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Zorluk: OrtaBuoyancy and Archimedes' Principle

A solid metal sphere is suspended from a digital spring scale and lowered completely into four different storage tanks, each containing a different liquid. The true weight of the sphere in the air remains constant.

The liquids and their approximate densities are:
- Gasoline: 0.75 g/cm30.75 \text{ g/cm}^3
- Glycerin: 1.26 g/cm31.26 \text{ g/cm}^3
- Freshwater: 1.00 g/cm31.00 \text{ g/cm}^3
- Ocean water: 1.03 g/cm31.03 \text{ g/cm}^3

Arrange the liquids in order based on the apparent weight shown on the spring scale when the sphere is completely submerged, from the GREATEST apparent weight to the LEAST apparent weight.

  1. 1Gasoline (0.75 g/cm30.75 \text{ g/cm}^3)
  2. 2Freshwater (1.00 g/cm31.00 \text{ g/cm}^3)
  3. 3Ocean water (1.03 g/cm31.03 \text{ g/cm}^3)
  4. 4Glycerin (1.26 g/cm31.26 \text{ g/cm}^3)

Cevap

Gasoline, Freshwater, Ocean water, Glycerin
The correct order follows the fluid densities from lowest to highest. A fluid with a lower density displaces less mass for a given volume, exerting a smaller upward buoyant force. Because Apparent Weight = True Weight - Buoyant Force, the smallest buoyant force results in the largest apparent weight. Therefore, gasoline (lowest density) yields the greatest apparent weight, and glycerin (highest density) yields the least apparent weight.

Adım Adım Çözüm

1
Identify the relationship between true weight, apparent weight, and buoyant force.
Apparent Weight = True Weight - Buoyant Force
A submerged object experiences an upward buoyant force that opposes gravity, reducing the measured weight on the scale.
2
Determine how the buoyant force relates to the different liquids.
Buoyant Force is directly proportional to the density of the liquid.
According to Archimedes' principle, buoyant force equals the weight of the displaced fluid. Since the same sphere is completely submerged every time, the displaced volume is constant, making buoyant force depend entirely on fluid density.
3
Correlate fluid density with apparent weight.
Lower fluid density produces a smaller buoyant force, resulting in a greater apparent weight.
Since apparent weight is calculated by subtracting the buoyant force from the constant true weight, subtracting a smaller value leaves a larger apparent weight.
4
Order the liquids from lowest density to highest density.
Gasoline (0.75), Freshwater (1.00), Ocean water (1.03), Glycerin (1.26).
This sequence represents the progression from the smallest buoyant force (greatest apparent weight) to the largest buoyant force (least apparent weight).

Anahtar Kavram

The apparent weight of a submerged object is its true weight minus the buoyant force. For a constant volume, a lower density fluid exerts a smaller buoyant force, resulting in a greater apparent weight.
Tahmini Süre:1m 0s
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Konular

Buoyancy and Archimedes' Principle

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