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69

Using your definition of "falling," heavier objects do fall faster, and here's one way to justify it: consider the situation in the frame of reference of the center of mass of the two-body system (CM of the Earth and whatever you're dropping on it, for example). Each object exerts a force on the other of $$F = \frac{G m_1 m_2}{r^2}$$ where $r = x_2 - x_1$ ...


45

I am sorry to say, but your colleague is right. Of course, air friction acts in the same way. However, the friction is, in good approximation, proportional to the square of the velocity, $F=kv^2$. At terminal velocity, this force balances gravity, $$ m g = k v^2 $$ And thus $$ v=\sqrt{\frac{mg}{k}}$$ So, the terminal velocity of a ball 10 times as ...


35

As other answers say, if someone just jumps off of the international space station(ISS), they would still be in orbit around the earth since the ISS is traveling at 17,000 miles per hour (at an altitude of 258 miles). Instead of just jumping, imagine the astronaut had a jet pack that could cancel that speed of 17,000 miles per hour in a very short time ...


19

Ball 1 will drop faster in air, but both balls will drop at the same speed in vacuum. In vacuum, there is only the gravitational force on each ball. That force is proportional to mass. The accelleration of a object due to a force is inversely proportional to its mass, so the mass cancels out. Each ball will accellerate the same, which is the ...


16

While everyone agrees that jumping in a falling elevator doesn't help much, I think it is very instructive to do the calculation. General Remarks The general nature of the problem is the following: while jumping, the human injects muscle energy into the system. Of course, the human doesn't want to gain even more energy himself, instead he hopes to transfer ...


12

It depends on how you define the problem. Humans have re-entered the atmosphere from the International Space Station many times, by riding in either a Space Shuttle or a Soyuz capsule. Someone re-entering without a spacecraft of some sort would obviously have to wear some kind of pressure suit (as Felix Baumgartner did in his jump). How elaborate is the ...


11

You will die. Terminal velocity is a bit more than 50 m/s. The bottom of your ramp appears to have a radius less than 2m. That means you'll be exposed to more than 125g as you zip around the bottom. Nice knowing you.


11

Other answers & comments cover the difference in acceleration due to friction, which will be the largest effect, but don't forget that if you are in an atmosphere there will also be buoyancy to consider. The buoyancy provides an additional upward force on the balls that is equal to the weight of the displaced air. As it is the same force on each ball, ...


11

Analyzing the acceleration of the center of mass of the system might be the easiest way to go since we could avoid worrying about internal interactions. Let's use Newton's second law: $\sum F=N-Mg=Ma_\text{cm}$, where $M$ is the total mass of the hourglass enclosure and sand, $N$ is what you read on the scale (normal force), and $a_\text{cm}$ is the center ...


10

That is an excellent example for a nice quote I read on the internet: "Common sense may be common, but it certainly isn't sense" :-) As it is hard to lift heavy objects, we assume that it must be easier for them to drop. Now, Newton's laws point out that light and heavy objects will fall with the same velocity. But is there an intuitive reason? Yes! The ...


10

If we are throwing two objects directly to the ground you are right. So from our kinematic equations: $$V_f = V_i + at$$ I would ask your teacher. What happens to the $V_f$ if $V_i=0$? Then Follow it up with what would $V_f$ be if $V_i$ was very large? The initial velocity DOES have an effect here. HOWEVER: Make sure that you are not misinterpreting ...


9

The paradox appears because the "rest frame" of the Earth is not an inertial reference frame, it is accelerating. Keep yourself in the CM reference frame and, at least for two bodies, there is no paradox. Given an Earth of mass M, a body of mass $m_i$ will fall towards the center of mass $x_{CM}=(M x_M + m_i x_i)/(M+m_i)$ with an acceleration ...


9

He "only" flew at the maximum speed of 370 m/s or so which is much less than the speed of the meteoroids – the latter hit the Earth by speeds between 11,000 and 70,000 m/s. So he was about 2 orders of magnitude slower. The friction is correspondingly lower for Baumgartner. Note that even if he jumped from "infinity", he would only reach the escape velocity ...


9

The reason that jumping can make a relatively large difference is that the kinetic energy is proportional to the square of the velocity. Thus relatively small changes to the velocity can result in relatively large changes to the kinetic energy. In addition, the velocity which a human can achieve in jumping is a substantial percentage of the velocity of fatal ...


9

As an addition to already posted answers and while realising that experiments on Mythbusters don't really have the required rigour of physics experiments, the Mythbusters have tested this theory and concluded that: The jumping power of a human being cannot cancel out the falling velocity of the elevator. The best speculative advice from an elevator ...


