What is the mass, how to calculate it, and how does it differ from the weight?

The concept with which we are familiar from early childhood is mass. And yet in the course of physics with its study, some difficulties are connected. Therefore, it is necessary to clearly define what a mass is. How can you find out? And why is it not equal to the weight?

Determination of mass

The natural scientific meaning of this quantity is that it determines the amount of matter that is contained in the body. For its designation, it is customary to use the Latin letter m. The unit of measurement in the standard system is kilogram. In tasks and everyday life, extrasystemic: gram and ton are often used.

In the school course of physics, the answer to the question "What is mass?" Is given in studying the phenomenon of inertia. Then it is defined as the ability of the body to resist changing the speed of its movement. Therefore, the mass is also called inert.

What is weight?

First, it is a force, that is, a vector. The mass is a scalar quantity. The weight vector is always attached to the support or suspension and is directed in the same direction as the gravity, that is, vertically down.

The formula for calculating the weight depends on whether this support (suspension) moves. In the case of resting the system, the following expression is used:

P = m * g, where P (in English sources W is used) - body weight, g - acceleration of gravity. For the ground, g is assumed to be equal to 9.8 m / s ² .

From it, the mass formula can be derived: m = P / g.

When moving downward, that is, in the direction of the action of the weight, its value decreases. Therefore, the formula takes the form:

P = m (g - a). Here, "a" is the acceleration of the movement of the system.

That is, when these two accelerations are equal, a state of weightlessness is observed, when the weight of the body is zero.

When the body begins to move up, it is said about the increase in weight. In this situation, an overload condition occurs. Because the body weight increases, and its formula will look like this:

P = m (g + a).

How does mass relate to density?

Very simple. The greater the density of the substance from which the body consists, the more important its mass will have. After all, density is defined as the ratio of two quantities. The first of these is mass, the volume is the second. To denote this value, we have chosen the Greek letter ρ. The unit of measurement is the ratio of kilograms to cubic meters.

Proceeding from all the above, the mass formula takes the following form:

M = ρ * V, in which the letter V denotes the volume of the body.

Entertaining tasks

After explaining the question of what a mass is, you can start solving problems. Those who have entertaining content will be more interested in students.

Task number 1. Condition: Winnie the Pooh gave two identical liter pot. In one of them honey, in another oil. How to find out in which honey without opening them?

Decision. The density of honey is greater than that of oil. The first has a value of 1430 kg / m ³ , and the second - 920 kg / m ³ . Therefore, with the same volume of pots, the one with honey will be heavier.

To more accurately answer the question of the problem, you need to calculate the mass of honey and butter in the pots. The volume of them is known - this is 1 liter. But the calculations require a value in cubic meters. So first you need to translate. One cubic meter contains 1000 liters. Therefore, when calculating the result, it is required to take the value of the volume equal to 0.001 m ³ .

Now we can use the mass formula, in which the density is multiplied by the volume. After simple calculations, we obtain the following mass values: 1.43 kg and 0.92 kg, for honey and oil, respectively.

Answer: a pot of honey is heavier.

Task number 2. Condition: The clown without problems raises the weight, on which it is written that its mass is 500 kilograms. What is the real mass of a weight if its volume is equal to 5 liters, and the substance from which it is made is a cork?

Decision. In the table, you need to find the density of the plug. It is equal to 240 kg / m ³ . Now you need to translate the value of the volume, it will be 0.005 m ³ .

Knowing these quantities, it is not difficult to use the already known formula to calculate the weight of the shuffle. It is obtained equal to 1.2 kg. Now it is clear why the clown is not at all difficult.

Answer. The real weight of the weight is 1.2 kg.

Problem 3. Condition: The genie was sitting in a lamp whose volume is unknown. But its density at that moment was 40,000 kg / m ³ . When he was released from the bottle, he began to have the parameters of an ordinary human body: a volume of 0.08 m ³ , density of 1000 kg / m ³ . What is the volume of a lamp?

Decision. First you need to know its mass in a normal state. It will be equal to 80 kg. Now you can proceed to find the volume of the lamp. We will assume that Jin occupies all the space inside it. Then it will be necessary to divide the mass into a density, that is, 80 to 40,000. A value of 0.002 m ^{3 is} obtained. What is equal to two liters.

Answer. The volume of the lamp is 2 liters.

Tasks for calculating the mass

Continuing the conversation about what a mass is, there must be a solution to tasks related to life. Here are two situations that clearly demonstrate the application of knowledge in practice.

Task number 4. Condition: In 1979, a tanker accident occurred, which resulted in oil entering the bay. Its spot had a diameter of 640 m and a thickness of about 208 cm. What is the mass of the spilled oil?

Decision. The density of oil is 800 kg / m ³ . In order to use the already known formula, you need to know the volume of the spot. It is easy to calculate if you take a stain for a cylinder. Then the volume formula will be:

V = π * r ² * h.

And r is the radius, and h is the height of the cylinder. Then the volume will be equal to 668794.88 m ³ . Now you can count the mass. It will turn out this: 535034904 kg.

Answer: The mass of oil is approximately 535036 tons.

Task number 5. Condition: The length of the longest telephone cable is 15,151 km. What is the mass of copper that went into making it, if the cross-section of wires is 7.3 cm ² ?

Decision. The density of copper is 8900 kg / m ³ . The volume is found by the formula, which contains the product of the base area to the height (here the length of the cable) of the cylinder. But first you need to convert this area into square meters. That is, divide this number by 10,000. After calculations it turns out that the total cable volume is approximately 11,000 m ³ .

Now we need to multiply the density and volume values to find out what the mass is equal to. The result is the number of 97,900,000 kg.

Answer: The mass of copper is 97900 tons.

Another problem related to the mass

Task number 6. Condition: The biggest candle weighing 89867 kg was a diameter of 2.59 m. What was its height?

Decision. The density of wax is 700 kg / m ³ . The height will need to be found from the volume formula. That is, V must be divided by the product π and the square of the radius.

And the volume itself is calculated by mass and density. It is equal to 128.38 m ³ . The height was 24.38 m.

Answer: The height of the candle is 24.38 m.