It's not exactly clear but this probably means that the decay rate was still appreciable after 40 days, so you can rule out a half-life that is much less than that.
I think I'd approach it this way. Assume the source is reasonably pure and macroscopic--say a few grams. Pick a credible mass number, and estimate the number of alpha emitters in the source. Compare that number to the number of decays, at the specified rate, in one second, an hour, a day, 40...
Good questions. To which I would add: What is the mass of the source and its atomic weight, or equivalently the number of gram-moles it contains? A flux of 3.5x10^6 particles per second is one thing if it's coming from a 5 kg source, and something else if it's produced by 1 mg.
Reference...
I don't know if you'd find it helpful, but I like to start from Newton's law for this type of problem.
Net Force = Mass x Acceleration.
You've found the acceleration. The mass is 100/g kg.
The net force is the applied force less the frictional force = 40 - 100.μ N (where μ is the frictional...
I think you have the wrong sign for the acceleration; but I agree something is strange here. The block was accelerated at almost g, which as far as I can see is incompatible with a 40 N force and a 100/g kg mass. Have you checked the given data, including units?
It has no effect that isn't already accounted for: weight by definition acts only vertically, and in this case is balanced by the normal force. You have the coresponding mass in the term that includes g.
Yes. As I should have remembered. (For a Niven ring, if you've come across that, it's worse--the situation is unstable and the ring will fall towards the star.)
I'm not sure what you did here. What do you mean by "adjusted 'R'"--the radius of the Dyson sphere? Are you referring to two different orbits or an eccentric orbit? (By Kepler's laws, how does the period vary with eccentricity?)
I meant the (single) speed of the (single) centre of mass of the two blocks taken together. I was trying to lead you towards the view you're asking about at the end,
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I think that is what you're expected to do.
Note that in later parts of the problem there are actual collisions; I think...
As I understand it you have a series of (time, distance) measurements.
Some things to consider in addition to the point you made.
How smooth a curve would the data represent? How will you use the data to find velocity and acceleration. How will you find the maximum velocity and acceleration...
Have you tried it? Start with point (b). For the upper current your thumb points towards you and your fingers are under your hand. For the lower current your thumb points away from you and your fingers are above your hand . . .
Try applying the right-hand rule to each of the currents separately and combining the results. Remember that fields add as vectors. and that the diagram is symmetric except for the directions of the currents.
Try to visualise what will happen if the whole system is at rest and then someone starts pulling the "plank". As I said, it might help if you start by imagining there's no spring and the mass is on a very slippery surface.
Also note that the question talks about "compression" of the spring.
Glad it worked out.
Just for completeness: You can use Gauss's law for this calculation. I don't think I've ever done it that way, but you might find it quicker if you get comfortable with the concepts. It involves constructing a (small) cylindrical closed surface. Look for articles on the...
One of the properties of Helmholtz coils (two coils face-to-face, separated by their own diameters, if I remember correctly) is that they produce an extremely uniform field at the midpoint of the line joining their centres. This was invaluable for people doing magnetic resonance, because it...
You need to take account of the fact that the force from your ring of matter is acting at an angle. By symmetry there are no horizontal forces in the resultant; so what you want is the vertical component of the force you have now--you need another factor of
h/(r2 + h2)1/2
inside the...
Close, but you need to make it clear what you're doing. For example, if you're trying to use Gauss's law for the entire plane, you haven't got a closed surface to integrate over. And the area and mass of the sheet are both infinite, so your first equation can't apply to the whole plane, and it's...
It looks as though you're thinking of part (b) as another statics problem; you don't seem to have used the fact that the masses are moved a further distance and then released. Have you visualised what will happen then?