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2 years ago

You hang a light in front of your house using an

Physics

1 answer:

Kaylis [27]2 years ago

6 0

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

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