the diagram shows a piece of wood in the shape of a cuboid.
diagram: 3cm width, 20cm length, 1.2m for the volume of cuboid
The piece of wood is 3cm by 20cm by 1.2m.
The mass of wood will float in sea water if the density of the wood is less than the density of the sea water.
In a large pool, 1 litre of sea water has a mass of 1030g.
Will the piece of wood float in this pool?
You Must show how you get your answer. (4 marks worth)
My work:
1 m = 100cm
1.2m= 120cm
3 times 20 times 120 = 7200cm3
which is the volume of the cuboid
vol of wood= 3*20*120=7200cm3
density of wood= M/V=8000/7200=1.111g/cm3
density of water=1030/1000cm3=1.03g/cm3
so no the wood will not float as it has more density then water
1 litre = 1000cm3 which is the volume of the water,
density of pool is 1030g/1000cm3 to get 1.03g/cm3
what's the volume of the water though?
Anyone know? Please help!
To determine whether the piece of wood will float in the pool, we need to compare its density with the density of sea water.
First, we need to convert the volume of the cuboid from centimeters cubed (cm³) to liters (L). Since 1 L is equal to 1000 cm³, we can divide the volume (7200 cm³) by 1000 to get the volume in liters:
7200 cm³ ÷ 1000 = 7.2 L
Next, we calculate the mass of the piece of wood using its density. Density is calculated by dividing the mass (m) by the volume (V):
Density (D) = mass (m) / volume (V)
We know that the volume of the wood is 7.2 L. To find the mass, we rearrange the formula:
mass (m) = density (D) x volume (V)
Since the density of wood is not given in the problem, we cannot calculate the exact mass. However, we can still compare the density of the wood with the density of sea water to determine if it will float.
The density of sea water is stated as 1030 g/L.
If the density of the wood is less than 1030 g/L, it will float. If it is greater than or equal to 1030 g/L, it will sink.
To compare the densities, we need to calculate the mass of the wood using the density of 1030 g/L:
mass of the wood = density of sea water x volume of the wood
mass of the wood = 1030 g/L x 7.2 L
mass of the wood = 7425 g
Now, we compare the mass of the wood (7425 g) with the mass required for it to float. If the mass of the wood is less than the mass required to float, it will float; otherwise, it will sink.
Since the mass of the wood (7425 g) is less than the mass required for it to float in the pool, the piece of wood will float.