Difference between weight and mass. What is the difference between mass and weight and why there is a substitution of concepts

Gravity and weight are two concepts involved in gravitational field theory of physics. These two concepts are often misinterpreted and used in the wrong context. This situation is aggravated by the fact that at the ordinary level the concepts of mass (a property of matter) and weight are also perceived as something identical. This is why a correct understanding of gravity and weight is important for science. Often these two nearly similar concepts are used interchangeably. This article provides an overview of the basic concepts, their manifestations, special cases, similarities and, finally, their differences.
Analysis of basic concepts:

The force directed at an object from the planet Earth or from another planet in the Universe (any astronomical body in the broad sense) is the force of gravity. Force is an observable demonstration of the force of gravity. Numerically expressed by the equation Fheavy=mg (g=9.8m/s2).

This force is applied to each microparticle of the body; at the macro level, this means that it is applied to the center of gravity of a given body, since the forces acting on each particle separately can be replaced by the resultant of these forces. This force is a vector force, always directed towards the center of mass of the planet. On the other hand, Ft can be expressed in terms of the gravitational force between two bodies, usually different in mass. An inversely proportional connection will be observed with an interval between interacting objects in a square (according to Newton’s formula).

In the case of a body on a plane, it will be the gap between the body and the center of mass of the planet, which is its radius (R). Depending on the height of the body above the surface, Fstrand and g change, as the gap between connected objects increases, respectively (R+h), where h shows the height above the surface. This implies the dependence that the higher the object is above the level of the Earth, the less gravity and the less g.

Body weight, characteristics, comparison with gravity

The force with which a body acts on a support or vertical suspension is called body weight (W). This is a vector, directional quantity. The atoms (or molecules) of the body are repelled from the particles of the base, resulting in partial deformation of both the support and the object, elastic forces arise and, in some cases, the shape of the body and support at the macro level changes slightly. A support reaction force arises; in parallel, an elastic force also arises on the surface of the body in response to the support reaction—this is weight. Body weight (W) is vectorially opposite to the ground reaction force.

Special cases, equality is observed for all of them W= m(g-a):

The stand is stationary in the case of an object on the table, or it moves uniformly with a constant speed (a = 0) In this case, W = F heavy.

If the support accelerates downward, then the body also accelerates downward, then W is less than Fweight and the weight is completely zero if the acceleration is equal to the acceleration of gravity (at g=a, W=0) In this case, there is a manifestation of weightlessness, the support moves with acceleration g and therefore there will be no various stresses and deformations from externally applied contact-mechanical force. Weightlessness can also be achieved by placing a body at a neutral point between two identical gravitating masses or by moving the object away from the source of gravity.

A homogeneous gravitational field inherently cannot cause “stress” in the body, just as a body moving under the influence of F gravity will not feel gravitational acceleration and remains a weightless, “stress-free” body. Near a non-uniform field (massive astronomical objects), a freely falling body will experience various tidal forces and the phenomenon of weightlessness will be absent since different parts of the body will accelerate unevenly and change their shape.

Stand with body moving up. The equivalent of all forces will be directed upward, therefore the F reaction of the support will be greater than Fweight and W greater than Fweight, and this state is called overload. Overload factor (K) – how many times the weight is greater than Fheavy. This value is taken into account, for example, when flying into space and military aviation, since mainly in these areas it is possible to achieve significant speeds.

Overload increases the load on human organs, mainly the musculoskeletal system and the heart are most heavily loaded, due to an increase in blood weight and internal organs. Overload is also a directional quantity and its concentration in a certain direction for the body must be taken into account (blood rushes to the legs or to the head, etc.) Permissible overloads up to a K value of no more than ten.

Key differences

These forces are applied to unequal “areas”. The F-tension is applied to the center of gravity of the object, and the weight is applied to the support or suspension.
The difference lies in the physical essence: gravity is a gravitational force, while weight is of an electromagnetic nature. Essentially, a body that is not subject to deformation from external forces is in weightlessness.
Ft and W can differ both in quantitative value and in direction; if the acceleration of the body is not zero, then W of the body is either greater or less than the force of gravity, as in the above cases (if the acceleration is directed at an angle, then W is directed towards the acceleration) .
Body weight and gravity at the planet's poles and equator. At the pole, an object lying on the surface moves with acceleration a = 0, since it is on the axis of rotation, therefore, F and W will coincide. At the equator, taking into account the rotation from west to east, the body experiences centripetal acceleration and the focus of all forces, according to Newton’s law, will be directed towards the center of the planet, in the direction of acceleration. Opposed to the force of gravity, the reaction force of the support will also be directed towards the center of the earth, but it will be less than Fheavy and the weight of the body will accordingly be less than Fheavy.

Conclusion

In the 20th century, the concepts of absolute space and time were challenged. The relativistic approach placed not only all observers, but also the movement or acceleration, on the same relative basis. This has led to confusion as to what exactly is meant by gravity and weight. The scale in an accelerating elevator, for example, cannot be distinguished from the scale in a gravitational field.

Gravitational force and weight thus became essentially dependent on the act of observation and the observer. This caused the concept to be abandoned as superfluous in fundamental disciplines such as physics and chemistry. However, representation remains important in physics teaching. The ambiguity introduced by relativity led, beginning in the 1960s, to discussions about how to define weight, choosing between the nominal definition: force due to gravity or the operational definition, determined directly by the act of weighing.

