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
The change in the internal energy of the ideal gas is determined as -28 J.
<h3>
Work done on the gas</h3>
The work done on the ideal gas is calculated as follows;
w = -PΔV
w = -1.5 x 10⁵(0.0006 - 0.0002)
w = -60 J
<h3>Change in the internal energy of the gas</h3>
ΔU = w + q
ΔU = -60J + 32 J
ΔU = -28 J
Thus, the change in the internal energy of the ideal gas is determined as -28 J.
Learn more about internal energy here: brainly.com/question/23876012
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Answer:
D.
Explanation:
P
The symbol for lead is Pb: it comes from the latin name for it, which is <em>plumbum</em><em>.</em>

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the product formed here in given reaction is :
The diesel engine has no ignition system. (C)
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This may be a big part of the reason that Diesel engines always
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