Buoyant Force and Displacement Volume of a Boat in Lake Superior

AI Thread Summary
The discussion centers on calculating the buoyant force and the volume of water displaced by a boat with a total mass of 15,450 kg in Lake Superior. The buoyant force is calculated using the formula Fb = mg, resulting in 154,500 N when using g = 10 m/s². However, the volume of displaced water was incorrectly calculated as 154,500 m³, which is too large. To find the correct volume, one must consider the density of water, which is approximately 1,000 kg/m³. Ultimately, the volume of displaced water corresponds to the mass of the boat, requiring proper conversion and understanding of density.
disneygirl828
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Homework Statement


A boat full of people lazily drifts along in Lake Superior. The boat has a mass, including people of 15,450kg.
A. What is the buoyant force?

B. What is the volume of the displaced liquid in cubic meters?




The Attempt at a Solution


A. Fb=mg
Fb=?
m=15,450kg
g= 10m/s
(15450kg)(10m/s)
=154500kg*m/s^2
B.
=154500m^3
 
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disneygirl828 said:

Homework Statement


A boat full of people lazily drifts along in Lake Superior. The boat has a mass, including people of 15,450kg.
A. What is the buoyant force?

B. What is the volume of the displaced liquid in cubic meters?




The Attempt at a Solution


A. Fb=mg
Fb=?
m=15,450kg
g= 10m/s
(15450kg)(10m/s)
=154500kg*m/s^2
B.
=154500m^3

While "154500kg*m/s^2" is technically correct, it is usual practice to convert the "kg*m/s^2" units to its well-known designation "N" for Newtons, the unit of force.

The displaced water should be equivalent in weight to the weight of the boat. Your value for the volume of displaced water is too large. What is the density of water in kg/m3?
 
gneill said:
While "154500kg*m/s^2" is technically correct, it is usual practice to convert the "kg*m/s^2" units to its well-known designation "N" for Newtons, the unit of force.

The displaced water should be equivalent in weight to the weight of the boat. Your value for the volume of displaced water is too large. What is the density of water in kg/m3?
so the volume of the displaced water would be 15450kg? How do you convert kg*m/s^2 to Newtons?
 
disneygirl828 said:
so the volume of the displaced water would be 15450kg? How do you convert kg*m/s^2 to Newtons?

The volume of the displaced water would be that volume of water which has a mass of 15450kg. To find that volume you will need to know the density of water (kg/m3).

The Newton is defined to be 1 kg*m/s2.
 
Thank you SO much :)
 
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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