9

it is because the Force at work here (gravity) is also dependent on the mass gravity acts on a body with mass m with $$F = mg$$ you will plug this in to $$F=ma$$ and you get $$ma = mg$$ $$a = g$$ and this is true for all bodies no matter what the mass is. Since they are accelerated the same and start with the same initial conditions (at rest and ...


9

Newton's gravitational force is proportional to the mass of a body, $F=\frac{GM}{R^2}\times m$, where in the case you're thinking about $M$ is the mass of the earth, $R$ is the radius of the earth, and $G$ is Newton's gravitational constant. Consequently, the acceleration is $a=\frac{F}{m}=\frac{GM}{R^2}$, which is independent of the mass of the object. ...


9

indeed there would be a (very small) and homogenous pressure within the blob, coming from surface tension. This pressure is calculated by the Kelvin Equation and is significant in small droplets (reason for small droplets to have a higher vapour pressure than bulk liquid) In Your 100 m blob, this extra pressure is negligible of course. There is another ...


8

In the global, cartoon, sense, yes, this problem is equivalent to having a whole row of carefully designed, placed and arranged ramps so that you fall onto the first one, get "flung" out such that you then land on the next one and so on, until dissipation wastes away the energy. Obviously this can be done since it is the same principle as is used in say ...


8

OK, based on the comments I interpret the question as Universal gravitation tells us that the gravitation force on a heavy object is larger than that on a light object, so why doesn't the heavy one fall faster? Start with Newton's gravitation (as simplified for objects in the neighborhood of the Earth's surface): $$ F_g = mg $$ The answer arises from ...


6

There are two ways that mass could effect the time of impact: (1) An object which is very massive has a stronger attraction to the earth. Logically, this might make the object fall faster and so reach the ground sooner. (2) An object which is very massive is difficult to get moving. (I.e. it has very high inertia.) Thus one might logically expect the very ...


6

The best way to prove something is wrong, is by performing a simple experiment, giving a counterexample. Take two identical objects (balls, pens, books). Throw one of the objects upwards and the other object downwards, so they have different initial velocities. The moment you let them go, they are in free fall. I am quite convinced the latter one will be one ...


6

Yes--- he argued as follows in Dialogue concerning the Two Principal World Systems: suppose you tie a heavy object to a light one with a rope, would the light object fall slower and retard the heavy object, or would the heavy and light object together be a heavy object that falls more quickly? He concludes that neither: they both fall at the same rate. This ...


6

Blaise Gassend has created this simulation of "An elevator that breaks at the counterweight.": More discussion of various possible failure modes of a space elevator: Blaise Gassend discusses and simulates other possible failure modes at Animation of a Broken Space Elevator by Blaise Gassend. Bradley Carl Edwards. "A Hoist to the Heavens". IEEE Spectrum ...


6

1) Why can't a balloon float into space? A balloon rises because it is filled with a gas that is less dense than the air surrounding the balloon. Roughly speaking, the atmosphere gets less dense the higher up you go, so the highest altitude your balloon can reach is simply the altitude where the density is the same as whatever you filled your balloon ...


6

Suppose you pick two people at random. From one, you pluck a single hair from their head. Is it possible to tell who had the hair plucked by weighing the people? Technically, plucking a hair makes a person very slightly lighter, so you get a tiny bit of information about who had the hair plucked by weighing the people. But the information is very slight ...


5

Imagine an hourglass with just one stone inside. When the stone start to falling a scale would stop to measure it's weight, but it will measure a spike corresponding to the moment when it hits the bottom. The bigger the airtime, the bigger the spike. It is like concentrating the weight of the stone in a very specific time interval: when it hits. However the ...


5

While writing out my progress on the problem, I managed to give myself the answer. So, I thought that I may as well share the solution as I have seen many people in my class get stuck here. If I have a kinetic energy equal to $K = (1/2)mv^2$ And I later have a velocity equal to half the original $v$ What happens to $K$? Shouldn't it be 1/4th the original? ...


5

An possible (simplistic) answer would be the following: a simple model for the bouncing ball is a spring that shrinks to absorb all the initial kinetic energy and restores fully. To put it into equations, call $v_0$ the initial velocity of the ball, $m$ its mass and $K$ the spring stiffness. The initial kinetic energy is $\frac12mv_0^2$. If the spring ...


5

The big object has more inertia. If you have a big object and a small object, the gravitational force on the big object is greater. Why, then, doesn't it fall faster? The answer is that the big object needs more force to accelerate the same way. This is actually quite obvious if you view it in a different context. For example, suppose you have a ...



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