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4 November, 07:09

A 20.0 kg wood ball hangs from a 1.30 m - long wire. The maximum tension the wire can withstand without breaking is 600 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the largest speed this projectile can have without causing the cable to break?

Original Work:

m = 20 kg wood ball +.9 kg projectile = 20.9 kg

Ft max = 600 N

1.3 m radius

F = mAr = Ft - Fg

m (v^2) / r = Ft - Fg

v = sqrt ((r (Ft - Fg)) / m)

v = sqrt ((1.3m (600N - (20.9 kg) (9.81))) / 20.9 kg)

v = 4.96 m/s

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Answers (1)
  1. 4 November, 10:36
    0
    115 m/s

    Explanation:

    Momentum before = momentum after

    mu = (M + m) v

    u = (M + m) v / m

    u = (20.0 + 0.900) v / (0.900)

    u = 23.2 v

    Sum of the forces in the radial direction:

    ∑F = ma

    T - (M + m) g = (M + m) v² / r

    600 - (20.0 + 0.900) (9.8) = (20.0 + 0.900) v² / 1.30

    v = 4.96

    u = 23.2 (4.96)

    u = 115 m/s

    You correctly found the speed of the ball/projectile after the collision. You just have to use conservation of momentum to find the projectile's speed before the collision.
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