Balance and measuring cylinder (or cup) are two commonly used tools for measuring density, but sometimes due to limitations in experimental conditions or the absence of measuring cylinder (or cup) or balance, or even the absence of both equipment, how should solid density be measured? The following examples are used to illustrate the classification.

1、 Lack of balance scales

A measuring cylinder (or cup) is provided in the equipment, and its volume can be measured using the "liquid" method. Considering that the object is floating, and the V-row can be measured using a measuring cylinder, this can be obtained.

Example 1: If I give you one measuring cylinder and one empty glass tube, and enough water, how can I measure the density of the empty glass tube?

Solution: (1) Fill the measuring cylinder with an appropriate amount of water and record the scale V1 reached by the water surface;

(2) Gently place the small test tube with its mouth facing upwards into the graduated cylinder, allowing it to float on the water surface in the cylinder. When it is still, record the scale V2 reached by the water surface to determine the gravity of the glass tube;

(3) Immerse the small test tube in water to fill it with water and sink it to the bottom of the graduated cylinder. Record the mark V3 reached by the water surface;

(4) The density of glass.

If the given solid material cannot "float" directly in a known density liquid (such as water), we can take measures to make it "float". For example, the clay can sink directly into the water, but if it is squeezed into a bowl shape, it can float; Toothpaste skin sinks in water, but if you try to make it hollow and seal its mouth, it can float... For solids with a density greater than the known liquid density and cannot deform, such as stones and metal blocks, how can you make them float? Objects with density less than that of liquid (such as wood, foam, plastic, etc.) can be used as props. See Example 2 for specific operations.

Example 2: Give you a measuring cylinder, one small stone, one wooden block, and enough fine thread and water. How can you measure the density of the stone?

Solution: (1) Pour an appropriate amount of water into the measuring cylinder, then place a wooden block in it to float, and record the scale V0 reached by the water surface;

(2) Place the small stone on the wooden block so that it still floats on the water surface, and record the scale V1 reached by the water surface at this time;

(3) Immerse the small stone with the fine thread tied in it in water and record the scale V2 reached by the water surface at this time;

(4) Density of small stones

If the given solid can float but cannot sink directly in a liquid of known density, measures can be taken to make it sink. For example, if a wooden block cannot sink in water, it can be pressed into the water with a pin, thin wire, etc; It can also be dropped using solids with a density greater than water.

2、 Shortage cylinder (or measuring cup) type

How can the solid volume be measured without providing a measuring cylinder (or cup)? There are four methods:

1. Drainage method

Example 3: Give you a pre adjusted balance (with weights) and a beaker filled with water, and use only these equipment (without any other auxiliary tools) to measure the density of a packet of metal particles.

Analysis: The key to this question is to determine the mass of the spilled liquid, but without other auxiliary tools, it may be better to use a balance to indirectly measure it.

Solution:

① Weigh the mass of the metal particles to be tested;

② Weigh the total mass of the beaker and water;

③ Pour the metal particles into a beaker filled with water (with some water overflowing), and weigh the total mass of water and metal particles in the beaker;

④

⑤

2. Integer method

If the object being measured is easy to shape, such as potatoes or plasticine, they can be shaped into cubes, rectangular prisms, etc., and then the relevant length can be measured with a ruler to obtain the volume of the object.

3. Equal volume method

Use a balance to weigh the mass of a liquid with the same volume and known density as the object, and then indirectly obtain the value of V.

Example 4: One empty beaker, one balance with weights, enough water, one dropper, two fine wires, measure the volume of small stones.

Solution: (1) Pour an appropriate amount of water into an empty cup and measure its mass;

(2) Put the small stones with fine threads into the water and mark the new liquid surface with the threads;

(3) Take out the stone from the beaker, add water to the beaker until the liquid level reaches the mark, and use a balance to weigh the total mass of the beaker and water at this time;

（4）

4. Buoyancy method

When an object is submerged, according to Archimedes' principle, it is known that.

Example 5: How to measure the density of a stone with a beaker filled with water and a thin wire.

Solution: (1) Measure the mass of the stone using a balance;

(2) Weigh the weight of a beaker containing an appropriate amount of water using a balance;

(3) Hanging a stone with a thin thread and immersing it in water without touching the bottom, its mass is;

(4) The buoyancy experienced by the stone, therefore;

(5) Stone density

3、 No balance, no measuring cylinder class

1. Buoyancy method

Some equipment may not provide scales and measuring cylinders (or cups), but spring scales and platform scales are provided. In this case, the buoyancy method can be used, as shown in Example 5 for specific methods.

2. Suspension method

Place the object to be tested into the original supply liquid, adjust the density of the original supply liquid by adding or subtracting appropriate liquids, so that the object can suspend in the liquid, and then measure the density of the liquid with a density meter, which is the density of the object to be tested.

3. Floating method

This method can be used for objects with regular shapes. Let the object float in a liquid with a known density, measure the height of the object above the water surface and the total height h of the object with a scale, and then we know:

so

4、 Although given a balance and measuring cylinder, the balance does not have weights

It is difficult to obtain the mass of a solid without weights on a balance. It is advisable to use a liquid with a known density (such as water) as a bridge and use the arm like properties of the balance to measure the mass of the liquid with a known density instead of the mass of the object.

Example 6. How to measure the density of small stones with a leveled homemade equal arm lever with a tray, two identical beakers, a measuring cylinder, a dropper, a fine wire, and an appropriate amount of water?

Solution: (1) Place two beakers on the left and right plates respectively. Add water to the left and a stone to the right. Use a dropper to adjust the amount of water in the left cup to restore balance to the lever;

(2) Pour water into a measuring cylinder and measure the volume of water;

(3) Measure the volume of stones using drainage method;