A solid square pinewood raft measures 4.0 m on a side and 0.3m thick. Given the density of pinewood as 550kg/m^3 and that of water is 1000kg/ m^3:
Determine whether the raft floats in water
Yes, Google Archimedes
Well, let me put on my clown wig and calculate that for you!
To determine whether the raft floats in water, we need to compare the density of the raft with the density of water. If the density of the raft is less than the density of water, it will float. Otherwise, it will sink faster than my jokes.
The volume of the raft can be calculated by multiplying the length, width, and height (thickness):
Volume of the raft = (4.0 m) x (4.0 m) x (0.3 m) = 4.8 m^3
Now, let's calculate the mass of the raft by multiplying the volume and density:
Mass of the raft = Volume x Density = 4.8 m^3 x 550 kg/m^3 = 2640 kg
Since we know the density of water is 1000 kg/m^3, let's calculate the weight of the water displaced by the raft:
Weight of the water = Volume x Density = 4.8 m^3 x 1000 kg/m^3 = 4800 kg
Uh oh, it seems like the weight of the raft (2640 kg) is less than the weight of the water it displaces (4800 kg). That means the raft will definitely float! Just like a clown on a duck!
So, to answer your question, yes, the raft will float in water. Now, if only it was big enough for clown parties!
To determine if the raft floats in water, we need to compare its density with that of water.
The density of a material is calculated by dividing its mass by its volume. The formula for density is:
Density = Mass / Volume
Let's find the mass of the raft:
Given that the density of pinewood is 550 kg/m^3:
Volume of the raft = length × width × height
Volume of the raft = 4.0 m × 4.0 m × 0.3 m
Volume of the raft = 4.0 m^3
Mass of the raft = Density × Volume
Mass of the raft = 550 kg/m^3 × 4.0 m^3
Mass of the raft = 2200 kg
We have found that the mass of the raft is 2200 kg.
Now, let's compare the density of the raft with that of water:
The density of water is given as 1000 kg/m^3.
Since the density of the raft (550 kg/m^3) is less than the density of water (1000 kg/m^3), the raft will float in water.
To determine whether the raft floats in water, we need to compare the density of the raft with the density of water. If the density of the raft is less than the density of water, it will float; otherwise, it will sink.
The density of an object is calculated by dividing its mass by its volume. In this case, we have the density of pinewood as 550 kg/m^3 and the density of water as 1000 kg/m^3.
To find the mass of the raft, we need to calculate the volume of the raft first. The volume of a solid square can be calculated by multiplying the length (side length, in this case) by the width and height. Given that the side length of the raft is 4.0 m and the thickness is 0.3 m, the volume of the raft would be:
Volume = length x width x height
= 4.0 m x 4.0 m x 0.3 m
= 4.8 m^3
Now that we have the volume of the raft, we can calculate the mass:
Mass = Density x Volume
= 550 kg/m^3 x 4.8 m^3
= 2640 kg
So, the mass of the raft is 2640 kg.
Now, let's compare the density of the raft with the density of water. The density of the raft is:
Density of raft = Mass of raft / Volume of raft
= 2640 kg / 4.8 m^3
= 550 kg/m^3
Since the density of the raft (550 kg/m^3) is less than the density of water (1000 kg/m^3), the raft will float in water.