Recent content by haruspex

Both formulas are of the form A(N-1)-(A-1)(L). The N-1 shows that we are to take one body as given, so all motion is relative to that. The (A-1) implies that each linkage is assumed to remove all but one of the A degrees of freedom of a rigid component. That works if the connectivity is a tree...

When the hole first appears, yes it is reduced to S-A. As a result, the boat accelerates downwards. But as the water level rises in the boat, the water accelerated through the hole exerts pressure on the boat+water system. As this restores the buoyancy to somewhere close to its original...

For the same reason we do not add ##h_1## to ##h_2## to find the depth just below the hole.

The first equation looks right, but you then dropped a factor of 2.

I agree with the words but cannot relate them to your equations. Which of those terms is the external field? (Why would that term involve d?)

So what field must the induced charge produce in the cylinder?

I think the apparent contradiction is explained by the small part of the field that emanates from the sides of the cylinder. But you still have not said whether this is the conductor case or the insulator case. If conductor, what must the net field in the cylinder be?

If you are looking at the conducting case, what is the net field in the conductor? What does that tell you about the induced charges?

Suppose that at first the polarisation of waves from X is in the plane of the page. Imagine an ant looking at X from B. In the diagram as shown, we are looking down on the top of the ant. The ant sees the polarisation as horizontal. If we rotate the transmitter about line AB then the ant sees...

Relative to the sinking boat, but it is stationary relative to the surrounding water. Yes, but only until the water has entered the boat. Bernoulli is basically a conservation of work equation. The water is accelerated through the hole, but then what? Initially , in principle, it has the...

That would mean the hole might as well be the full width of the boat, in which case it would sink immediately.

It says the cable is "rectilinear", i.e. straight.

The pressure below the hole is ##(h_2)\rho g +p_a## and the pressure just above it is ##(h_1)\rho g +p_a##.

The problem description makes no sense to me. I cannot come up with a diagram that matches the numbers, and it looks like @Guillem_dlc can't either. I read the 7kg m2 as being the MoI about the object's centre, which is not how it is interpreted in the OP. But that only makes the numbers crazier.

The rate of flow of water into the boat is determined by ##\Delta h##, that in turn determines the rate of sinking, and ##\Delta h## determines the buoyant force. Since the hole is small, the boat sinks slowly, i.e. at a terminal velocity. Thus, ##\Delta h## is constant and the buoyant force...