Issue 15

The fifteenth episode of the program is devoted to new physical quantities - body mass and its weight. These concepts are often confused and weight is measured in kilograms. But this is a gross mistake and Professor Daniil Edisonovich Quark will explain why this is so. Is it possible to change your body weight or even make it completely weightless? Physics answers in the affirmative. Want to know how to do this? Then watch a physics video lesson from the Academy of Entertaining Sciences, dedicated to body mass and weight.

Body mass and weight

What is the difference between mass and body weight? It seems to be the same thing. But why then, standing on the scales, can we change their readings by performing certain actions (raising our arms or bending our torso)? A physics video lesson is what you need to clarify these questions. Yes, there is a difference. From a physics point of view, it is wrong to ask the seller how much a particular product weighs. The right thing to do is to ask what its mass is! Weight is a vector quantity, a force. She always has a direction. If body weight remains unchanged, its weight can be changed. For example, putting a banana on the scale and pressing it with your hand, we will get more weight, while the mass of the banana will remain the same. Body weight is the force with which this body, being attracted to the ground, presses on the support or stretches the suspension. If body mass is measured in kilograms, then weight, like any force, is measured in newtons. Now it is clear why it is incorrect to say that body weight is equal to so many kilograms? So, body weight is always measured in newtons, while body mass can be measured in grams, kilograms, etc. Unlike body weight, body weight is not a constant value. It can increase or decrease, while body weight remains the same. Body mass is a scalar quantity. Why does it take your breath away if you swing hard on a swing? Professor Quark believes that this is a feeling of weightlessness, similar to that which occurs in space. How does it happen that the body’s weight becomes zero, even for a moment? And it turns out this way because at the moment of falling the body does not press on anything and does not pull anything back, therefore, it has no weight. Here is another example proving that the weight of a body can change while its mass remains constant. In water, all bodies weigh less than on land. Otherwise we could not swim, but went straight to the bottom. An elephant with a body weight of 1 ton weighs more on land than in water. Whales weighing more than 30 tons are able to soar in the water like birds.

. (In the case of several supports, weight is understood as the total force acting on all supports; however, for liquid and gaseous supports in the case of immersion of a body in them, an exception is often made, i.e. then the forces of the body acting on them are excluded from the weight and included in force Archimedes). The International System of Units (SI) unit of weight is newton, and the GHS unit dyne is sometimes used.

Weight P of a body at rest in an inertial frame of reference, coincides with the force of gravity acting on the body, and is proportional to the mass and acceleration of gravity at a given point:

The weight value (with a constant body mass) is proportional to the acceleration of gravity, which depends on the height above the Earth’s surface (or the surface of another planet, if the body is located near it, not the Earth, and the mass and size of this planet), and, due to the non-sphericity of the Earth, and also due to its rotation (see below), from the geographic coordinates of the measurement point. Another factor influencing the acceleration of gravity and, accordingly, the weight of a body are gravitational anomalies caused by the structural features of the earth's surface and subsoil in the vicinity of the measurement point.

When the system moves, the body - support (or suspension) relative to the inertial reference frame with acceleration, the weight ceases to coincide with the force of gravity:

However, a strict distinction between the concepts of weight and mass is accepted mainly in physics, and in many everyday situations the word “weight” continues to be used when in fact we are talking about “mass”. For example, we say that an object "weighs one kilogram" even though a kilogram is a unit of mass. In addition, the term “weight” in the meaning of “mass” is traditionally used in the cycle of human sciences - in the combination “weight of the human body”.

Notes

Determination of mass

The natural scientific meaning of this value is that it determines the amount of substance contained in the body. To denote it, 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, non-systemic ones are often used: gram and ton.

In a school physics course, the answer to the question: “What is mass?” given when studying the phenomenon of inertia. Then it is defined as the ability of a body to resist changes in the speed of its movement. Therefore, the mass is also called inert.

What is weight?

Firstly, this is force, that is, a vector. Mass is a scalar weight that is always attached to a support or suspension and is directed in the same direction as the force of gravity, that is, vertically downward.

The formula for calculating weight depends on whether the support (suspension) is moving. When the system is at rest, the following expression is used:

P = m * g, where P (in English sources the letter W is used) is the weight of the body, g is the acceleration of free fall. For the earth, g is usually taken equal to 9.8 m/s 2.

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

When moving downwards, 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 system.

That is, if 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 upward, we speak of 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?

Solution. 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 you take the spot as a cylinder. Then the volume formula will be:

V = π * 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 535036 tons.

Task No. 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 cm 2?

Solution. The density of copper is 8900 kg/m3. The volume is found using 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 10,000. After calculations, it turns out that the volume of the entire cable is approximately equal to 11,000 m 3.

Now you need to multiply the density and volume values to find out what the mass is equal to. The result is the number 97900000 kg.

Answer: the mass of copper is 97900 tons.

Another problem related to mass

Task No. 6. Condition: The largest candle, weighing 89867 kg, had a diameter of 2.59 m. What was its height?

Solution. Wax density is 700 kg/m3. The height will need to be found from That is, V needs to 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 m 3. The height was 24.38 m.

Answer: the height of the candle is 24.38 m.