A wooden block of volume 5.00 x 104 m3 floats partially submerged in water, and a small steel object of mass m is placed on top of the block. When m = 0.25 kg, the system is in equilibrium and the top of the wooden block is at the level of the water. What is the density of the wood?a.500 kg.m-3b.1500 kg.m-3c.1000 kg.m-3d.800 kg.m-3
Question
A wooden block of volume 5.00 x 104 m3 floats partially submerged in water, and a small steel object of mass m is placed on top of the block. When m = 0.25 kg, the system is in equilibrium and the top of the wooden block is at the level of the water. What is the density of the wood?a.500 kg.m-3b.1500 kg.m-3c.1000 kg.m-3d.800 kg.m-3
Solution
The density of an object is defined as its mass divided by its volume. In this case, we know that the wooden block is floating in water, which means that the weight of the water displaced by the block is equal to the weight of the block itself. This is known as Archimedes' principle.
The weight of the water displaced by the block is equal to the volume of the block multiplied by the density of water (which is 1000 kg/m^3) and the acceleration due to gravity (which is approximately 9.8 m/s^2).
So, the weight of the water displaced is:
Weight_water = Volume_block * Density_water * g Weight_water = 5.00 x 10^4 m^3 * 1000 kg/m^3 * 9.8 m/s^2 Weight_water = 4.9 x 10^8 N
Since the system is in equilibrium, the weight of the water displaced is equal to the weight of the block plus the weight of the steel object. The weight of the steel object is its mass multiplied by the acceleration due to gravity:
Weight_steel = m * g Weight_steel = 0.25 kg * 9.8 m/s^2 Weight_steel = 2.45 N
So, the weight of the block is:
Weight_block = Weight_water - Weight_steel Weight_block = 4.9 x 10^8 N - 2.45 N Weight_block = 4.9 x 10^8 N
The density of the block is its weight divided by its volume and the acceleration due to gravity:
Density_block = Weight_block / (Volume_block * g) Density_block = 4.9 x 10^8 N / (5.00 x 10^4 m^3 * 9.8 m/s^2) Density_block = 1000 kg/m^3
So, the density of the wood is 1000 kg/m^3, which corresponds to option c.
Similar Questions
A solid metal cube has a mass of 5 kg and side of length of 0.5m. Calculate the density of this metal cabe ② A Cube box has a density of 325 kg/m³ and and mass of 8kg. Calculate the length of each side of the box 3 You are given a rock to find out the density. Desenbe and experiment you performed to determine the density of this rock. Calculate the change in pressure when an object, plunched from 45 m below the surface of the water 200 m below. Density of water 1000 kgm³ & gravitational field strength 9.8N/kg ⑤ A potato is submerged into a bucket of water. State whether potato will sink or giving reasons for your answers ⑥ Calculate the pressure at the surface of a liquued when the force is 0.4 N and surface is 0.02 m²
The ship is made of steel.The density of steel is 7800 kg / m 3 and the density of water is 1000 kg / m3 .Explain why the ship floats in the water
A solid cube is floating in equilibrium in liquid mercury. The cube is made of iron of density7900 kg m–3.The cube floats with 42% of its volume above the surface of the mercury.What is the density of the mercury?A 3300 kg m–3B 4600 kg m–3C 14 000 kg m–3D 19 000 kg m–3
A block of wood has specific gravity 0.70. When placed in water, what percent of the volume of the wood is above the surface?Select one:a.50%b.30%c.70%d.0, the block sinks.e.100%
A log of wood has a mass of 2 kg2 kg and a volume of 0.03 m30.03 m 3 . Calculate the density of the log.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.