A 400 g bird, flying horizontally at 3.50 m/s, suddenly collides with a stationa

Question

A 400 g bird, flying horizontally at 3.50 m/s, suddenly collides with a stationary vertical bar, hitting it 25.0 cm below the top (see figure). The bar is uniform, 85.0 cm long, has a mass of 2.50 kg, and is hinged at its base. The collision stuns the bird so that it just stops and does NOT stick to the bar. (a) Find the magnitude of the angular momentum of the bird about the hinge just before the collision. (b) Find the angular speed of the bar just after it is hit by the bird (c) Find the angular speed just as the bar hits the ground? [Hint: The interaction between the bird and the bar is so quick you can ignore gravity for the collision, but NOT for what happens to the bar after. Also the collision is NEITHER elastic NOR completely inelastic]

Explanation / Answer

A)

angular momentum of the bird ,

L = mvr

L = 0.400 * 3.50 * (0.85 - 0.25)

L = 0.84 Kg.m^2/s

B)

now, as the angular momentum of bird - bar system is conserved during collision

I*w = L

2.5 * 0.85^2 /3 * w = 0.84

w = 1.4 rad/s

the angular speed of bar after collision is 1.4 rad/s

C)

Now, using conservation of energy ,

0.5 * 2.5 * 0.85^2 /3 * w^2 = 2.5 * 0.85^2 /3 * 0.5 * 1.4^2 + 0.5 * 2.50 * 9.8 * 0.85

solving for w

w = 6.05 rad/s

the angular speed of rod before hitting ground is 6.05 rad/s

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