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
Answer:
volume of water is 1066.50 acre feet
Explanation:
given data
dia = 2 in = 0.166 feet
area = 26 km² = 26 × 247.105 acre = 6424.73 acre
to find out
volume of water
solution
we know volume of water is express as
volume = area × dia ....................1
put here value in equation 1
volume = 6424.73 acre × 0.166 feet
volume = 1066.50
so volume of water is 1066.50 acre feet
Answer:
1.25 kgm²/sec
Explanation:
Disk inertia, Jd =
Jd = 1/2 * 3.7 * 0.40² = 0.2960 kgm²
Disk angular speed =
ωd = 0.1047 * 30 = 3.1416 rad/sec
Hollow cylinder inertia =
Jc = 3.7 * 0.40² = 0.592 kgm²
Initial Kinetic Energy of the disk
Ekd = 1/2 * Jd * ωd²
Ekd = 0.148 * 9.87
Ekd = 1.4607 joule
Ekd = (Jc + 1/2*Jd) * ω²
Final angular speed =
ω² = Ekd/(Jc+1/2*Jd)
ω² = 1.4607/(0.592+0.148)
ω² = 1.4607/0.74
ω² = 1.974
ω = √1.974
ω = 1.405 rad/sec
Final angular momentum =
L = (Jd+Jc) * ω
L = 0.888 * 1.405
L = 1.25 kgm²/sec
Well, those are good ones. Now how about a <u><em>thermometer</em></u> to <em>measure the temperature</em> ?
Answer:
False
Explanation:
Please see the attached file