Raft acceleration homework problem

[silently_loud]

A raft is constructed of wood having a density of 600.0 kg/m3. The area of its top surface is 5.7 m2, and its volume is 0.50 m3. When the raft is placed in fresh water having a density of 1.0x10^3 kg/m3, how much of it is below water level?

What is the upward acceleration of a helium filled balloon of volume 0.0230 m3 if the mass of the balloon's shell is 0.005 kg? (The density of air is 1.20 kg/m3 and that of helium is 0.177 kg/m3.

I keep getting the 1st question wrong, I only have one try. I tried Fb=volumexgxdensity

Then weight=mg=densityxvolumex9.8

Then I did w/fbx100= %

then did h=volume/area
then hx%

I keep getting it wrong, please help.

 

[Kurdt]

The weight of the raft is supported by the weight of the volume of water displaced. So you have to equate the weight of the raft with the equivalent of water to find the volume of water displaced. You should then be able to work out how much of the raft is submerged.

 

[Moetasim]

I would first like to commend you for attempting to solve these problems and seeking help when needed. It shows determination and a willingness to learn, which are important qualities in science.

Now, let's tackle the first question. To find the amount of the raft that is below the water level, we can use the equation V = Ah, where V is the volume of the submerged part, A is the area of the top surface, and h is the height of the submerged part. We know that the total volume of the raft is 0.50 m3 and the area of the top surface is 5.7 m2. We also know that the density of fresh water is 1.0x10^3 kg/m3. So we can rearrange the equation to solve for h:

h = V/A = (0.50 m3) / (5.7 m2) = 0.0877 m

This means that the height of the submerged part of the raft is 0.0877 m. To find the percentage of the raft that is below the water level, we can use the equation % = (Vsubmerged / Vtotal) x 100. Plugging in the values, we get:

% = (0.0877 m3 / 0.50 m3) x 100 = 17.54%

So 17.54% of the raft is below the water level.

Moving on to the second question, we can use the buoyancy force equation, Fb = ρfluid x g x Vdisplaced, to find the upward force on the balloon. We know that the density of air is 1.20 kg/m3 and that of helium is 0.177 kg/m3. The volume displaced by the balloon is equal to its own volume, which is given as 0.0230 m3. Plugging in the values, we get:

Fb = (1.20 kg/m3 - 0.177 kg/m3) x 9.8 m/s2 x 0.0230 m3 = 0.0241 N

This is the upward force on the balloon. To find the acceleration, we can use Newton's second law, F = ma, where F is the net force and m is the mass of the balloon. Rearranging the equation, we get:

a = F/m = (0.0241