Calculating the Minimum Height for a Steel "Boat" to Float

[quick]

The bottom of a steel "boat" is a 6.00 m x 9.00 m x 5.00 cm piece of steel(density of steel = 7900 kg/m^3) . The sides are made of 0.460 cm-thick steel.

what minimum height must the sides have for this boat to float in perfectly calm water? in cm

i have that F_B (buoyancy force) is equal to W_boat (weight of boat) is equal to W_B + 2*W_s1 + 2*W_s2. where w is the weights and it equal rho*g*V. F_B = density of water*g*total volume and total volume is equal to 6*9*(h+ .05)

any suggestions would really help

 

[Tide]

Give this a try:

$$Weight_{bottom} + 2\rho_{steel} g \ h (L + W) = \rho_{water} g (L-2\times0.046)(W-2\times0.046)(h-0.05)$$

 

[wais]

To calculate the minimum height for the sides of the steel "boat" to float, we need to determine the buoyancy force (F_B) and the weight of the boat (W_boat). We can use the formula F_B = W_boat, where W_boat is equal to the weight of the boat (W_B) plus the weight of the two sides (W_s1 and W_s2).

First, let's calculate the weight of the boat (W_B). This can be found by multiplying the density of steel (7900 kg/m^3) by the volume of the bottom of the boat (6.00 m x 9.00 m x 0.05 m). This gives us a weight of 2,385 kg.

Next, we need to calculate the weight of the two sides (W_s1 and W_s2). Since the sides are made of steel, we can use the same formula as above, but with a different volume. The volume of one side is 6.00 m x h m x 0.0046 m (where h is the height of the sides). So, the total weight of the two sides is 2 x (7900 kg/m^3) x (6.00 m x h m x 0.0046 m) = 87.48 h kg.

Now, we can plug these values into the formula F_B = W_boat. This gives us 2,385 kg + 87.48 h kg = F_B. We also know that the buoyancy force (F_B) is equal to the density of water (1000 kg/m^3) multiplied by the total volume of the boat (6.00 m x 9.00 m x (h + 0.05 m)). So, we can set these two values equal to each other and solve for h.

2,385 kg + 87.48 h kg = (1000 kg/m^3) x (6.00 m x 9.00 m x (h + 0.05 m))

Simplifying this equation gives us:

2,385 kg + 87.48 h kg = 54,000 kg x (h + 0.05 m)

Dividing both sides by 54,000 kg gives us:

0.04417 + 0.00162 h = h + 0.05

Subtracting h from