# Tag Info

37

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 $r = x_2 - x_1$ ...

32

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 ...

12

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 ...

11

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 ...

9

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 ...

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 ...

9

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

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.

8

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 ...

8

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 ...

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 ...

7

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 ...

7

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 ...

6

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

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 ...

5

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 ...

5

Depends how much fuel you have. The space shuttle and other craft need such large heat shields because they use it to dump all their kinetic energy 'for free'. The shuttle only uses it's engines for takeoff and has only some small thrusters available in orbit. If you also had some form of propulsion as well as a space suit and could generate all the thrust ...

5

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 ...

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

I would guess you've heard that an airplane in a spin or some other critical state can dive to build up speed, then when it pulls out of the dive the increased speed increases the lift and can allow the pilot to regain control. You are presumably asking if the same idea can be used for a falling person. The problem is that an aircraft wing is carefully ...

4

It is difficult to determine which will fare better. Small mammals can survive a fall from arbitrary distances. Here's one article I found talking about cats. A chief contributor to small mammals' survival is that they have a lower terminal velocity due to the way wind resistance scales. Wind resistance scales with the area of the animal, while weight ...

4

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 ...

4

The person hits the ground at the same speed in both scenarios. Once you're in the air, you fall towards the ground with a constant acceleration of about 10 m/s^2. Everything falls the same way - rocks, cannonballs, people - regardless of size or somersaulting. There may be some small effects from air resistance, but not enough to be noticeable. The ...

4

I believe that is covered by this answer I posted some time ago to a related (but not quite the same) question. Adapting it to your notation, $$t = \frac{1}{\sqrt{2G(m + M)}}\biggl(\sqrt{r_0 R(r_0 - R)} + r_0^{3/2}\cos^{-1}\sqrt{\frac{R}{r_0}}\biggr)$$ The same formula is given in the Wikipedia article Qmechanic mentioned in a comment.

4

No. You, your bottle and drink within it, all (regardless of the bottle orientation) move with the same acceleration that amounts to gravitational acceleration. In case you are standing on the ground, you and bottle are at rest, while drink (neglecting the constrains of the bottle) moves with gravitational acceleration toward your thirsty throat. :) Edit: ...

4

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 ...

4

UPDATE 2: If allowed to freely design the spacesuit the answer is yes.(see below) Initial answer before clarification The short answer is no. (SEE UPDATE) The longer answer is that there are a few key obstacles. One is that the person on the space station is in a relatively stable orbit around the planet. So while jumping from the space station would ...

4

Let $v$ denote the speed of sound, and let's use your equations. Combine the second and third equations to get $$\frac{h}{v} = t-t_1$$ so that $$t_1 = t-\frac{h}{v}$$ and therefore using the first equation $$h = \frac{1}{2}g\left(t-\frac{h}{v}\right)^2$$ Putting this in standard form to use the quadratic equation gives  h^2 - ...

3

In fact, in case B, if the rocket really accelerate at g, downward, in the vicinity of earth, it is "free-fall" : m stay midair. Except this detail, the main difference between the rockets and the elevator is the thrust. No thrust pushes the elevator during free fall. No thrust means no force applied on its inhabitants, so no feeling of gravity. But, if ...

3

From searching I find that the survival rate from a fall depends on the deceleration rate that the body undergoes on impact, and that depends on the surface of the fall. Water is less punishing than land. Here is a quote, which I will not source, but can be found on the net. Stone states that jumping from 150 feet (46 metres) or higher on land, and 250 ...

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