A 10cm times 10cm times 10cm wood block with a density of 700kg/m^{3} floats in water. What is the distance from the top of the block to the water if the water is fresh? and If it's seawater?
figure the weight:
weight= density*volume*g
then the weight of the water displaced is equal to that..
weight=densitywater*g*10cm*10cm*depth
solve for depth.
weight= density*volume*g
weight=700*10cm*9.81
weight=68670
weight=densitywater*g*10cm*10cm*depth
68670=700*9.81*10cm*10cm*d
d=.1
it isnt right:-(
the volume is not 10 cm. It is 1000cm^3
oh ok
weight= density*volume*g
weight=700*1000cm*9.81
weight=6867000
weight=densitywater*g*10cm*10cm*depth
6867000=700*9.81*10cm*10cm*d
d=10
still didn't work,am i missing something?
To determine the distance from the top of the block to the water, we need to compare the density of the wood block to the density of the water. If the density of the object is less than the density of the liquid, it will float.
For fresh water:
1. Convert the dimensions of the wood block from centimeters (cm) to meters (m) for consistency: 10 cm = 0.10 m.
2. Calculate the volume of the wood block: Volume = length x width x height = 0.10 m x 0.10 m x 0.10 m = 0.001 m^3.
3. Calculate the buoyant force acting on the wood block: Buoyant force = density of water x volume of the wood block x gravitational acceleration.
For fresh water, the density is approximately 1000 kg/m^3, and gravitational acceleration is 9.8 m/s^2. Thus, the buoyant force is:
Buoyant force = 1000 kg/m^3 x 0.001 m^3 x 9.8 m/s^2 = 9.8 N.
4. Calculate the weight of the wood block: Weight = mass x gravitational acceleration. The mass of the wood block can be calculated using its density:
Density = mass / volume, rearranging the equation gives: Mass = Density x Volume.
Mass = 700 kg/m^3 x 0.001 m^3 = 0.7 kg.
Weight = 0.7 kg x 9.8 m/s^2 = 6.86 N.
5. Since the wood block is floating, the buoyant force is equal to the weight of the block: 9.8 N = 6.86 N.
6. The remaining force acting on the wood block is the difference between the weight of the block and the buoyant force: 9.8 N - 6.86 N = 2.94 N.
7. This force is the force due to the water's displacement, and it acts on the top surface of the block.
8. Finally, calculate the distance from the top of the block to the water by dividing the force due to the water's displacement by the area of the top surface of the block:
Distance = Force / Area = 2.94 N / (0.1 m x 0.1 m) = 29.4 N/m^2.
For seawater:
The density of seawater is approximately 1025 kg/m^3. Repeat the above steps using this density to find the distance from the top of the wood block to the water's surface.