An 960 kg ball hanging from the ceiling by a light wire 115

An 9.60 kg ball, hanging from the ceiling by a light wire 115 cm long, is struck in an elastic collision by a 2.40 kg ball moving horizontally at 5.50 m/s just before the collision. Find the tension in the wire just after the collision.

Solution

Here,

mass , m1 = 9.6 kg

length of wire , L = 115 cm = 1.15 m

m2 = 2.4 Kg

u1 = 5.5 m/s

let the final velocities are v1 , v2

Using conservation of momentum

2.4 * 5.5 = 2.4 * v1 + 9.6 v2 ----(1)

as the collision is elastic

v2 - v1 = 5.5

solving 1 and 2

v1 = -3.3 m/s

v2 = 2.2 m/s

tension in the wire = m1 * (g + v2^2/L)

tension in the wire = 9.6 * (9.8 + 2.2^2/1.15)
tension in the wire = 134.5 N

the tension in the wire is 134.5 N