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How Is This Possible?

In the famous 1971 footage from Apollo 15, astronaut David R. Scott dropped a hammer and a feather at the same time on the surface of the Moon, thus confirming Galileo's hypothesis that gravity accelerates all objects at the same rate, regardless of mass or composition:

Undoubtedly that has been hammered into your brain since grade school. So, how do you explain this neat little video from the clever folks over at MIT:

Two wood boards are connected by a hinge. A small cup is mounted near one end of the upper board with a tee for a ball on the end. The board is lifted to a certain height, and when released the ball ends up in the plastic cup. This shows that the board has moved farther than the ball in the same period of time.

To see the video, visit the MIT News Multimedia website: Link - via Science2.0

So, the hinged plank has to travel in an arc, which is longer than the straight path that the ball falls through in order for the ball to fall into the cup. Notice that the plank hits the tabletop before the ball. Assuming air resistance doesn't come into much play (after all, the plank has more surface area than the ball) Does this mean that gravity affects the plank more than the ball? Is Galileo wrong?


The end of the stick (with the golf tee on it) is traveling in an arch.

The ball is not because it is dropping straight down.

As a result of this the end of the stick must travel a greater distance (in the same amount of time) as the ball.

This causes the ball to appear to go faster, when it is actually dropping at a constant rate.

If you dropped the wood, and the ball together (without a hinge) they would travel together at the same rate, and land simultaneously.
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opee, you've got it backwards. They're saying that the board went faster than the ball, because the board had to travel farther. Also, if you watch the video, when the board lands it is a few inches lower than the ball is at the same moment.

My guess: The ball received a very slight "bump" as it came over the lip of the tee it was sitting on. This slowed it just enough to make the difference seen in the video.
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Opee's first 3 sentences are correct, but then the logic fails:

If the ball travels less distance, and "arrives" after the wood plank, then it's traveling at less speed. If it's traveling at less speed, then it's accelerated less by gravity.

The question is why the wood plank falls faster.
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Or to put it another way, isolate only the vertical motion of the ball and cup; the cup has a shorter distance to travel.

Galileo’s hypothesis relates to gravity which is only the force straight down, so it holds true.
Admittedly there is a small force to the right from the wood falling, and it's counter force because the hinge holds the wood in place. But the resistance from that force is hardly enough to slow the wood up.
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Notice that the ball starts higher than the board, higher than the edge of the cup. The confusion lies in assuming the board has farther to travel. The distance that should be measured is the height only, not the arc. Gravity will pull the board straight down at the same rate. It's the pivot, or the hinge that makes the board accelerate. The ball falls straight down and the cup, which started lower than the ball, ends up underneath it, so the ball ends up in the cup.

If a ball is thrown in an arc and another ball is dropped at the same height as the top of that arc at the same moment that ball reaches the top of the arc, both balls will hit the ground at the same time.

Mythbusters did this with a bullet. A bullet fired straight hit the ground at the same time as a bullet dropped from the height of the gun.

http://dsc.discovery.com/videos/mythbusters-simultaneous-bullet-release.html
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The trick is the board has a center of gravity (the center of the board). This is the point that is accelerated by gravity at 9.8ft/sec2. The pivot end does not "fall" at all and the far end "falls" at an acceleration greater than the average for the whole board. The ball simply falls at 9.8 ft/sec2 thus arrives after the free end of the board.
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Let's assume the board is dropped from a height of 20 inches (this is just an estimate and it does not need to be accurate). The tee mounted to the board is supporting the ball approximately 1.5 to 2 inches above the top of the board, so the ball is starting out at a height of 21.5-22 inches. It is no mystery why the ball hits after the board; it was dropped from a greater height.
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Robert Young, you're right. It's the center of mass of the board that accelerates due to gravity. The end of the board will thus sweep downward faster than the board's center of mass, and therefore the ball. Galileo wasn't wrong, it's just nobody seems to understand physics.
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Actually, the center of gravity will accelerate a bit less than 9.8 ft/sec2 due to the angle of release, but the free end will still have greateracceleration than the center so it will still beat the ball.
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There's no contradiction with Galileo or Newton, and air resistance doesn't have anything to do with it.

Galileo says: in the absence of external forces, the center of mass of an object falls with an acceleration g, independent of the object's mass.

There are two problems here: 1) we should be looking at the acceleration of the center of mass of the board (which is halfway along, not at the end), and 2) there ARE external forces acting on the board (a slight upward force from the hinge).

Taking these facts into account is an elementary exercise in classical mechanics,* and the result is the following:

- the center of mass (middle) of the board moves with acceleration 3g/4. Note this is less than g because of the upward force from the hinge.
- the end of the board moves with twice the acceleration of the middle, 3g/2, which is greater than g, and therefore greater than the acceleration of the ball.

As an even more spectacular example, imagine that we attached a very light 50 foot stick to the board, with one end at the hinge. As the board falls, the other end of the stick would swing down at over 100 m/s. Is the end of the stick "falling" faster than the ball? No -- it's not free-falling. It's attached to a board. We need to take the whole setup into account before making random guesses about what will happen.

