F
Finn Mac Cool
Guest
*NOTE: This post is very long and uses a lot of equations which (while relatively simple) might still be more than people are willing to do for a message board debate. If this is the case for you, look to the bottom of the post and youll find the very simply analogy version of most of what Ive been saying here*
What a lot of this comes down to is Newtons second law: Force = Mass x Acceleration. This can also be read as Mass = Force / Acceleration, or Acceleration = Force / Mass. For the purposes of this post, Mass will always be measured in kilograms (hereafter kg), Acceleration will always be measured in meters per second per second (how many meters per second an object gains with each second, hereafter referred to as m/s/s), and Force will always be measured in Newtons (1 kg of Mass x 1 m/s/s of Acceleration, hereafter referred to as N).
Lets say the helicopter was accelerating upward at 2 m/s/s (Im aware the real acceleration is probably far different, but Ill call it this for simplicitys sake). Now lets say the helicopter had a mass of 1500 kg (again, a VERY rough estimate). Multiply those two together, and the helicopters net force comes to 3000 N. I say net force because some of the force exerted by the propellers had to go to canceling out the downward force of gravity, and so couldnt be used for acceleration upwards.
Now look at Clark. If he just hung onto the rope, he would still exert a downward force, but not much of one. This force would be Clarks mass (Ill guess about 100 kg) times the acceleration of gravity (10 m/s/s). So, simply by hanging on to the helicopter, Clark exerts 1000 Newtons of force. Since Clarks force is working in the opposite direction of the helicopters force, Clarks 1000 N must be subtracted from the helicopters 3000 N, leaving it with a net force of 2000 N. Since the mass of the helicopter remains constant, this change in force must reduce its acceleration. Acceleration = Force / Mass; Acceleration = 2000 N / 1500 kg; Acceleration = 1.333 m/s/s. Now obviously, using his mass and gravity alone, Clark can only reduce how fast the helicopter accelerates, not stop it or bring it down. This is where we run into the point of contention.
For Clark to bring the helicopter down, he must increase his downward acceleration, as he cant change his mass. They key to this lies in Clarks arms. Now, I dont know what the mass of the average human arm is, but lets say that both arms total about 10 kg. The rest of his body (90 kg) will still be pulling down with the standard gravity acceleration (90 kg times 10 m/s/s = 900 N). Clarks arms are key because he can move them down at a very fast rate. Lets say that Clarks arms (which are holding the rope) can accelerate at 300 m/s/s (for someone who can run at multiple Mach speeds, this probably wouldnt be too hard). With a mass of 10 kg, this comes to a force of 3000 N. Combined with the effect of gravity on the rest of Clarks body, he is pulling down on the helicopter with 3900 Newtons. This cancels out the helicopters net force, and still leaves 900 N to pull it down with. This is simple physics: if you have two competing forces on an object, the stronger force will be the one to move it; the weaker force can merely slow it down. Clark pulled down on the helicopter with greater force than the propellers pushed it up, so the helicopter went down instead of up.
There are some who argue that Clark should have been lifted off of the ground and been unable to exert force with his arms without a foothold or some similar thing. I have two responses to this:
1) Clark would have been lifted off the ground if he hadnt been pulling down on the rope the whole time. If he had ceased to sufficient force on the helicopter, even for an instant, he would have been pulled up. However he maintained a force that was greater than or at least equal to the helicopters net force from the instant he grabbed onto the rope.
