Physics homework on Hydrostatics

[kalupahana]

Homework Statement

10% of a boat sink in water when it is float, from its total volume. 70% of its total volume sinks, when 1200kg loaded into it

I) Calculate the mass of boat.
II) The boat totally sink due to a hole in bottom of it, with that 1200kg load, with a uniform rate of 100kg of water mass per minute. Find the time taken to sink the boat.
III) Find the force needed to lift the boat up to the water level(without 1200Kg load)?
Take density of Water as 1000Kgm^-3 and mean density of materials which were taken to built the boat is 2500Kgm^-3

Homework Equations

u=vρg

ρ=m/v

The Attempt at a Solution

I) u=vρg -----> mg=vρg -------> m=vρ

boat without load ---> m= 10v/100 x 1000 ------>v=m/100 ------(1)
boat with loaf ----> m+1200 = 70v/100 x 1000 ----> v = (m +1200)/700 -----(2)

from 1 and 2
6m = 1200 --------> m=200kg

II) Volume of the boat = 200/100 = 2m³ (from 1)

the total mass needed to sink boat
u=vρg -----> mg=vρg -------> m=vρ
m = 2 x 1000 = 2000kg

the mass of water needed to sink the boat = 2000 - 1200- 200 = 600kg
the time taking to sink the boat = 600/100 = 6min

III) This is the part that i stuck,,, Why they given the density of materials which were taken to built the boat, the mass of boat and volume of boat can be find without it. please tell me above steps are correct,,, help me

 

[anathema]

to find the force needed to lift the boat up to the water levelYour calculations for parts I and II seem to be correct. For part III, you need to use the concept of buoyancy. The force needed to lift the boat up to the water level is equal to the weight of the water that the boat displaces. This can be calculated using Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces.

To calculate the buoyant force, we need to first find the volume of water that the boat displaces. This can be calculated using the volume of the boat (2m3) and the density of water (1000 kg/m3).

Volume of water displaced = 2m3 x 1000 kg/m3 = 2000 kg

Next, we need to find the weight of this water. This can be calculated using the density of water (1000 kg/m3) and the volume of water displaced (2000 kg).

Weight of water displaced = 2000 kg x 1000 kg/m3 = 2000000 N

Therefore, the force needed to lift the boat up to the water level is 2000000 N. This is the same as the weight of the water displaced, which makes sense according to Archimedes' principle.