Calculating Weight of Truck on Ferry Boat

AI Thread Summary
The discussion revolves around calculating the weight of a truck that causes a ferry boat to sink 4 cm in water. The buoyant force is determined using the formula for the weight of the displaced fluid, which is derived from the volume of the submerged portion of the boat. The volume of displaced water is calculated as 0.96 m³, leading to a buoyant force of approximately 9,400 N. This value represents the weight of the truck, highlighting the importance of distinguishing between weight and mass in calculations. The problem is confirmed as solved, with a note on potential marking issues in online systems.
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[SOLVED] Bouyant force

1. A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat sinks 4.00 cm (0.04 m) in the water. What is the weight of the truck?



2. F(sub: B) = F(sub: g)[displaced fluid] = m(sub: f)g
(magnitude of bouyant force = weight of the fluid displaced)

F(sub: B) = F(sub: g)[object] = m(sub: o)g
bouyant force = weight of floating object

m = ρV
(mass = density × volume)




3. Well, the volume of the boat is (4.0 m)(6.0 m)(0.04 m) = (0.96 m³); I mean, the volume of the displaced water is that. ;)

Density of fresh water = 1.00 × 10³ kg/m³

F = ρV(g)
F = (1.00 × 10³ kg/m³)(0.96 m³)(9.81 m/s²)
F = 9.4 × 10³ N


Am I correct?
 
Last edited:
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Correct - and an extra bonus point for quoting the weight of the truck not it's mass.
Although you will probably get the answer marked wrong by some dumb online marking system that expects mass.
 
All right! Thanks. :)

Problem solved!

EDIT: Ermmm... How do I mark it solved?
 
Found it. :)
 
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