2) Why would his arms suddenly be unable to pull down on the object just because he wasnt anchored down. Clark is holding onto the rope and, even if he was in mid-air at the time, he could still have the muscles in his arms go downward. Now, any human being who tried that would merely move upward as others have said, because the force they exerted down would be miniscule to the force they were being moved up by. However this rule goes out the window when the force exerted downward is greater than the upward force. Imagine that, instead of Clark, a missile was attached to the helicopter. That missile would be relatively small, with low enough mass that it wouldnt stop the helicopter by gravity alone. But then suppose that the jet fuel inside the missile fired. If the missile was pointing down, it would exert a powerful force in that direction, far more than the helicopters net force. The missile would have nothing to hold onto beyond the helicopter itself, but would still exert force downward and either take the helicopter down with it or break of the piece it was attached to. Why would Clarks arms suddenly be incapable of moving down without a foothold? If I was in Clarks position my arms wouldnt move, but thats because the force mine can exert is far less than the propellers force, but Clarks arms exert a force greater than the propellers, so instead of his arms failing to move down while the helicopter went up, Clarks arms would go down and the helicopter would fail to go up.
*SIMPLE ANALOGY*
Think of Clark and the helicopter like a vertical tug of war. Imagine yourself playing tug of war with someone else where youre standing in the West and the other person is standing in the East. There are two factors to determine who wins in tug of war: who is the heaviest and who is the strongest. If youre just as strong as your opponent, but he weighs more, then he is going to win, because you will have to pull on the rope a lot more to move him than he does to move you. Similarly, if you both weigh the same, but youre stronger than your opponent is, you are going to win, because you can pull back much harder on the rope than he can. Now suppose youre playing tug of war with someone heavier and stronger than you are, but the other guy isnt even going to try. He will hold onto the rope, but wont pull back on it. Unless this guy is like sumo wrestler heavy, you will win, because, while his weight is still an obstacle to pulling him forward, you dont have to deal with him pulling back on the rope, which normally cancels out a lot of the energy you put into pulling the rope. Finally, imagine that youre playing tug of war, not with a person, but with a small rocket. The rocket weighs much less than you do, but it launches itself way from you at very high speeds. Despite having much greater weight and pulling your hardest, its no match for the energy the rocket puts into flying away from you, and it will win.
Hopefully you can see how all this relates. Both Clark and the helicopter were pulling on the rope. The helicopter weighed more, but Clark pulled back much harder on the rope. In the end Clark won this tug of war because he exceeded the helicopters strength by far more than the helicopter exceed Clarks weight.
What a lot of this comes down to is Newtons second law: Force = Mass x Acceleration. This can also be read as Mass = Force / Acceleration, or Acceleration = Force / Mass. For the purposes of this post, Mass will always be measured in kilograms (hereafter kg), Acceleration will always be measured in meters per second per second (how many meters per second an object gains with each second, hereafter referred to as m/s/s), and Force will always be measured in Newtons (1 kg of Mass x 1 m/s/s of Acceleration, hereafter referred to as N).
Lets say the helicopter was accelerating upward at 2 m/s/s (Im aware the real acceleration is probably far different, but Ill call it this for simplicitys sake). Now lets say the helicopter had a mass of 1500 kg (again, a VERY rough estimate). Multiply those two together, and the helicopters net force comes to 3000 N. I say net force because some of the force exerted by the propellers had to go to canceling out the downward force of gravity, and so couldnt be used for acceleration upwards.
Now look at Clark. If he just hung onto the rope, he would still exert a downward force, but not much of one. This force would be Clarks mass (Ill guess about 100 kg) times the acceleration of gravity (10 m/s/s). So, simply by hanging on to the helicopter, Clark exerts 1000 Newtons of force. Since Clarks force is working in the opposite direction of the helicopters force, Clarks 1000 N must be subtracted from the helicopters 3000 N, leaving it with a net force of 2000 N. Since the mass of the helicopter remains constant, this change in force must reduce its acceleration. Acceleration = Force / Mass; Acceleration = 2000 N / 1500 kg; Acceleration = 1.333 m/s/s. Now obviously, using his mass and gravity alone, Clark can only reduce how fast the helicopter accelerates, not stop it or bring it down. This is where we run into the point of contention.
