Solving a Buoyancy Problem: Determining the Weight of a Truck on a Ferry Boat

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In summary, the problem involves finding the weight of a truck based on the amount of water it displaces when loaded onto a ferry boat. The equation used is P=m/v, with the density of water as P and the volume of the displaced water as v. The answer is 960 kg.
  • #1
TRBMan
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Homework Statement


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 in the water. What is the weight of the truck?


Homework Equations


[tex]\rho[/tex]=m/v
and others


The Attempt at a Solution


none. My teacher gave my class chapter to read and complete on our own. I have no idea where to begin to start solving this problem.
 
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  • #2
Water must be displaced to get the buoyancy to hold up the truck. The weight of the water displaced will be same as the weight of the truck.
 
  • #3
do i use the P=m/v equation and solve for m?
i would use the density of water for P, and the volume of the water displaced for v, right? I think i understand.
would the answer be 960 kg?
 
  • #4
That's it.
 

1. What is the concept of buoyancy?

Buoyancy is the upward force that a fluid exerts on an object that is partially or fully submerged in it. It is caused by the difference in pressure between the top and bottom of the object, with the higher pressure at the bottom pushing the object upwards.

2. How is buoyancy calculated?

Buoyancy is calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. This can be calculated using the equation Fb = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. What factors affect buoyancy?

The buoyant force on an object is affected by the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. It is also affected by the shape and density of the object itself, as well as the depth of the object in the fluid.

4. How does buoyancy relate to objects of different densities?

If an object is less dense than the fluid it is submerged in, it will experience a greater upward buoyant force and will float. If an object is more dense than the fluid, it will sink as the downward gravitational force is greater than the upward buoyant force.

5. Can buoyancy be negative?

No, buoyancy is always a positive force. It can only be perceived as negative if an object is denser than the fluid, causing it to sink. However, the buoyant force itself is still a positive force acting in the opposite direction to the gravitational force.

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