Find the force required to lift a 200 N object submerged in a fluid with a density of 1,000 kg/m³.
The correct answer and explanation is :
To calculate the force required to lift a 200 N object submerged in a fluid, we need to apply the principle of buoyancy, also known as Archimedes’ principle. This principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the displaced fluid.
Step-by-Step Calculation:
- Determine the Buoyant Force:
The buoyant force (( F_b )) is given by the equation:
[
F_b = \rho \cdot V \cdot g
]
where:
- ( \rho ) is the density of the fluid (1,000 kg/m³),
- ( V ) is the volume of the object,
- ( g ) is the acceleration due to gravity (approximately 9.81 m/s²). The volume of the object can be found from the relationship between weight and buoyant force.
- Object’s Weight and Buoyant Force:
Since the object weighs 200 N and we are considering it submerged, the buoyant force must be equal to or greater than the weight of the object to lift it. The weight of an object is the gravitational force acting on it and is given by:
[
W = m \cdot g
]
where ( m ) is the mass of the object. However, we already know the weight is 200 N, and this weight is being counteracted by the buoyant force of the displaced fluid. - Force Required to Lift the Object:
The total force required to lift the object will be the weight of the object minus the buoyant force, because the buoyant force counteracts some of the weight:
[
F_{\text{lift}} = W – F_b
] If the buoyant force is equal to the object’s weight (200 N), then the force required to lift the object would be zero. If the buoyant force is less than the object’s weight, the force required to lift it would be the difference.
Since the question specifies a 200 N object and does not give the volume or specific details, a reasonable assumption is that the buoyant force exactly balances the weight, resulting in no additional force being required to lift the object if it is floating or neutrally buoyant.
Conclusion:
The force required to lift the object depends on its volume and the buoyant force exerted by the fluid. If the object is floating or neutrally buoyant, the force required to lift it is zero. However, if it is fully submerged and the buoyant force does not fully counteract the weight, the required force would be the difference between the object’s weight and the buoyant force.