Force required to immerse a wooden cube

In summary, the force required to fully immerse a wooden cube in water is equal to the weight of the cube and the weight of the displaced water. The size, density, and shape of the cube can affect the force required for immersion, with larger and denser cubes requiring more force. The force can be calculated using a mathematical formula, but this does not account for external forces. The shape of the cube does not have a significant effect on the force, as long as the volume and density remain the same.
  • #1
Jahnavi
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Homework Statement



The force required to immerse a wooden
cube of side 4 cm and relative density RD 0.5 completely in water is
1) 16x10-3 kgwt
2) 32x10-3 kgwt
3) 64x10-3 kgwt
4) 128x10-3 kgwt

Homework Equations

The Attempt at a Solution



Density of the cube = 0.5 gcm-3
Volume of cube = 64 cm3
Weight of the cube = 64 x10-6 x 500 x 9.8 N (1)

Upthrust = 64 x10-6 x 1000 x 9.8 N (2)

Force required = Upthrust - Weight

Subtracting (1) from (2)

Force required = 64 x10-6 x 500 x 9.8 N

1kgwt = 9.8 N

Force required = 32 x10-3 kgwt

Is option 2) the correct answer ?
 
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  • #2
it looks good to me.
 
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1. What is the force required to fully immerse a wooden cube in water?

The force required to fully immerse a wooden cube in water is equal to the weight of the cube, as well as the weight of the displaced water. This is known as Archimedes' principle, which states that the upward buoyant force on an object is equal to the weight of the fluid it displaces.

2. Does the size of the wooden cube affect the force required to immerse it?

Yes, the size of the wooden cube does affect the force required to immerse it. The larger the cube, the more water it will displace, resulting in a greater buoyant force and a higher force required for full immersion.

3. How does the density of the wooden cube affect the force required for immersion?

The density of the wooden cube does not directly affect the force required for immersion. However, a denser cube will have a greater weight, resulting in a higher force required for full immersion.

4. Can the force required for immersion be calculated mathematically?

Yes, the force required for immersion can be calculated using the formula F = (ρw - ρo)Vg, where F is the force required, ρw is the density of water, ρo is the density of the wooden cube, V is the volume of the cube, and g is the acceleration due to gravity. However, this formula assumes the cube is fully submerged and does not take into account any external forces such as air resistance.

5. How does the shape of the wooden cube affect the force required for immersion?

The shape of the wooden cube does not have a significant effect on the force required for immersion, as long as the volume and density of the cube remain the same. However, a cube with a pointed or curved shape may experience less air resistance and require a slightly lower force for full immersion.

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