Question

Please do all of number 4

show detailed work

It 4. The weight of a rectangular block of low-density material is 15.0 N. With a thin string, the center of the horizontal bottom face of the block is tied to the bottom of a beaker partly filled with wa (pwaw" 1000 kg/m3 10.0 N. when 25.0% of the block's volume is submerged, the tension in the string is ater a) Find the buoyant force on the block. b) Oil of density 800 kg/m is now steadily added to the beaker.o to the beaker, forming a layer above dded 60.0 N. At this moment, 25.0% of the block,ngbreaks wh k's volume is in the oil? rrounding the block. The string breaks when its tension ock's volu What additional fraction of the block's volume is in he sil below the wa reaches block e is still oi

Answer 1

For part a, the idea is that the forces acting on the blockare balanced. There are three forces

    Buoyancy pushesup      gravity pulls down, 15.0N    string pulls down, 10.0 N

Since the forces must be balanced, B must equal 25.0N

The force from the oil and the water on thesides of the beaker is horizontal. Pressure from a fluid alwaysacts perpendicular to the area it pushes on.

when the oil is added, more of the block is nowsubmerged (within the oil). This adds to the buoyancy force (nowfrom water and oil) so the tension in the string increases.

Then the tension increases to 60 N, this meansthe additional 50 N in tension must be balanced by the increase ofthe buoyancy force due to the oil. So the B force of just the oilis 50 N. There are now several ways to figure out what fraction ofthe block is in the oil (i.e. the "additional" volume).

The B force exerted by a fluid is equal to the weight of thefluid displaced, which is prop to the density of the fluid. We knowthe density of the oil is 800, while the density of water is 1000.So oil is 0.8 times the density of water.

B part

Consider the 25% of the block that is in the water. Thiscaused a B force of 25 Newtons from the water. If this 25% weresubmerged in oil instead, the B force from the oil would onlybe

          0.8 * 25 N = 20 N

So now we know... every 25% of the block submerged in oilcauses a B force of 20 N.

We want to know what % of the block submerged causes 50 N of Bforce. Use a simple proportion:

      25% / 20N  =   x % / 50 N     and you findthat    x = 62.5

So the additional volume submerged in the oil is 62.5% of theblock.

now if the block is floating we know the B forcefrom the oil is equal to 15.0 Newtons because this is the weight ofthe block (B force balances force of gravity). So again we use thesame idea of a ratio...

      25% / 20 N  =   x % / 15 N  

x = 18.75       so with the block floating, 18.75% of it is submerged (note that thisis 3/4 of 25% and 15 N is 3/4 of 20 N... and we already establishedthat every 25% that is submerged in the oil creates a B force of 20N).