A wooden block 2m*1m*0.5m and of specific gravity0.76 is floating in w...
**Buoyancy and Archimedes' Principle**
Buoyancy is the upward force exerted on an object submerged in a fluid (liquid or gas), which opposes the weight of the object. This force is a result of the pressure difference between the top and bottom of the object. The principle that explains buoyancy is known as Archimedes' Principle.
**Archimedes' Principle states:**
"When a body is partially or completely submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the body."
**Calculating the Buoyant Force:**
To determine the load that can be placed on a floating wooden block without sinking, we need to calculate the buoyant force acting on the block. The buoyant force is equal to the weight of the fluid displaced by the block.
**1. Calculate the Volume of the Wooden Block:**
The volume of the wooden block can be calculated using its dimensions:
Volume = Length * Width * Height = 2m * 1m * 0.5m = 1 m^3
**2. Calculate the Weight of the Fluid Displaced:**
The weight of the fluid displaced is equal to the weight of the water that would occupy the same volume as the wooden block.
Weight of water = Volume of water * Density of water * Acceleration due to gravity
Given:
Density of water = 1000 kg/m^3 (approximate value)
Acceleration due to gravity = 9.8 m/s^2
Weight of water = 1m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 9800 N
**3. Calculate the Buoyant Force:**
The buoyant force acting on the wooden block is equal to the weight of the fluid displaced:
Buoyant force = Weight of water = 9800 N
**4. Calculate the Maximum Load:**
To determine the maximum load that can be placed on the block without sinking, it should not exceed the buoyant force. Since the buoyant force is 9800 N, the maximum load that can be placed on the block is also 9800 N.
**Explanation:**
When the wooden block is placed in water, it displaces an amount of water equal to its own volume. According to Archimedes' Principle, the block experiences an upward buoyant force equal to the weight of the displaced water. This buoyant force counteracts the weight of the block, leading to its floating.
To completely immerse the wooden block in water, a load greater than the buoyant force needs to be applied. However, if the load exceeds the buoyant force, the block will sink as the downward force exceeds the upward buoyant force.
Therefore, the maximum load that can be placed on the block without sinking is the same as the buoyant force, which in this case is 9800 N.
Overall, the load that may be placed on the wooden block so that it may completely immerse in water is 9800 N.
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