Western Civilization is forever indebted to the people of ancient Greece and Rome. Among the numerous contributions these societies made are in the fields of art, literature and philosophy; however, perhaps their greatest gift to future generations was the modern perception of government. The contemporary idea of democracy, while borne out of the political struggles in the city of Athens, came to fruition in the Roman Republic, surviving, despite the constant interference of the emperor, through the Roman Empire. Although the present definition of democracy has changed considerably, one must still recognize its early evolution in that eternal city, Rome.
From Monarchy to Representation
The Roman Republic emerged out of what one historian called “the ashes of the monarchy.” Years underneath the unyielding yoke of a king taught the people of Rome that they had to safeguard against the rule, and possible oppression, of one individual. The real authority or imperium of the republic, and later empire, was to be divided among three basic elements - elected non-hereditary magistrates, a Senate to advise and consent, and popular assemblies. Unfortunately for many people in Rome, in the early stages of the Republic, power lay solely in the hands of the elite, the old landowning families or patricians. The remainder and largest share of the city’s population - the plebeians - had few if any rights. This unequal division of power would not last very long.
36/12= 3 3 IS THE AMOUT OF HALFLIVES
ONE HALF LIFE = 300
TWO HALF LIFE = 150
THREE HALF LIFE = 75
*Divide 600 three times
The magnitudes of the forces that the ropes must exert on the knot connecting are :
- F₁ = 118 N
- F₂ = 89.21 N
- F₃ = 57.28 N
<u>Given data :</u>
Mass ( M ) = 12 kg
∅₂ = 63°
∅₃ = 45°
<h3>Determine the magnitudes of the forces exerted by the ropes on the connecting knot</h3><h3 />
a) Force exerted by the first rope = weight of rope
∴ F₁ = mg
= 12 * 9.81 ≈ 118 kg
<u>b) Force exerted by the second rope </u>
applying equilibrium condition of force in the vertical direction
F₂ sin∅₂ + F₃ sin∅₃ - mg = 0 ---- ( 1 )
where: F₃ = ( F₂ cos∅₂ / cos∅₃ ) --- ( 2 ) applying equilibrium condition of force in the horizontal direction
Back to equation ( 1 )
F₂ = [ ( mg / cos∅₂ ) / tan∅₂ + tan∅₃ ]
= [ ( 118 / cos 63° ) / ( tan 63° + tan 45° ) ]
= 89.21 N
<u />
<u>C ) </u><u>Force </u><u>exerted by the</u><u> third rope </u>
Applying equation ( 2 )
F₃ = ( F₂ cos∅₂ / cos∅₃ )
= ( 89.21 * cos 63 / cos 45 )
= 57.28 N
Hence we can conclude that The magnitudes of the forces that the ropes must exert on the knot connecting are :
F₁ = 118 N, F₂ = 89.21 N, F₃ = 57.28 N
Learn more about static equilibrium : brainly.com/question/2952156
