The concept that we are familiar with from early childhood is mass. Nevertheless, in the course of physics, certain difficulties are associated with its study. Therefore, it is necessary to clearly define what mass is. How can I recognize her? And why is it not equal to weight?
Mass determination
The natural scientific meaning of this quantity is that it determines the amount of substance that is contained in the body. To designate it, it is customary to use the Latin letter m. The unit of measurement in the standard system is kilogram. In tasks and everyday life, non-systemic ones are often used: grams and tons.
In the school physics course, the answer to the question: βWhat is mass?β given in the study of the phenomenon of inertia. Then it is defined as the ability of the body to resist changes 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 applied to the support or suspension and is directed in the same direction as the force of gravity, that is, vertically downward.
The formula for calculating the weight depends on whether this support (suspension) is moving. If the system is at rest, the following expression is used:
P = m * g, where P (the letter W is used in English sources) is the body weight, g is the acceleration of gravity. For land g, it is customary to take equal to 9.8 m / s 2 .
From it, the mass formula can be derived: m = P / g.
When moving down, that is, in the direction 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, with the equality of these two accelerations, a state of weightlessness is observed when the body weight is zero.
When the body begins to move up, then they talk about weight gain. In this situation, an overload condition occurs. Because the body weight is increasing, and its formula will look like this:
P = m (g + a).
How is mass related to density?
Very simple. The higher the density of the substance of which the body is composed, the greater 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 denote this value, the Greek letter Ο was chosen. The unit of measure is the ratio of kilogram to cubic meter.
Based on the foregoing, the mass formula takes the following form:
m = Ο * V, 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 that have entertaining content will be more interesting to students.
Task No. 1. Condition: Winnie the Pooh was presented with two identical liter pots. In one of them is honey, in the other is oil. How to find out in which honey without opening them?
Decision. The density of honey is greater than that of butter. 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 harder.
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 calculations, a value in cubic meters will be required. Therefore, you must first complete the translation. One m 3 contains 1000 liters. Therefore, when calculating the result, it will be necessary to take a volume value equal to 0.001 m 3 .
Now a mass formula can be used in which density is multiplied by volume. After simple calculations, the following mass values ββare obtained: 1.43 kg and 0.92 kg, for honey and oil, respectively.
Answer: a pot of honey is heavier.
Problem number 2. Condition: The clown without any problems lifts a kettlebell, which says that its mass is 500 kilograms. What is the actual mass of a weight if its volume is 5 liters and the substance of which it is made is a cork?
Decision. In the table you need to find the value of the density of the cork. It is equal to 240 kg / m 3 . Now you need to translate the volume value, it turns out 0.005 m 3 .
Knowing these values, it is not difficult to use the already known formula to calculate the mass of fake weights. It turns out equal to 1.2 kg. Now itβs clear why the clown is not at all hard.
Answer. The actual mass of the weight is 1.2 kg.
Task number 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 / m 3 . When he was released from the bottle, he began to have the parameters of an ordinary human body: volume 0.08 m 3 , density 1000 kg / m 3 . What is the volume of the lamp?
Decision. First you need to find out its mass in normal condition. It will be equal to 80 kg. Now you can move on to finding the volume of the lamp. We assume that Jin occupies all the space inside her. Then you need to divide the mass by density, that is, 80 by 40,000. The result is a value of 0.002 m 3 . Which is equal to two liters.
Answer. The volume of the lamp is 2 liters.
Tasks for calculating mass
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.
Task No. 4. Condition: In 1979, a tanker accident occurred, as a result of which oil fell into the bay. Its spot had a diameter of 640 m and a thickness of about 208 cm. What is the mass of 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 spot for a cylinder. Then the volume formula will be like this:
V = Ο * r 2 * h.
Moreover, 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 like this: 535034904 kg.
Answer: the mass of oil is approximately equal to 535036 tons.
Task number 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 wire cross section 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 by the height (here the cable length) of the cylinder. But first you need to translate this area into square meters. That is, divide this number by 10000. After the calculations, it turns out that the volume of the entire cable is approximately 11000 m 3 .
Now you need to multiply the density and volume 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 number 6. Condition: The largest candle weighing 89867 kg was 2.59 m in diameter. What was its height?
Decision. The density of the wax is 700 kg / m 3 . Height will need to be found from the volume formula. That is, V must be divided by the product of Ο 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 m 3 . The height was 24.38 m.
Answer: the height of the candle is 24.38 m.