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Overview of mathematical measurement
There are various methods to measure the density of objects, which can develop students' thinking. I summarized the following measurement methods:

First, measure the solid density.

Basic principle: ρ = m/v;

1, weighing method:

Equipment: balance, measuring cylinder, water, metal block and string.

Step: 1) Weigh the mass of the metal block with a balance;

2) Inject a proper amount of water into the measuring cylinder, and the reading volume is V 1.

3) Tie the metal block with a string, put it into a measuring cylinder, immerse it, and read the volume as V2.

Calculation expression: ρ=m/(V2-V 1)

2, the specific gravity cup method:

Equipment: beaker, water, metal block, balance,

Step: 1), fill the beaker with water and put it on the balance to weigh the mass as m1;

2) Gently put the metal block into water to overflow some water, and then put the beaker on the balance to weigh the mass m2;

3) Take out the metal block, put the beaker on the balance, and weigh the mass m3 of the beaker and the remaining water.

Calculation expression: ρ = ρ water (m2-m3)/(m 1-m3)

3, Archimedes principle law:

Equipment: spring scale, metal block, water, string.

Step: 1), tie the metal block with a string, and weigh the weight g of the metal block with a spring scale;

2) completely immerse the metal block in the water, and weigh the apparent weight of the metal block in the water g/

Calculation expression: ρ=Gρ water /(G-G/)

4, buoyancy method (a):

Equipment: wood block, water, fine needle, measuring cylinder.

Step: 1), inject a proper amount of water into the measuring cylinder, and read the volume as v1;

2) put the wood block into water, float and stand, and read the volume v2;

3) Insert the wood block with a fine needle, completely immerse the wood block in water, and read the volume as V3.

Calculation expression: ρ = ρ water (V2-V 1)/(V3-V 1)

5, buoyancy method (2):

Equipment: scale, cylindrical cup, water, small plastic cup, small stone.

Step: 1), put a proper amount of water in the cylindrical cup, then gently put the plastic cup mouth up and let it float, and use a scale.

Measure the height of water in the cup h1;

2) Gently put the pebbles into the cup, float, and measure the water surface height H2 with a scale;

3) Take the pebbles out of the cup, put them into the water, sink them into the water, and measure the height h3 of the water with a scale.

Calculation expression: ρ = ρ water (h2-h 1)/(h3-h 1)

6, densitometer method:

Equipment: eggs, densimeter, water, salt, glass.

Step: 1), pour a proper amount of water into the glass, gently put the eggs in, and the eggs will sink;

2), gradually add salt to the water, while stirring with a densimeter until the eggs float, and measure the salt water with a densimeter.

Density is equal to the density of eggs;

Second, the density of liquid:

1, weighing method:

Equipment: beaker, measuring cylinder, balance, liquid to be measured.

Step: 1). Weigh the beaker with a balance (M 1).

2) pour the liquid to be measured into a beaker and measure the total mass m2;

3) Pour the liquid in the beaker into the measuring cylinder and measure the volume V. ..

Calculation expression: ρ = (m2-m1)/v.

2. Specific gravity cup method

Equipment: beaker, water, liquid to be treated and balance.

Step: 1), weigh the burned mass m1with a balance;

2) Fill the beaker with water and weigh the total mass m2;

3) Pour water into the beaker, fill the beaker with the liquid to be measured, and weigh out the total mass of M3.

Calculation expression: ρ = ρ water (M3-M 1)/(M2-M 1)

3, Archimedes principle law:

Equipment: spring scale, water, measured liquid, pebbles, string.

Step: 1), tie the small stone with a string, and weigh the gravity g of the small stone with a spring scale;

2) Immerse the small stones in water, and weigh the apparent weight g/

3) Immerse the small piece in the liquid to be measured, and weigh the apparent weight G// of the small piece with a spring scale.

Calculation expression: ρ = ρ water (G-G/)/(G-G/)

4.u-tube method:

Equipment: U-tube, water, liquid to be measured, balance.

Step: 1), pour a proper amount of water into the U-shaped tube;

2) slowly inject the liquid to be measured from the nozzle of the U-shaped tube along the tube wall.

3) Measure the water height h 1 and the liquid height h2 in the pipe with a scale (as shown in the figure).

Calculation expression: ρ = ρ water h 1/h2.

(Note: The condition of using this method is that the liquid to be tested is insoluble in water, and the density of the liquid to be tested is less than that of water. )

5, densitometer method:

Equipment: density meter, liquid to be tested.

Methods: put the densimeter into the liquid to be measured and read the density directly.