A block of metal which weighs 60 newtons in air and 40 newtons

under water has a density, in kilograms per meter cubed, of:

buoyant force = 20N = rhowater g V = 9800 V

so
V = 20/9800

mass = 60/g = 60/9.8

so rho metal = mass/volume = (60/9.8) / (20/9800)= 3000 kg/m^3 or three times the density of water

Explain it extensively

Well, that metal must be pretty shy if it's trying to hide from the water! But no worries, I'm here to help you solve the mystery of its density.

If we know the weight of the metal in air is 60 newtons and it decreases to 40 newtons under water, that means the water is pushing up on it with a force of 20 newtons (60 - 40 = 20). This force is equal to the weight of the water displaced by the metal.

Now, to calculate density, we need to use the formula: Density = mass/volume.

Since we already have the weight, we can use the formula: Weight = mass x gravitational acceleration (which is approximately 9.8 m/s^2).

Let's calculate the mass of the metal first. In air, its weight is 60 newtons, so the mass would be 60/9.8 = 6.12 kilograms.

Now, to calculate the volume of the metal, we can divide the weight of the water displaced (20 newtons) by the density of water (which is approximately 1000 kg/m^3).

So, the volume of the metal is 20/1000 = 0.02 m^3.

Lastly, we can plug in the values we have into the density formula: Density = mass/volume.

Density = 6.12 kg / 0.02 m^3 = 306 kg/m^3.

So, the density of the metal is approximately 306 kilograms per meter cubed. Voila!

To find the density of the block of metal, you can use the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.

Here's how you can derive the density of the block of metal:

1. Determine the weight of the block in air: The weight of the block in air is given as 60 newtons.

2. Determine the weight of the block under water: The weight of the block under water is given as 40 newtons.

3. Calculate the difference in weight: The difference in weight between the block in air and under water represents the buoyant force acting on the block. In this case, the difference is 60 N - 40 N = 20 N.

4. Determine the volume of the block: The volume of the block can be calculated using the equation for buoyancy: Buoyant force = Weight of the fluid displaced = Density of fluid x gravitational acceleration x Volume of fluid displaced. Since the gravitational acceleration is constant, we can rearrange the equation to find the volume: Volume of fluid displaced = Buoyant force / (Density of fluid x gravitational acceleration). In this case, the fluid is water, so the density of water is 1000 kg/m³, and the gravitational acceleration is approximately 9.8 m/s².

Volume of fluid displaced = 20 N / (1000 kg/m³ x 9.8 m/s²)

5. Calculate the density of the block: Finally, the density of the block can be determined using the equation: Density = Mass / Volume. Since weight is given, you can use the formula: Density = Weight / (Volume x gravitational acceleration).

Density = 60 N / (Volume of fluid displaced x 9.8 m/s²)

By plugging in the values you obtained in steps 4 and 5, you can calculate the density of the block of metal.

3000