A WOOD OF (DENSITY = 600KG/M³) OF MASS 120KG FLOATS IN WATER.HOM MUCH WEIGHT CAN BE PUT ON THE WOOD TO MAKE IT JUST SINK??

To determine how much weight can be added to a piece of wood so that it just sinks in water, we need to consider the principles of buoyancy and density. The wood has a density of 600 kg/m³ and a mass of 120 kg. First, we need to calculate the volume of the wood and then the buoyant force acting on it when it is submerged in water.

Calculating the Volume of the Wood

The volume of an object can be calculated using the formula:

Volume = Mass / Density

For the wood:

• Mass = 120 kg
• Density = 600 kg/m³

Plugging in the values:

Volume = 120 kg / 600 kg/m³ = 0.2 m³

Understanding Buoyancy

When an object is placed in a fluid, it displaces a volume of fluid equal to the volume of the object. The buoyant force acting on the object is equal to the weight of the fluid displaced. In this case, the fluid is water, which has a density of approximately 1000 kg/m³.

Calculating the Buoyant Force

The buoyant force can be calculated using the formula:

Buoyant Force = Volume of Displaced Water × Density of Water × g

Where:

• Volume of Displaced Water = Volume of the wood = 0.2 m³
• Density of Water = 1000 kg/m³
• g = acceleration due to gravity (approximately 9.81 m/s², but we can ignore it for weight calculations since we will compare forces)

Thus, the buoyant force is:

Buoyant Force = 0.2 m³ × 1000 kg/m³ = 200 kg

Determining the Total Weight for Sinking

For the wood to just sink, the total weight of the wood plus any additional weight must equal the buoyant force. The weight of the wood is:

Weight of Wood = Mass × g = 120 kg

Let’s denote the additional weight we can add as W. The equation for the total weight becomes:

120 kg + W = 200 kg

W = 200 kg - 120 kg = 80 kg

Final Result

Therefore, you can add a weight of up to 80 kg to the wood for it to just sink in water. This calculation illustrates the balance between the weight of the object and the buoyant force acting on it, which is a fundamental concept in fluid mechanics.