Solved: Calculating Force Needed for Archimedes' Principle

AI Thread Summary
To determine the force required to hold a solid cube of foam plastic underwater, the relevant equations include Archimedes' principle, which states that the buoyant force equals the weight of the displaced fluid. The cube has a volume of 25m^3 and a density of 800kg/m^3, leading to a mass calculation of 0.02kg. However, the initial calculations contain unit errors, and the correct force must account for the buoyant force acting on the cube. The discussion emphasizes the need to apply Archimedes' principle correctly to find the total force required to keep the cube submerged. Understanding these principles is crucial for solving the problem accurately.
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Homework Statement



A solid cube of foam plastic has a volume of 25m^3 and a density of 800kg/m^3. How large a force is required to hold it under water?

Homework Equations


P = F/A
Fb = ρgV
ρ = m/V

The Attempt at a Solution


ρ = m/V
800 = m / 0.000025
m = 0.02kg

so F = mg = 0.02 x 9.8 = 0.196
I understand that the force required to keep it under water will be greater than this but I'm having a hard time finding the right equation.
 
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anyone ?
please
 
For starters look at the equation below that I copied.

800 = m / 0.000025

You have an error with your units.

Are you familiar with Archimedes Principle? If so, please state it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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