Recent content by haruspex

That gives the right moments equation, but it is not right as a force diagram. The weight W, applied where it is, is not equivalent to a greater force applied at O. Why not consider the horizontal bar and the diagonal bar as the system and just write ##(y+z)W=xF##?

@gleem is taking moments about P, not O. I see no conflict.

How come you have relocated W to act at point O? The horizontal distance from P to the hanging mass is what matters.

Is it possible to move between sections? If so, maybe some not intending to use phones moved to where phone usage was low.

Because I could not be sure which you wanted and I felt it would be an easy mistake to make. But you seem to know what you are doing.

Yes, just be clear about which reference frame you want.

That is called coalescence. It is the case which maximises the lost KE and corresponds to coefficient of restitution = 0. Yes. In general, one does not know how long the collision process lasts, so the acceleration is unknown. An elastic collision approximates SHM, so the acceleration...

True, I was being lazy, which could mislead a student .I should have specified mechanical energy. Ah, no, that doesn’t do it because that would allow one of the bodies to have turned some of the KE into elastic potential energy and not released it because of some latch feature. So I have to...

Yes, use momentum, but that is only one equation and you need two. Are you familiar with coefficient of restitution? That is a property of the pair of materials involved. The value is from 0 to 1, with 0 being coalescence and 1 being perfectly elastic. (In an oblique collision, you have to...

Because you are specifying an impossible combination of conditions. In an actual one dimensional collision, there are two unknowns, the two final velocities. By requiring conservation of (kinetic) energy, conservation of momentum and specifying one of the final velocities (a stationary bullet)...

Your first calculation doesn’t assume "all the energy is transferred to the target". It assumes the target gets all the energy the bullet originally had, but says nothing about the energy the bullet is left with. If you were to continue and calculate that you would find it still has rather a...

The ant is always advancing to a new bit of rope, so it covers an increasing fraction of the rope. As that fraction increases, the speed with which the target moves away from it decreases. If that fraction gets big enough, its rate of crawl exceeds the rate at which the rope ahead of it is...

Edit: only just saw @Ibix' solution. Seems to be even a very similar choice of variable names. The rope starts at length L and grows at rate u. If at time t the ant is x from the far end of the rope then in further time dt the whole rope grows from ##L+ut## to ##L+ut+udt##, and the rope...

This is a common misconception. When you draw a force in an FBD, the direction shown only says which direction you are taking as positive. The equations written from it can then be checked against the diagram. One should not normally care, when drawing the diagram, which way it really acts. A...

It is called utility theory. Generally, the value one has for money is monotonically increasing but concave. The more you have, the less value each additional $ has. It makes insurance logical, but most other forms of gambling utterly illogical. An exception is where there is extra value in...