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isaac Physics- An anchored buoy

i am stuck here with this very booky question:

An iron anchor of mass m=500kg and density ρ=8000kgm−3 is attached by a light, thin cable to a light spherical buoy of radius r intended to mark its position.

(Assume water has density ρ𝗐=1000kgm−3)

How large must the radius of the buoy be to prevent the anchor dragging it under the surface when the water is too deep for the cable to reach the bottom? Give your answer to 3 significant figures.

any help would be appreciated

Reply 1

Arctic Kitten

add a g for expression for Ub :smile:

I forgot it
20181027_214954-compressed.jpg.jpeg

(edited 5 years ago)

image-156a7d4d-6f25-4b6b-bb07-1876e91272206784146666696719985-compressed.jpg.jpeg19.5KB

Reply 2

Almavaligarous

verily you have indeed been very helpful, except what would mg be?

(edited 5 years ago)

Reply 3

Almavaligarous

Original post by Arctic Kitten

add a g for expression for Ub :smile:

I forgot it
20181027_214954-compressed.jpg.jpeg

verily you have indeed been very helpful, except what would mg be? becuase i keep finding mg as 4905, but when i put that in the equation, the radius comes out as 1.55 but that is incorrect

(edited 5 years ago)

Reply 4

the bear

Original post by Almavaligarous

verily you have indeed been very helpful, except what would mg be?

the LHS ( which needs a g on the first term as AK mentioned ) represents the weight of water displaced by the submerged items. this tells us the upwards force. in order to prevent the bouououy being pulled under this upwards force needs to balance the weight of the anchor ( = mg )

Reply 5

Arctic Kitten

Original post by Almavaligarous

verily you have indeed been very helpful, except what would mg be? becuase i keep finding mg as 4905, but when i put that in the equation, the radius comes out as 1.55 but that is incorrect

Arranging and you will get

20181027_230734-compressed.jpg.jpeg

which should give 0.471 m.

Reply 6

Vinny C

They used to hide contraband anchored to the riverbed by blocks of salt. The salt would dissolve and two days later... up it pops! Clever or what?

thank you indeed

Original post by Almavaligarous

verily you have indeed been very helpful, except what would mg be? becuase i keep finding mg as 4905, but when i put that in the equation, the radius comes out as 1.55 but that is incorrect