What you’re describing sounds like the monkey pulls up a distance, then stops, then pulls up a distance then stops, … In that case, every time he pulls up, he does apply more force (compared with just hanging) to accelerate upwards. But every time he stops, he applies less force (again compared with hanging) as he slows down and stops.
By the same token, surely the monkey only needs to exert more force than gravity is exerting to start the counterweight moving - and once it is is moving it will continue to move until the monkey again exerts less force, at which time both it and the monkey will slow down or stop.
Well, yes, I’m describing how rope climbing actually happens (doesn’t have to be a complete stop, but there is a distinct increase and decrease in speed typically as arms are swapped back and forth).
Exactly.
To say that he accelerates only one time can only be true if the entire distance he moves is basically just one arm’s reach/pull distance.
No.
The monkey will start to climb the rope and the bucket will rise. However, monkeys can climb fast enough that he can reach the top before the bucket gets there.
He can’t, it isn’t possible. If you treat the rope as massless half the energy the monkey expends climbing will go to raising the bucket. They will always be at the same level. If the rope does have mass, then the monkey sinks. He may delay the inevitable, but he cannot win. Of course, the pulley must be frictionless.
For one, in real life the monkey won’t be travelling up the rope at a constant speed. There will be acceleration and deceleration the whole way.
Two, while you can hang on a rope with both hands, when climbing it you have only one hand on the rope much of the time and that arm has to bear the force that both arms otherwise would. (Really, it’s going to bear a bit less since this will be the deceleration part of the accent, but it’s still more than each arm would bear while hanging.)
That sounds right to me.
Assuming we’re in word problem world, and a) the rope has mass, and b) the pulley is frictionless, what’s wrong with this scenario:
Currently they’re at equilibrium, the mass of the rope and bucket equal the mass of the monkey and rope.
The monkey attempts to climb. That will pull some of the rope to its side of the pulley, creating an imbalance.
Since they’re no longer at equilibrium, the bucket starts rising, regardless of what the monkey does, since the monkey’s side now has more mass. The bucket rises slowly at first, but accelerates until it reaches the top of the pulley and stops. (Then the monkey can climb all it wants.)
Yes, climbing requires more effort than hanging. Effort is energy, not force. Hanging does not require any expenditure of energy, while climbing does.
Well, you’re not a strong little monkey. It’s not implausible that a monkey could pull himself up a rope at a constant velocity. In that scenario, he only exerts extra force when he accelerates from hanging to his constant velocity. While he’s moving at a constant velocity, he only needs the same force as he needs when he’s just hanging in place.
Actually I am a monkey…I am locked in a room with about 50 other monkeys and they told us to just start typing…
But you got logged out of Youtube?
♫ Dear Boss, I write this note today to tell you of my plight.
And at the time of writing I am not a pretty sight. ♫
massless ropes, frictionless pulleys, monkeys who jerk while climbing or do it nice and slow…
It would seem that the problem is not defined thoroughly enough to be able to give a definitive answer.
So, to get this started off on a better foot… It is a European monkey or an African monkey?
There’s is no such thing as “exactly the amount of force required to”. There’s an exact energy required, but any force exceeding gravity can give that energy, ignoring friction. And even with friction and in a real world situation, there is no “exactly the amount of force.”
First off, the whole point of a pulley is to reduce the friction so the rope can “slide” from one side to the other more easily. If you have too much friction in your pulley, you no longer have a pulley and instead have a curved surface for the rope to slide on. So by definition, the pulley should have minimal friction. That is the point of the pulley in the problem statement.
Second,
You seem to be under the impression that a force cannot be in play without motion. This is false. Consider lying in your bed at night. You are simultaneously under the force of gravity pulling you down and the bed pushing you up. You are in equilibrium, not moving either up or down, but you are under two forces - two accelerations.
Tension in a rope is a force, even if the rope is not moving. Consider tug-o-war. You get two teams opposing each other, each team pulling on the rope as hard as they can. Are you asserting that if the rope is not moving, there are no forces being applied to it? That the people are not exerting force?
You seem to be conflating forces with work. Work does require motion. By definition, work is a force applied through a distance. Note that there’s the force thingy separate from the distance thingy. They are independent.
In order to stand up from a chair, you have to apply more force than your weight. Why? Your weight is countered by the force of body on the chair and legs against the ground. To lift, you have to move your weight higher in the gravity field, you have to exert additional force over your weight.
