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?
weight= density*volume*g
weight=700*(10^-3)*9.81
weight=3418.877985
weight=densitywater*g*10cm*10cm*depth
3418.877985=1000*9.81*.1*.1*d
d=34.85
it is't working...what am i missing?
weight= density*volume*g
weight=700*(0.001)*9.81
weight=6.86newton
weight=densitywater*g*10cm*10cm*depth
6.86=1000*9.81*.1*.1*d
6.86=98.1*d
d=.0699...which is still wrong
i have to get an answer in cm.
In order to solve this problem, we need to consider the principle of buoyancy. When an object is immersed in a fluid (such as water), it experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
To determine the distance from the top of the wood block to the water, we need to find the amount of water that the block displaces when it floats. This is equal to the volume of the block that is submerged in water.
The volume of the wood block is given as 10cm x 10cm x 10cm = 1000 cm³. Let's call the distance from the top of the block to the water surface "h".
The volume of the block submerged in water can be calculated using the equation:
Volume submerged = (surface area of the base) x h
The surface area of the base is 10cm x 10cm = 100 cm².
Therefore, the volume submerged is 100 cm² × h.
Now, let's use the principle of buoyancy to find the weight of the water displaced by the wood block:
Weight displaced = density of water × g × volume submerged
Using the information provided, the density of water is 1000 kg/m³ and g (acceleration due to gravity) is approximately 9.81 m/s².
Converting the volume submerged from cm³ to m³:
Volume submerged = (100 cm² × h) × (1 m² / 10,000 cm²) = (0.01 m²) × h
Therefore, the weight displaced is (1000 kg/m³) × (9.81 m/s²) × (0.01 m²) × h.
Equating this to the weight of the block (as it is floating), we have:
Weight displaced = Weight of the block
(1000 kg/m³) × (9.81 m/s²) × (0.01 m²) × h = 700 kg/m³ × (10 cm × 10 cm × 10 cm) × (1 m³ / 1,000,000 cm³) × (9.81 m/s²)
Simplifying, the above expression becomes:
0.00981 h = 0.7 × 9.81
Solving for h:
h = (0.7 × 9.81) / 0.00981
h ≈ 70 cm
Therefore, the distance from the top of the wood block to the water surface is approximately 70 cm.