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小丽同学在金沙江边捡到一块会吸水的小石头（吸水后石头的体积不变），回家后她想测量一下石头的密度。她先用电子秤测出石头的质量为60g，再把它放进一个容积为370m...

Mar 19, 2024

小丽同学在金沙江边捡到一块会吸水的小石头（吸水后石头的体积不变），回家后她想测量一下石头的密度。她先用电子秤测出石头的质量为60g，再把它放进一个容积为370mL的容器里，然后再缓慢地往容器里加水，直到水刚好装满。经测量，她一共往容器里加了340g的水。最后，小丽将小石块从容器中取出，抖掉水后，再测出它此时的质量为70g。若水的密度为。求：（1）小石头的体积；

Solution

Calculate the volume of water displaced by the stone when it is submerged. Since the container was filled to 370 mL and 340 g of water was added, the volume of water displaced is equal to the volume of the container minus the volume of water added:

V_{\text{water displaced}} = 370 \text{mL} - 340 \text{mL} = 30 \text{mL}

Convert the volume of water displaced to the volume of the stone. Since the stone's volume does not change when it absorbs water, the volume of water displaced is equal to the volume of the stone:

V_{\text{stone}} = V_{\text{water displaced}} = 30 \text{mL}

Answer

The volume of the stone is 30 mL.

Key Concept

Archimedes' Principle: The volume of fluid displaced by an object submerged in a fluid is equal to the volume of the object.

Explanation

By measuring the volume of water displaced by the stone, we can determine the volume of the stone itself, as they are equal according to Archimedes' Principle.

（2）干燥小石头的密度。

Solution

Calculate the mass of the dry stone

Calculate the density of the dry stone using its mass and volume

Answer

The density of the dry stone is

2.0 \text{ g/mL}

Key Concept

Density is defined as mass per unit volume. The equation for density is

\rho = \frac{m}{V}

where

\rho

is the density,

m

is the mass, and

V

is the volume.

Explanation

The density of the dry stone is found by dividing its mass (60 g before absorbing water, 70 g after releasing water) by its volume (30 mL). Since the stone's volume does not change after absorbing and releasing water, we use the initial mass to calculate its density.