Barton s pendulum

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Barton s pendulum

When the satellite is outside the atmosphere there are only conservative forces gravity acting and, if the satellite is in a circular orbit, its [speed] is constant. When it starts to enter the atmosphere there is a small drag force, since the atmosphere is thin high up.

Barton s pendulum

This force always opposes the motion and I would have guessed that it would slow the satellite down. Can you help me in figuring out why the satellite actually speeds up?

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Indeed, as long as the Barton s pendulum force remains small, the satellite will gain speed, because speed increases as altitude decreases. A drag force cannot change that trend unless it's large enough.

Barton s pendulum

The key point is that a spacecraft loses altitude at a steady rate during reentry. It's fairly easy to work this out quantitatively: Let's call M the mass of the satellite, V its speed and z its altitude.

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Therefore, the above relation translates into: For proper re-entry the angle of reentry a cannot be too small, or else the spacecraft could "bounce" off the atmosphere and be back into outer space after losing just a little bit of energy.

As the atmosphere becomes denser at lower altitudes, the drag force F will eventually exceed the above threshold and the spacecraft will slow down. What happens when the monkey decides to climb up the rope? He was a professor of mathematics at Oxford from to The above picture once illustrated a discussion of the puzzle by the mathematical columnist Sam Loydwho called the problem "Lewis Carroll's Monkey Puzzle", while stating that it was not known whether Lewis Carroll originated the question.

Unfortunately, the solution given by Loyd happens to be erroneous. Thus, if the monkey and the weight are initially motionless at the same height, they will always face each other no matter what the monkey does.

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For example, they will both be in free fall if the monkey lets go of the rope, and both falls stop when the monkey grabs the rope again. The reason for this is simply that all the forces that are acting on either the monkey or the balancing weight are always equal. There are only two such forces for each body; the downward weight and the upward tension of the rope.

The weights are equal because the two bodies have the same mass and the rope also exerts the same force on either body because of the numerous "ideal" assumptions made here, including the absence of swinging on the monkey's side so that the rope exerts only a vertical force in either case.

It's also essential to assume not only the lack of any friction, but also the absence of mass for both pulley and rope otherwise the rope's tension would not be the same on either side of an accelerating pulley and it would vary along the length of an accelerating rope.

Note also that a "perfect" rope retains its length and transmits instantly any change in its tension. When the same forces act on bodies of equal masses their speeds change in the same way, so that the speeds remain equal if they are originally so and we're told here of an original equilibrium where both speeds are zero.

Both motions will therefore mirror each other. This deceptively simple puzzle is an excellent way to start a healthy discussion about the fundamental principles of classical mechanics. How high could the light ball bounce? Up to 9 feet!

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Shortly before impact, both balls have the same downward speed V. An elastic bounce off the floor makes the heavy ball go upward at speed V to meet the light ball still going downward at speed V.

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One of the most famous cases was the crash on a ranch near Roswell, N.M. Although the government said it was a top-secret weather balloon, an Army officer who helped recover the debris came forward 30 years later claiming a cover-up, asserting that an alien spacecraft had crashed.

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position.

When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging. A clavicle fracture, also known as a broken collarbone, is a bone fracture of the clavicle.

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