The tension in the wire is caused by the elastic collision between the balls and the magnitude of this tension is determined as 18.81 N.
The speed of the balls after the collision is determined by applying the principle of conservation of linear momentum as shown below.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
9.2(0) + 2.8(3.5) = 9.2v₁ + 2.8(v₂)
9.8 = 9.2v₁ + 2.8v₂ -----(1)
u₁ + v₁ = u₂ + v₂
0 + v₁ = 3.5 + v₂
v₂ = v₁ - 3.5 ---(2)
Substitute (2) into (1)
9.8 = 9.2v₁ + 2.8(v₁ - 3.5)
9.8 = 9.2v₁ + 2.8v₁ - 9.8
19.6 = 12v₁
v₁ = 19.6/12
v₁ = 1.63 m/s
v = √T/μ
v² = T/μ
T = v²μ
where;
μ is mass per unit length of the wire = 9.2/1.3 = 7.08 kg/m
T = (1.63²) x 7.08
T = 18.81 N
Thus, the tension in the wire just after collision is 18.81 N.
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