Is is possible to set a swing into oscillations without touching the ground? This occurred to me while watching the second pirates movie. There is a scene where the ship's crew is suspended in a cage from a bridge in between two cliffs. They escape by swinging the cage towards one of the cliff. Is that even possible?

Update: From the answers, it is clear that it is possible to make the swing oscillate. Assuming the model Mark has proposed would there be limits to much you can swing? Is it possible to quantify it?

When you stick ice in a drink, AFAICT (the last physics I took was in high school) two things cool the drink:

• The ice, being cooler than the drink, gets heat transferred to it from the drink (Newton's law of cooling). (This continues after it melts, too.)
• The ice melts, and the cool liquid mixes with the drink, which makes the mixture feel cooler.

My first question is, to what extent does each of these cool the drink: which has a greater effect, and how much greater?

Secondly, how much of the cooling by the first method (heat transfer) is without melting the ice? That is, is there any significant amount of heat transfer to each speck of ice before it's melted, and how much does that cumulatively affect the drink's temperature?

I suppose all this will depend on a bunch of variables, like the shape and number of ice cubes and various temperatures and volumes. But any light that can be shed, let's say for "typical" situations, would be appreciated.

I'm trying to get motivated in learning the Atiyah-Singer index theorem. In most places I read about it, e.g. wikipedia, it is mentioned that the theorem is important in theoretical physics. So my question is, what are some examples of these applications?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in physics which overlap in the essence of their problems with those of small world networks. Which natural phenomena exhibit these kind of features similar to small world networks?

I would like to know that, so maybe I can look at those problems to get inspiration that can be taken to social network theory.

To suck water through a straw, you create a partial vacuum in your lungs. Water rises through the straw until the pressure in the straw at the water level equals atmospheric pressure. This corresponds to drinking water through a straw about ten meters long at maximum.

By taping several straws together, a friend and I drank through a 3.07m straw. I think we may have had some leaking preventing us going higher. Also, we were about to empty the red cup into the straw completely.

My question is about what would happen if Superman were to drink through a straw by creating a complete vacuum in the straw. The water would rise to ten meters in the steady state, but if he created the vacuum suddenly, would the water's inertia carry it higher? What would the motion of water up the straw be? What is the highest height he could drink from?

Ignore thermodynamic effects like evaporation and assume the straw is stationary relative to the water and that there is no friction.

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A mathematical model would be much appreciated.

A 0.66 kg copper rod rests on two horizontal rails 0.66 m apart and carries a current of 65 A from one rail to the other. The coefficient of static friction between rod and rails is 0.54. What is the smallest magnetic field (not necessarily vertical ) that would cause the rod to slide?

a)What is the angle of B from the vertical? (deg)

b) What is the magnitude of B?

What does an atom radiate: a wave packet or a single photon?

Been studying hopping conduction and something that everyone is taking for granted is bothering me.

Let's say we have a bunch of sites that are either unoccupied, singly occupied, or doubly occupied. Due to on-site Coulomb repulsion the two electron levels are separated by U energy at a doubly occupied site. Now everyone is saying that the two electrons on the double site are in the spin singlet state due to, I assume, Pauli exclusion. However the two electrons are not in the same energy level - they are separated by U so why is there a restriction on their spins?

Sorry for the layman question, but it's not my field.

Suppose this thought experiment is performed. Light takes 8 minutes to go from the surface of the Sun to Earth. Imagine the Sun is suddenly removed. Clearly, for the remaining 8 minutes, we won't see any difference.

However, I am wondering about the gravitational effect of the Sun. If the propagation of the gravitational force travels with the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent.

What is the state of the art of research for this thought experiment? I am pretty sure this is knowledge that can be inferred from observation.

For each statement select P for Positive, N for Negative, or Z for Zero charge (Neutral). (If the first answer is positive, the second negative, and the third neutral (zero net charge), enter PNZ.

A) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The rod is then removed. What is the final charge of the conductor?
B) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The conductor is then grounded while the rod is kept close. If the rod is first taken away, and THEN the ground connection is removed, what is the final charge of the conductor?
C) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The conductor is then grounded while the rod is kept close. If the ground connection is first broken, and THEN the rod is removed, what is the final charge of the conductor?

If I poured water into my tea, would I see more or less of the bottom of the tea-cup?

Intuitively, there would be as many particles blocking as many photons, and so I'd see the bottom just as clearly as before

For S and S' in standard configuration, the Galilean transformations are:

x' = x - vt, y' = y, z' = z, t' = t

From the Lorentz transformations for v << c:

x' = x - vt, y' = y, z' = z, t' = t - vx/c^2

So it looks as if the Galilean transformations become increasingly accurate for:

vx -> 0, v << c

And exact for v = 0 for all x.

Yet, all text books I've come across state that the Galilean transformatons become more accurate for the condition v << c only.

So what are the conditions under which the Galilean transformations become more accurate and why?

Inspired by How do we know that dark matter is dark? and What is the temperature of the surface and core of a neutron star formed 12 billion years ago now equal to?

Where exactly does CMB come from. I've seen it in documentaries as a huge sphere with Earth in the middle. But if all this radiation was ejected from the start of the universe some time after the big bang; why can we see it? Surely the radiation should be travelling away from us? Just like every galaxy is?