Which weighs more on earth: 100kg of steel or a 100kg polystyrene ball? Be as technically correct as possible
A:
Technically, 100 kg of steel and 100 kg of polystyrene weigh the same on Earth when measured on a scale, as they both experience the same gravitational force due to their equal mass. However, there are some nuances to consider:
Buoyancy Effect
Earth’s atmosphere exerts an upward buoyant force on objects, proportional to the volume of the object and the density of the surrounding air. Since polystyrene has a much lower density than steel, a 100 kg polystyrene ball will have a significantly larger volume and experience a greater buoyant force compared to 100 kg of steel.
As a result:
• Effective weight (apparent weight): The steel will weigh slightly more than the polystyrene on a scale because the buoyant force acting on the polystyrene reduces its apparent weight more.
Actual Weight
Weight is the gravitational force on an object and is given by:
Where and . Without considering buoyancy, both objects have the same weight of approximately (newtons).
Conclusion
• True weight (in a vacuum): Both are identical at 981 N.
• Apparent weight (in air): Steel is slightly heavier due to reduced buoyant force acting on it compared to the polystyrene ball.
Yup, the models are smart, but are trained to follow standard human patterns for this type of questions. And even on hackernews vast majority will not think that they would need to correct for buoyancy when actually attempting the experiment in standard conditions.
They very often get popular "tricky" questions wrong because they saw it so many times that they switch from internal reasoning to memorization/retrieval.
Q:
Which weighs more on earth: 100kg of steel or a 100kg polystyrene ball? Be as technically correct as possible
A: Technically, 100 kg of steel and 100 kg of polystyrene weigh the same on Earth when measured on a scale, as they both experience the same gravitational force due to their equal mass. However, there are some nuances to consider:
Buoyancy Effect
Earth’s atmosphere exerts an upward buoyant force on objects, proportional to the volume of the object and the density of the surrounding air. Since polystyrene has a much lower density than steel, a 100 kg polystyrene ball will have a significantly larger volume and experience a greater buoyant force compared to 100 kg of steel.
As a result: • Effective weight (apparent weight): The steel will weigh slightly more than the polystyrene on a scale because the buoyant force acting on the polystyrene reduces its apparent weight more.
Actual Weight
Weight is the gravitational force on an object and is given by:
Where and . Without considering buoyancy, both objects have the same weight of approximately (newtons).
Conclusion • True weight (in a vacuum): Both are identical at 981 N. • Apparent weight (in air): Steel is slightly heavier due to reduced buoyant force acting on it compared to the polystyrene ball.