For Clark to bring the helicopter down, he must increase his downward acceleration, as he cant change his mass. They key to this lies in Clarks arms. Now, I dont know what the mass of the average human arm is, but lets say that both arms total about 10 kg. The rest of his body (90 kg) will still be pulling down with the standard gravity acceleration (90 kg times 10 m/s/s = 900 N). Clarks arms are key because he can move them down at a very fast rate. Lets say that Clarks arms (which are holding the rope) can accelerate at 300 m/s/s (for someone who can run at multiple Mach speeds, this probably wouldnt be too hard). With a mass of 10 kg, this comes to a force of 3000 N. Combined with the effect of gravity on the rest of Clarks body, he is pulling down on the helicopter with 3900 Newtons. This cancels out the helicopters net force, and still leaves 900 N to pull it down with. This is simple physics: if you have two competing forces on an object, the stronger force will be the one to move it; the weaker force can merely slow it down. Clark pulled down on the helicopter with greater force than the propellers pushed it up, so the helicopter went down instead of up.
There are some who argue that Clark should have been lifted off of the ground and been unable to exert force with his arms without a foothold or some similar thing. I have two responses to this:
1) Clark would have been lifted off the ground if he hadnt been pulling down on the rope the whole time. If he had ceased to sufficient force on the helicopter, even for an instant, he would have been pulled up. However he maintained a force that was greater than or at least equal to the helicopters net force from the instant he grabbed onto the rope.
2) Why would his arms suddenly be unable to pull down on the object just because he wasnt anchored down. Clark is holding onto the rope and, even if he was in mid-air at the time, he could still have the muscles in his arms go downward. Now, any human being who tried that would merely move upward as others have said, because the force they exerted down would be miniscule to the force they were being moved up by. However this rule goes out the window when the force exerted downward is greater than the upward force. Imagine that, instead of Clark, a missile was attached to the helicopter. That missile would be relatively small, with low enough mass that it wouldnt stop the helicopter by gravity alone. But then suppose that the jet fuel inside the missile fired. If the missile was pointing down, it would exert a powerful force in that direction, far more than the helicopters net force. The missile would have nothing to hold onto beyond the helicopter itself, but would still exert force downward and either take the helicopter down with it or break of the piece it was attached to. Why would Clarks arms suddenly be incapable of moving down without a foothold? If I was in Clarks position my arms wouldnt move, but thats because the force mine can exert is far less than the propellers force, but Clarks arms exert a force greater than the propellers, so instead of his arms failing to move down while the helicopter went up, Clarks arms would go down and the helicopter would fail to go up.
*SIMPLE ANALOGY*
Think of Clark and the helicopter like a vertical tug of war. Imagine yourself playing tug of war with someone else where youre standing in the West and the other person is standing in the East. There are two factors to determine who wins in tug of war: who is the heaviest and who is the strongest. If youre just as strong as your opponent, but he weighs more, then he is going to win, because you will have to pull on the rope a lot more to move him than he does to move you. Similarly, if you both weigh the same, but youre stronger than your opponent is, you are going to win, because you can pull back much harder on the rope than he can. Now suppose youre playing tug of war with someone heavier and stronger than you are, but the other guy isnt even going to try. He will hold onto the rope, but wont pull back on it. Unless this guy is like sumo wrestler heavy, you will win, because, while his weight is still an obstacle to pulling him forward, you dont have to deal with him pulling back on the rope, which normally cancels out a lot of the energy you put into pulling the rope. Finally, imagine that youre playing tug of war, not with a person, but with a small rocket. The rocket weighs much less than you do, but it launches itself way from you at very high speeds. Despite having much greater weight and pulling your hardest, its no match for the energy the rocket puts into flying away from you, and it will win.
Hopefully you can see how all this relates. Both Clark and the helicopter were pulling on the rope. The helicopter weighed more, but Clark pulled back much harder on the rope. In the end Clark won this tug of war because he exceeded the helicopters strength by far more than the helicopter exceed Clarks weight.
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