This also applies when climbing. You are trying to move your weight upward against gravity, you have to have more force than gravity is pulling down in order to move upwards.
I suppose in free fall you would be correct. Once you start moving your inertia would keep you moving, so you do not need additional force. But you are not in free fall, you are under a gravity field that is pulling you down. If you let off that additional force, you stop moving.
Similarly, in order for you to lift a bucket on a rope, you have to pull on the rope with more force than the weight of the bucket. The bucket will not move up until the force exceeds the weight, i.e. the pull of gravity.
So, with this setup, somehow a monkey magically appears on a rope that hangs from a pulley with a bucket of sand of equal weight to the monkey on the far side. It is magically in equilibrium. This is the starting point. Go.
The monkey tries to climb, it pulls on the rope to lift itself against gravity. It is thereby applying more force than gravity is pulling down. It does not matter if the monkey is jerking or smoothly pulling, he is applying more force than his weight. Thus he starts to lift himself.
However, the rope is not rigidly attached. As the monkey pulls, the rope sees an increased tension. As all good ropes, it transfers that tension along the lenth to the other end causing the resistance to motion. Flowing over the pulley redirects the tension but does not change it. The bucket is now pulling down on the other end of the rope. The bucket weighs the same as the monkey. If the monkey is applying more force than the 10 lb weight, that increases the tension of the rope above the 20lb tension of monkey vs bucket. Ergo, there is more than 10 lbs pulling the bucket upwards. The bucket moves upwards, the monkey moves upwards, the rope rolls across the pulley, and the monkey travels half the distance he would otherwise normally travel for that amount of climb. He lifts with enough force to normally move 6 inches. He moves 6 inches up with respect to the rope. The monkey’s rope moves 3 inches down as the bucket moves up.
Now you can argue the weight of the rope and whether it makes a difference. For a heavy rope and the end free hanging below the monkey, then the monkey may shift enough rope to his side to disturb the equilibrium. If the monkey climbs fast, he may or may not be able to overcome this weight shift, depending on the relative weights and whatnot. But if the rope is sufficiently light, or as described above, it loops below the monkey and is tied to the bucket, then the weight shift is inconsequential.
The video demonstrates this. The climbing robot is not a monkey. It operates by spooling in the rope, not hand over hand jerking the rope. Yes, it is programmed to trigger on and then off. Watch the counterweights. They move smoothly up while the robot is moving smoothly up. They stop moving exactly with the robot. The counterweights do not only move when the robot stops and starts, but fully along the smooth portion of operation.
See also
You must be reading Chronos wrong somehow. There’s nothing wrong with what he describes. There is in fact no way for this monkey on a rope problem to not involve motion, even if the rope stays precisely “balanced” while the monkey “climbs” both the monkey and the counterweight will rise, ergo motion.
What RaftPeople is pointing out is that the monkey’s arms are only so long. Each pull he only lifts himself so far, because that is the range of travel of his arms/legs/tail. The distance to the pulley is likely to be much greater than that distance of one pull up. Thus in order to climb to the pulley, the monkey will need to make repeated pulls, i.e. climb. Even if the rope did not move (i.e. it was tied to the pulley), he would still need more than one motion to move all the way to the top.
Stand on a force gauge in an elevator.
Elevator stands still: 1G
Elevator accelerates upward: >1G
Elevator moves upward with constant speed: 1G
Elevator slows down: <1G
That’s what Chronos is describing.
He’s doing so in a way that either abuses the language of physics or shows a misunderstanding about the laws of physics. It’s entirely possible for the monkey to exert a force higher than 1G only in the very start of this single pull.
Chronos clearly states that climbing does not involve additional force over hanging. He states that beginning the climb is an acceleration, but the actual act of climbing is not an acceleration. This is false. The entire act of climbing, from starting motion to stopping motion, is an additional force above weight. If not, you would not be moving upwards, you would be [del]standing[/del] hanging still. Hanging is not climbing. Climbing is moving.
An acceleration does not mean you start moving. 1 acceleration can be offset by an equivalent acceleration in the opposite direction, resulting in net zero motion. This is equilibrium. Two opposing forces balance out. There is no motion, but there is still force, and by definition, a force is an acceleration.