Elastic Collision of a ball and wire

[Quincy]

Homework Statement

An 10.0 kg ball, hanging from the ceiling by a light wire 125 cm long, is struck in an elastic collision by a 1.20 kg ball moving horizontally at 7.50 m/s just before the collision. Find the tension in the wire just after the collision.

Homework Equations

M₁V_1o + M₂V_1o = M₁V_2f + M₂V_2f

The Attempt at a Solution

(1.2 kg)(7.5 m/s) = (10 kg)(Vf)

Vf = 0.9 m/s

Fc = mV^2/R = (10 kg)(0.9^2)/(1.25 m) = 6.48 N

Fc = T - mg
6.48 = T - (10 kg)(9.8)

T = 104.48 N -- Book says it's incorrect, what am i doing wrong?

 

[tiny-tim]

Hi Quincy!

An 10.0 kg ball, hanging from the ceiling by a light wire 125 cm long, is struck in an elastic collision by a 1.20 kg ball moving horizontally at 7.50 m/s just before the collision. Find the tension in the wire just after the collision.
…
why will the tension be different if the ball has a horizontal velocity?

Because although it has a purely horizontal velocity, it has a vertical acceleration.

Use F_total = ma. ​

 

[Quincy]

Hi Quincy!


Because although it has a purely horizontal velocity, it has a vertical acceleration.

Use F_total = ma. ​

I realized that right after i posted the problem :P, i edited it now but the answer's still incorrect.

 

[tiny-tim]

(1.2 kg)(7.5 m/s) = (10 kg)(Vf)

Nooo … you've ignored the momentum of the small ball after the collision.

Try again, using conservation of both momentum and energy. ​