- #1
leena19
- 186
- 0
Homework Statement
An empty boat floats in water with 10% of its volume submerged,and when it's loaded with 1200kg,the volume submerged will increase to 70% of the total volume.
(1) Calculate the mass of the empty boat
(2) If a leak develops and water starts to enter the boat which is loaded with 1200kg at a constant (average)rate of 100kg per minute,for how long the boat can float before sinking?
(3) what is the minimum force required to lift the sunken boat(without the load )upto the surface of water.Average density of the material of the boat is 2500kgm-3 and the density of water is 1000 kgm^-3
4) The mended boat with another load of 1200kg on board ,while sailing suddenly enters a region where water is uniformly mixed with air bubbles,.If the average vol. of an airbubble is1mm3 & the air bubble concentration is 3.5 *108 m-3,find the effective density of water.Neglect the mass of air.Hence show that the boat will sink.State any assuptions you make
5) Use the effects described in (4) to explainthe danger in the foll. act
'there's a deep pool at the foot of a tall waterfall,.A person starts to swim closer to the foot of the fall'
Homework Equations
The Attempt at a Solution
1) U = V[tex]\rho[/tex]g
mg = 1/10 V[tex]\rho[/tex]g --------------1
1200g=6/10 V[tex]\rho[/tex]g--------------2
1/2,
m=mass of boat=200kg ?
2) V= 1200/0.6*10-3
= 2m3
3/10 V[tex]\rho[/tex]g = m'g
m'=600kg, the amount of water needed to sink the boat
therefore,timetaken= 6 minutes ?
3)min.force required to lift the sunken boat,
R = mg - V[tex]\rho[/tex]g
=Vg(d-[tex]\rho[/tex])
=2*10(2500-1000)
=30,000N, i really hope i got this right ?
4) I'm not sure how I'm supposed to find the effective density,
tot. volume of air bubbles = 3.5*108*10-9
= 0.35 m3
effective density? what does it mean really?
The density of boat should be more than density of water to sink
For the assumption part,does it have to do with the surface tension of water being reduced?
or neglecting the increase in density of water as the depth increases?
I hope someone can help
.
Thank you