* Here's the calculation: the moment of inertia of the board is I=mL^2/3, where L is its length and m is its mass. The torque around the hinge is T=gmL cos(theta)/2, where g is the acceleration due to gravity, and theta is the angle between the board and the ground. For simplicity, Let's make the approximation that theta is small, so cos(theta) ~ 1. Then Newton's law says T=I d(theta)/dt, or d(theta)/dt ~ 3g/2L. The acceleration of the cup is then L d(theta)/dt = 3g/2.
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Thank you, Robert Young, for the right answer. Because if I tried to express the same, I would make it sound wrong! (And I know you're right, because... my H.S. physics teacher Mr. S. did this very problem on the board, many decades ago.)
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Imagine a cup nailed to toward the center of a propeller and another nailed at the tip. The angular velocity of the propeller has to be the same everywhere on it right? So, that means the outside cup has to be moving faster than the inside cup or they wouldn’t stay together. Just like racing someone on a track. Around the curves, the outside lane has to go faster to stay with the inside lane.

The angular velocity of the board in the experiment is going to be determined by it’s center of mass, which assuming the wood has the same mass throughout would be the geometrical center. So, the board is really falling from its center. Thus the heights are not equal. Unhinge the board and rotate it about its center to horizontal and you have a closer approximate of the heights.

Thus if the ball and board are traveling at the same speed, the board will win because it has less distance to travel. Galileo is still right.

The hinge causes a rotational velocity that also gives the cup a faster speed relative to the center of the board, which is closer to the velocity of the ball due to gravity. This is similar to the race track concept. Thus cup (and tip of the board) is moving faster than anyone.

I don’t think the tee changes much. The actual distance we are talking about is the top of the cup, not the board tip. So, the tee actually makes things more fair.

I would say this experiment falls in the realm of magician illusions. Their job is to trick our logic, not defy laws of physics.
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So many words telling the same story. Board and tee attached to something. Ball is not. Ball drops straight. Rest of stuff moves under it.
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It simply the release of stored potential kinetic energy. If you notice the string connecting the two planks of wood going taught, there will likely be a slight elastic effect and the plank being lifted also flexes slightly. Together they store enough energy that when released gives the falling plank the slight edge on the falling ball. No laws of physics are broken, just a clever illusion.
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This has nothing to do with gallileo's theory. Ball is freefalling but the plank is not.

Immagine that the plank is made of many sections. all sections will have the same acceleration in free fall (g) in this case they can not. you have to calculate the acceleration at the middle of the plank like david said. The acceleration at the end of the plank will be greater than that. It's like swinging a stick. you move your hand 10 cm, the tip of the stick moves much more than that
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Robert Young, I think you've found the answer: The ball appears to be 1 inch in diameter and falls at 9.8 ft/sec2 (imperial gravity). The board however seems to be metric at 1 meter long and therefore falls at 9.8m/sec2 which is approximately 3x faster!
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If dropped straight down, the ball and the board fall at the same rate, so the ball would stay sitting on the tee. But the board moves in an arc, which adds some forward motion to it and causes the tee to tilt an the way down. The ball, using its inertia to try to fall straight down, does not follow the arc. It rolls up the back of the dip in the top of the tee which gives it enough upward force to slow its fall momentarliy until the cup passes under it.
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Robert Young is correct about the center of gravity of the board, he just got the units wrong (g = 9.8 METERS /sec^2, not feet). Another way to think about it is to think of the AVERAGE distance the board is falling; the "fast" end of the board falls the greatest distance, the hinged end of the board doesn't fall at all. Thus the board (as a whole) is not falling faster than the ball at all.
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For the love of Pete, will you guys please use metric. acceleration due to gravity is 9.8 m/s^2. the center of the board accelerates at this rate but since the board is attached to a hinge and pivoting, the end accelerates faster.
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Mikerbaker was right. the ball starts higher than the cup. they fall the same vertical distance in the same time. The ball just happens to be over the cup when they have traveled the same vertical distance, and it continues to fall to the bottom of the now stopped cup. Stop over analyzing this guys.
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It is the classic "falling smokestack" except the board does not does not break. Why does the smokestack? Every particle in the 'stack is trying to fall at 9.8 m/s^2, but it is not in free fall. Instead, is is a mechanical linkage that pivots at one end. At some point the torsion becomes too great for the structure to bear, and it breaks somewhere along the length. If the board in this demonstration was long (or springy) enough you would see the board bend as the free end fails to keep up with the particles closer to the pivot.
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The plank is attached to the table. The pivot changes the whole plank initial vertical speed by increasing the speed of the free side.

The Galileo law works if the objects are free of any link because it would change the energy distribution.
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Reference aircraft wings and the effect of displacing air around the edge of a surface. The board displaces a considerable amount of air as it falls, some of the displaced air curls around the end of the board with the ball on it (as per the end of a wing), in part aiding in propelling the ball both right (toward the cup) and counteracting some of its ability to fall- giving the impression it moves slower.

Thoguh the 'arch' hypothesis remains true, the effect would be considerably reduced in a vacuum.
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It`s been said several times already, but since it`s so happily ignored:

guys, you`re all being way too difficult. The ball started higher because of the golf pin, and thus lands later. The cup started lower, and that`s how the ball ends up in the cup.
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