Created it, 05/10/15
Update it, 05/10/31
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MATHEMATICAL FORMS “PHYSICAL” 2nd PART
Quantitatively to express the various sizes relating to the study of the physical phenomena, one has recourse to the measuring units of the international system.
Some of these units are certainly familiar for you such as the meter or the kilogram; others probably will be unknown for you because they are used here for the first time.
The most known units are represented by their symbol (m = meter, kg = kilogram, S = second…) ; the others are indicated with their symbol like with their name written in all letters between brackets.
FORMULATE 37 - Calculation the speed of a body knowing the length and the duration of the course (time).
Statement : The speed expressed in meters a second is equal to the relationship between the distance covered expressed in meters and the duration of the course expressed in seconds.
v = d / t
Example :
FORMULATE 38 - Calculation of the distance covered by a body knowing the speed and the duration of the course.
(This formula is drawn from formula 37).
FORMULATE 39 - Calculation of the time put by a body to traverse a distance given with a given speed.
(This formula is drawn from formula 37).
FORMULATE 40 - Calculation of the acceleration of a body knowing the variation speed and the time during which this variation is carried out.
Statement : The acceleration expressed in meters a second a second (or meters a second square) is equal to the relationship between the variation the speed expressed in meters a second and the time expressed in seconds.
If the variation is positive (increase in speed), there is a positive acceleration simply called acceleration; so on the other hand, the variation is negative (reduction speed), one has a negative acceleration called deceleration.
Generally, the values which express a deceleration are preceded by the sign - (less).
Examples :
a) positive acceleration:
b) negative acceleration:
FORMULATE 41 - Calculation of the acceleration of a body having a mass given and subjected to the action of a given constant force.
Statement : The acceleration expressed in meters a second a second (or meters a second square) is equal to the relationship between the force expressed in newtons and the mass expressed in kilograms.
FORMULATE 42 - Calculation of the constant force which acts on a body having a given mass and a given acceleration.
FORMULATE 43 - Calculation of the mass of a body moving subjected to the action of a given force and having a given acceleration.
(This formula is drawn from formula 41).
FORMULATE 44 - Calculation of the weight of a body having a given mass and being subjected to the action of terrestrial gravity
Statement : The weight, expressed in newtons, is equal to the product bulk expressed in kilograms by the value of terrestrial gravity. This one is worth approximately 9,81 m / s^{2}
FORMULATE 45 - Calculation of the specific mass of a body having a given mass and a given volume.
One more correctly uses the denomination “weight unit” and sometimes the denomination “density absolute” instead of that of specific mass.
Statement : The specific mass of a body, expressed in kilograms per cubic meter, is equal to the relationship between the mass expressed in kilograms and the volume expressed in cubic meters.
OBSERVATION :
Generally, the specific mass of the bodies is expressed in grams per cubic centimeter (g / cm^{3}) or in kilograms per cubic decimetre (kg / dm^{3}).
In table I (figure 8), the specific masses of some bodies are indicated. All the values are expressed in kilograms per cubic decimetre; the values relating to the solids and the liquids, other than gases and of mercury, are those corresponding to the ambient temperature of 15 °C; those of gases and mercury are on the other hand those which correspond to the temperature of 0 °C.
FORMULATE 46 - Calculation of the volume of a body knowing its mass and its specific mass.
(This formula is drawn from formula 45).
FORMULATE 47 - Calculation of the mass of a body knowing its specific mass and its volume.
(This formula is drawn from formula 45).
FORMULATE 48 - Calculation of the specific heat of a body knowing its mass and the quantity of heat which it is necessary to provide to this body to obtain an increase in given temperature.
Statement : The specific heat, expressed in kilogram calories per kilogram per degree Celsius, is equal to the relationship between the quantity of heat expressed in kilogram calories and the product bulk expressed in kilograms by the increase in temperature expressed in degree Celsius.
In table II (figure 9) the specific heats of some bodies are indicated. All the values are expressed in kilogram calories per kilogram per degree Celsius (kcal / kg . °C) and is practically regarded as constants for temperatures ranging between 0 °C and 100 °C unless otherwise specified.
FORMULATE 49 - Calculation of the quantity of heat which must be provided to a body of specific heat and mass known to obtain an increase given in temperature.
(This formula is drawn from formula 48).
FORMULATE 50 - Calculation of the increase in temperature of a body to which one yields a given quantity of heat knowing the mass and the specific heat of the body (in calculation, one does not take into account the possible losses of heat which can occur at the time of the contribution of heat).
FORMULATE 51 - Calculation of the value of a temperature in degree Fahrenheit (measuring unit of the English system) knowing the value of this temperature in degree Celsius.
FORMULATE 52 - Calculation of the value of a temperature in degree Celsius knowing the value of this temperature in degree Fahrenheit (measuring unit of the English system).
FORMULATE 53 - Calculation of the value of a temperature in Kelvin (measuring unit of the absolute temperature) knowing the value of this temperature in degree Celsius.
Tk tc + 273,16
FORMULATE 54 - Calculation of the value of a temperature in degree Celsius knowing the value of this temperature in Kelvin.
FORMULATE 55 - Calculation of mechanical work relating to a body which moves under the action of a force directed in the direction of displacement.
Statement : The mechanical work, expressed in joules, is equal to the product of the force expressed in newtons by the length of the displacement of the force expressed in meters.
FORMULATE 56 - Calculation of the kinetic energy of a body moving knowing its mass and its speed at the moment considered.
Statement : The kinetic energy, expressed in joules, is equal to the semi-finished product of the mass expressed in kilograms by the square the speed expressed in meters a second.
Kinetic energy : Ec = (1 / 2) x 0,25 x 7,5^{2} = 7,03 J
FORMULATE 57 - Calculation of the consumption knowing the quantity of energy absorptive for a given length of time.
Statement: The power, expressed in Watts, is equal to the relationship between the quantity of absorptive energy, expressed in joules, and the time expressed in seconds.
P = W / t
FORMULATE 58 - Calculation of absorptive energy knowing the consumption and the duration of consumption.
(This formula is drawn from formula 57).
Absorptive energy : W = 1 500 x 3 600 = 5 400 000 J
FORMULATE 59 - Calculation of the quantity of heat (thermal energy) correspondent with a given mechanical work (mechanical energy).
Statement : Quantity of heat (expressed in kilogram calories) obtained by the total thermal transformation of mechanical work roughly equal to the product of this work (expressed in joules) by number 0,000238.
OBSERVATION :
Number 0,000238 is not a fixed coefficient.
Indeed, it indicates how much kilogram calories one can obtain from a mechanical work (i.e. of corresponding energy) expressed in joules. This number thus depends on the measuring unit chosen for the mechanical energy; by using the calorie instead of the kilogram calorie, one must replace number 0,000238 by number 0,238.
FORMULATE 60 - Calculation of mechanical work (mechanical energy) correspondent with a quantity of heat given (thermal energy).
Statement : Mechanical work (expressed in joules) correspondent with a quantity of heat given (expressed in kilogram calories) is roughly equal to the product of the quantity of heat by number 4 200.
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