A concept that we are familiar with from early childhood is the mass. And yet, in the course of physics, some difficulties are associated with its study. Therefore, it is necessary to clearly define what mass is. How can you recognize her? And why is it not equal to weight?
Determination of mass
The natural scientific meaning of this value 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 the kilogram. In tasks and everyday life, off-system ones are also often used: grams and tons.
In a school physics course, the answer to the question: "What is mass?" given in the study of the phenomenon of inertia. Then it is defined as the ability of a body to resist a change in the speed of its movement. Therefore, the mass is also called inert.
What is weight?
Firstly, it is a force, that is, a vector. Mass is a scalar quantity. The weight vector is always attached to the support or suspension and is directed in the same direction as gravity, i.e. vertically down.
The formula for calculating the weight depends on whether thethis support (suspension). In the case of system rest, the following expression is used:
Р=mg, where Р (the letter W is used in English sources) is the weight of the body, g is the free fall acceleration. For the earth, g is usually taken equal to 9.8 m/s2.
The mass formula can be derived from it: m=P / g.
When moving down, that is, in the direction of the weight, its value decreases. Therefore, the formula becomes:
Р=m (g - a). Here "a" is the acceleration of the system.
That is, when these two accelerations are equal, a state of weightlessness is observed when the body weight is zero.
When the body starts to move upwards, they talk about weight gain. In this situation, an overload condition occurs. Because body weight increases, and its formula will look like this:
P=m (g + a).
How is mass related to density?
Very simple. The greater the density of the substance of which the body is composed, the more important its mass will be. After all, density is defined as the ratio of two quantities. The first of these is mass, volume is the second. To designate this value, the Greek letter ρ was chosen. The unit of measurement is the ratio of kilogram to cubic meter.
Based on the above, the mass formula takes the following form:
m=ρV, in which the letter V denotes the volume of the body.
Entertaining tasks
After clarifying the question of what mass is, you can begin to solve problems. Those of themthat have engaging content will keep students more interested.
Task number 1. Condition: Winnie the Pooh was presented with two identical liter pots. One contains honey, the other contains oil. How to know which honey is in without opening them?
Decision. The density of honey is greater than that of butter. The first is 1430 kg/m3 and the second is 920 kg/m3. Therefore, with the same volume of pots, the one with honey will be heavier.
To more accurately answer the question of the problem, you will need to calculate the mass of honey and oil in pots. Their volume is known - it is 1 liter. But in the calculations you will need a value in cubic meters. So the first thing to do is to translate. One m3 contains 1000 liters. Therefore, when calculating the result, you will need to take a volume value equal to 0.001 m3.
The mass formula can now be used, in which density is multiplied by volume. After simple calculations, the following mass values \u200b\u200bare obtained: 1.43 kg and 0.92 kg, for honey and oil, respectively.
Answer: the honey pot is heavier.
Problem number 2. Condition: The clown lifts a weight without any problems, on which it is written that its mass is 500 kilograms. What is the actual mass of a weight if its volume is 5 liters and the substance it is made of is cork?
Decision. In the table, you need to find the value of the cork density. It is equal to 240 kg/m3. Now you need to translate the value of the volume, you get 0.005 m3.
Knowing these quantities, it is not difficult to use the already known formula tocount the mass of the fake weight. It turns out equal to 1.2 kg. Now I understand why the clown is not hard at all.
Answer. The actual mass of the kettlebell is 1.2 kg.
Problem No. 3. Condition: The genie was sitting in a lamp, the volume of which is unknown. But its density at that moment was 40,000 kg/m3. When it was released from the bottle, it began to have the parameters of an ordinary human body: volume 0.08 m3, density 1000 kg/m3. What is the volume of the lamp?
Decision. First you need to find out its mass in the normal state. It will be equal to 80 kg. Now we can move on to finding the volume of the lamp. We will assume that Jean occupies all the space inside it. Then you need to divide the mass by the density, that is, 80 by 40,000. The value will be 0.002 m3. Which is equal to two liters.
Answer. The volume of the lamp is 2 liters.
Mass Calculation Problems
The continuation of the conversation about what mass is, should be the solution of tasks related to life. Here are two situations that will clearly demonstrate the application of knowledge in practice.
Problem No. 4. Condition: In 1979, a tanker accident occurred, as a result of which oil got into the bay. Its slick 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/m3. In order to use the already known formula, you need to know the volume of the spot. It is easy to calculate if we take the spot for a cylinder. Then the volume formula will be:
V=πr2h.
Moreover, r is the radius, and h is the height of the cylinder. Then the volume will be equal to 668794.88 m3. Now you can calculate the mass. It will turn out like this: 535034904 kg.
Answer: the mass of oil is approximately equal to 535036 tons.
Problem 5. Condition: The length of the longest telephone cable is 15151 km. What is the mass of copper that went into its manufacture if the cross section of the wires is 7.3 cm2?
Decision. The density of copper is 8900 kg/m3. The volume is found by a formula that contains the product of the area of the base and 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 10000. After calculations, it turns out that the volume of the entire cable is approximately equal to 11000 m3.
Now you need to multiply the density and volume values to find out what the mass is. The result is the number 97900000 kg.
Answer: the mass of copper is 97900 tons.
Another mass challenge
Problem 6. Condition: The largest candle weighing 89867 kg was 2.59 m in diameter. What was its height?
Decision. Wax density - 700 kg/m3. The height will need to be found from the volume formula. That is, V must be divided by the product of π and the square of the radius.
And the volume itself is calculated by mass and density. It turns out to be equal to 128.38 m3. The height was 24.38 m.
Answer: the height of the candle is 24.38 m.
