How Long Can a Leaking Boat Loaded with 1200kg Float Before Sinking?

[leena19]

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\rhog
mg = 1/10 V\rhog --------------1
1200g=6/10 V\rhog--------------2

1/2,
m=mass of boat=200kg ?

2) V= 1200/0.6*10^-3
= 2m³

3/10 V\rhog = 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\rhog
=Vg(d-\rho)
=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

 

[dotman]

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

I only have a minute, and I haven't looked at your previous steps at all. But I wanted to say that by effective density, they mean the density of the water/air mixture taken together as a single unit. Whatever the initial density of the water is, when you have so many air bubbles (0.35m3 you calculate, I didn't check), these air bubbles are going to replace the same volume of water.

Since your neglecting the mass of the air, this means effectively you will have in, say, where you originally had 1m3 of water with some density, you will now have only 0.65 percent of that water mass contributing to the density in the same 1m3 volume. So the density will drop, and you can calculate that.

As for assumptions, well, if you want to use numbers, you need to know the temperature of the water; the density varies slightly based on temperature. Whether or not the water is fresh water or saltwater will also affect the density; I don't get the impression they're asking about this, except for the fact that when I think of a boat in the water, I think of the ocean, not a lake. But I live near an ocean.

Hope this helps, good luck!

 

[LowlyPion]

3)min.force required to lift the sunken boat,
R = mg - V\rhog
=Vg(d-\rho)
=2*10(2500-1000)
=30,000N, i really hope i got this right ?

2 is the Volume of the material of the boat? If the average density is 2500 kg/m³ and its mass is 200 kg ... it's volume is ...?

 

[leena19]

Thank you,dotman
Thank you,LowlyPion

Thank you so much for your help!

2 is the Volume of the material of the boat? If the average density is 2500 kg/m3 and its mass is 200 kg ... it's volume is ...?

2/25 or 0.08m³.
I messed up again :(
then,R would be = 2/25*10*1500= 1200N ?

I only have a minute, and I haven't looked at your previous steps at all. But I wanted to say that by effective density, they mean the density of the water/air mixture taken together as a single unit. Whatever the initial density of the water is, when you have so many air bubbles (0.35m3 you calculate, I didn't check), these air bubbles are going to replace the same volume of water.

Since your neglecting the mass of the air, this means effectively you will have in, say, where you originally had 1m3 of water with some density, you will now have only 0.65 percent of that water mass contributing to the density in the same 1m3 volume. So the density will drop, and you can calculate that.

so now the volume of water(without air bubbles)would be,
1-0.35=0.65m³
which would mean the density of water/air mixture=1000*0.65 = 650kgm^-3?

As for the density of the boat,
do I divide the total mass of (1200+200) by 2? or by 0.08?
I have a strong feeling it's by 2,but I'm not very sure,
(dividing by 2 ,gives me the density of the boat as 700kgm^-3,so since the density of the boat is more than that of water,the boat sinks?)

As for assumptions, well, if you want to use numbers, you need to know the temperature of the water; the density varies slightly based on temperature.

I like this assumption too,which would be to neglect the change in density of water and the boat due to changes in temperature?

5) Use the effects described in (4) to explain the 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'

If the density of the water mixture is less than the density of the person,
the guy would drown