Recent content by haruspex

Quite, because those velocities represent available choices and it is reasonable to rank choices based on the outcomes. What makes the usage in post #1 awkward is that there are three fluids each with a fixed density, so it is more natural to think of choosing a fluid than of choosing a density...

That would have been clearer, yes. But consider.. 1. "Cars of velocities v1 > v2 > v3 are driven from A to B. Rank the cars in order of increasing time taken." 2. "A car is driven at velocities v1 > v2 > v3 from A to B. Rank the velocities in order of increasing time taken."

The wording is awkward but not actually wrong. It means rank the fluids according to the buoyant forces they are exerting, but since the only way the fluids have been assigned labels is by their density variable names, those are what have to be listed. Yes, necessarily.

I have always assumed that Archimedes figured this out by imagining replacing the submerged portion with an equal volume of water, exactly filling the void in the water that would be created by removing the submerged portion. Clearly that water would float, so the force exerted on it by the...

What did Archimedes realise about the quantity of fluid displaced by a floating object?

To my eye, those two curves look different. The second is close to being a quadrant of a circle but the first exhibits changing curvature along its length. What is the displacement / time equation for a dropped stone?

That analogy works, but it is not clear how you used it in this question. I assume you reversed it, so taking the given E/x graph as analogous to -v/t you drew the s/t graph corresponding to the latter, i.e. its integral. Something like that, but you have not followed your analogy very...

I am not sure I understand either of those two descriptions. As I read them, you are saying that both have negative gradients increasing monotonically in magnitude, the only difference being that yours starts at zero and the given answer starts positive. If so, both are valid. What the...

The given answer does not require exact linearity.

Yes, same strain with longer wire means greater elongation. Take note of two things about your first attempt: you made an assumption which you realised might not be valid you failed to use all the information provided So next time you are tempted to make an assumption, what should you do?

Not a good assumption. You have not considered what determines when a wire of a given material will break.

You are being chased by a bear. You can run at the same speed in any direction. Which way do you run? The a priori knowledge comes from millions of years of evolution.

I don’t even know what that means. Treat the minute hand as fixed (i.e. work in the frame of the minute hand). The tip of the hour hand moves at constant speed. It will be moving away from that of the minute hand fastest when its motion is directly away from it, so the line joining the tips is...

Either will do in principle, but I think it is more obvious if you take the longer hand as stationary. The tip of the shorter hand can move directly away from the tip of the longer hand, but the converse is never true. You cannot take a tangent to a circle from a point inside it.

Whoa, too much deference!☺️ Nothing to apologise for. My post #10 was wrong and I am glad you picked that up.