Compute the force needed on the following shapes to completely submerge them in water for each of these materials: oak of average density, Styrofoam, and hollow aluminum with a 0.5cm wall thickness. A cube 10cm on a side, a cylinder 5cm long and 9cm in diameter, a sphere 15cm in diameter. If the cubes are just placed in water and not forced under how far down into the water does each cube sink? Write what densities you used.
what is your thinking? One never want to get the reputation of an answer moocher.
well wouldn't the force needed to submerge them just be the buoyant force? and to get that all you do is take the density*volume*accerlaration due too gravity
and then i'm not sure exactly how to get how far theym sink. i think it's something to do with net force. which would be the buoyant force minus the weight
right on the first paragraph. For the second, you need to balance the displaced weight of water to equal the weight of the block.
weightwater=weightblock
densitywater*g*l*w*heightsubmerged= density*g*volume*g
Now on the curved surfaces, you have a tricky calculation on the volume of the submerged height.
To compute the force needed to completely submerge various shapes in water, we'll need to consider the buoyant force acting on each shape. The buoyant force is equal to the weight of the fluid displaced by the object. To determine the force, we'll first calculate the volume of each shape, then multiply it by the density of water (1 g/cm³) to obtain the weight of the fluid displaced.
Now, let's calculate the force needed to submerge each shape for the given materials:
1. Cube:
- Side length: 10 cm
- Volume: (10 cm)³ = 1000 cm³
- Density of Oak: 0.75 g/cm³
- Weight of the fluid displaced: (1000 cm³) * (1 g/cm³) = 1000 g
- Force needed to submerge: 1000 g * 9.8 m/s² = 9800 N
2. Cylinder:
- Length: 5 cm
- Diameter: 9 cm
- Radius: 4.5 cm
- Volume: π * (4.5 cm)² * 5 cm = 319.05 cm³
- Density of Styrofoam: 0.03 g/cm³
- Weight of the fluid displaced: (319.05 cm³) * (1 g/cm³) = 319.05 g
- Force needed to submerge: 319.05 g * 9.8 m/s² = 3134.59 N
3. Sphere:
- Diameter: 15 cm
- Radius: 7.5 cm
- Volume: (4/3) * π * (7.5 cm)³ = 1767.15 cm³
- Density of Hollow Aluminum: 2.7 g/cm³
- Weight of the fluid displaced: (1767.15 cm³) * (1 g/cm³) = 1767.15 g
- Force needed to submerge: 1767.15 g * 9.8 m/s² = 17318.67 N
Next, let's determine how far down each cube will sink if they are just placed in water without any external force:
1. Cube:
- Using the given density of Oak (0.75 g/cm³), we can determine its weight:
- Weight of the cube: (1000 cm³) * (0.75 g/cm³) * 9.8 m/s² = 7350 N
- Since the weight of the cube is less than the force needed to submerge it (9800 N), it will completely sink.
2. Cylinder:
- Using the given density of Styrofoam (0.03 g/cm³), we can determine its weight:
- Weight of the cylinder: (319.05 cm³) * (0.03 g/cm³) * 9.8 m/s² = 94.28 N
- Since the weight of the cylinder is less than the force needed to submerge it (3134.59 N), it will completely sink.
3. Sphere:
- Using the given density of Hollow Aluminum (2.7 g/cm³), we can determine its weight:
- Weight of the sphere: (1767.15 cm³) * (2.7 g/cm³) * 9.8 m/s² = 47140.93 N
- Since the weight of the sphere is greater than the force needed to submerge it (17318.67 N), it will only partially sink.
In summary, the force needed to completely submerge each shape for the given materials are as follows:
Cube (Oak): 9800 N
Cylinder (Styrofoam): 3134.59 N
Sphere (Hollow Aluminum): 17318.67 N
The cubes made of Oak and Styrofoam will completely sink when placed in water without any external force. However, the sphere made of Hollow Aluminum will only partially sink.