Physics Problems

[ZekeusAurelius]

Hello if anybody could help that would be awesome!

The velocity of a solid sphere sinking in water is proportional to the square of its diameter. A 1 in diameter sphere sinks at 0.5 m/s. If this sphere were divided into N smaller spheres that each sank at 20 mm/s, what is N?

A 2.5 in diameter top spins on a table at constant 2000 RPM. The top's spindle tip in contact with the table is not stationary but traverses a circle 7 inches in diameter on the table top with a linear velocity of 3 in/s. A dizzy, non-crawling ant on the top's outer surface ravels 440 ft before the top falls off the edge of the tale. How long did the top spin?

[sxk1693]

[sxk1693]

To elaborate more,

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Therefore,
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[sxk1693]

I have a vague idea on the second one. Does this involve angular velocity?

[ZekeusAurelius]

Ahh ok that makes more sense. I tried doing the first proportion, but I didn't know how to get the 'N', and with the second problem I don't understand what it means by 'traverses a circle' and how to incorporate all the different velocities they give you.

[sxk1693]

[ZekeusAurelius]

[nsguy1350]

[Fredfredburger]

[ZekeusAurelius]

The answer is supposed to be 19.9, it's from Set B of this year

[darksaber21]

Basically, you need to figure out the linear velocity traveled by the top's own spinning and the actual linear velocity.


First, convert 2000 RPM to ft/sec:
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Now, using the formula [unparseable or potentially dangerous latex formula], you should get:
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Now, using the basic rate equation (440 ft = 5280 in)
[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[calcguy]

This is problem 13B-37. Nsguy's solution is correct except he used the top diameter instead of the radius, 1.25 inches. Make that correction and you get the answer on the key, 19.9 sec.

[101dalmatians]

nsguy makes mistakes!!!!!!!!!!!!!!!!!! ooooooooooh.... (:P nsguy! dont take anythin seriously)

[101dalmatians]

Well I mean nsguy - you miss the matrix question on basically every calc test... just like i skip the scaling... so... yeah...