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You have been accepted into a boat building competition. You get to pick between two boat plans. Boat A’s plans has the dimensions of 45m wide and 126m long and exerts 2300Pa of pressure. Boat B’s plans has the dimensions of 6m wide and 115m long and exerts 2700Pa of pressure. In order for the boat to float, the force applied to the water must not exceed 2.0 X 10 6 N. Would you pick Plan A or Plan B?

Answer :

Answer:

the force B  is less than the maximum force consequently Boat B floats

Explanation:

To solve this exercise let's use the pressure defined

         P = [tex]\frac{F}{A}[/tex]

         F = P A

let's start for boat A

let's search the area

         A = l a

         A₁ = 45 126

         A₁ = 5670 m²

the force applied by this ship is

         F₁ = 2300 5670

         F₁ = 1.3 10⁷ N

         

now we do the calculation for ship B

          A₂ = 6 115

          A₂ = 690 m²

          F₂ = P₂ A₂

          F₂ = 2700 690

          F₂ = 1.8 10⁶ N

indicate that the force should not be greater than F₀ = 2.0 10⁶ N, let's look for the relationship with each one

          [tex]\frac{F_1}{F_0}[/tex] = 1.3 10⁷/2 10⁶

         F₁ = 6.5 F₀

This force is greater than the one that can resist therefore the ship and sinks

          [tex]\frac{F_2}{F_o}[/tex] = 1.8 /2  

          F₂ = 0.9 F₀

therefore this force is less than the maximum force consequently Boat B floats

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