(a) The velocity of the first ball before the collision with the second ball is 11.18 m/s.
(b) The final velocity of the two balls after the collision is determined as 5.59 m/s.
<h3>
Speed of the block when pushed by the spring</h3>
The speed of the block when pushed by the spring is calculated as follows;
K.E = Ux
¹/₂mv² = ¹/₂kx²
mv² = kx²
v² = kx²/m
v² = (25 x 0.5²)/0.05
v² = 125
v = 11.18 m/s
<h3>Final velocity of the two balls after the collision</h3>
The velocity of the two balls after the collision is calculated as follows;
Pi = Pf
where;
- Pi is initial momentum
- Pf is final momentum
m1u1 + m2u2 = v(m1 + m2)
0.05(11.18) + 0.05(0) = v(0.05 + 0.05)
0.559 = 0.1v
v = 5.59 m/s
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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
That would be C .............
<h3>Answer : </h3><h3 /><h3>A ) The larger gear can be moved by applying a relatively small force on the smaller gear.</h3>
<h3>B )
The force applied on the smaller gear is transmitted without any loss to the larger gear .</h3><h3 /><h3>
C ) the direction of motion can be changed without changing the direction of the applied force .</h3>
D ) the system would continue to move without any further, after and initial force has set in motion.