible to create a ccw moment if you hold the chain vertical with your hands and push the end of the chain in a cw direction with your feet. no friction needed. Although, without using realistic numbers for the forces, in the 2 min. I just took it, is not for sure whether the moment you impose cancels the one from the off centered mass. If I have time in my 12 hr work day I will finish it ![[smile]](/data/assets/smilies/smile.gif "[smile] [smile]")
Interesting.
![[peace]](/data/assets/smilies/peace.gif "[peace] [peace]")
Fe
Interesting.
Fe
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