Question

4.<100> A troll is attempting to break down the gates of Minas Tirith with a fallen tree of 5680 kg. However, trolls are not too bright and don’t understand basic physics. It swings the tree at the gate like a club with a downward motion. The door is struck with an initial velocity of 27 m/s at an angle that is 64o below the horizontal. The tree then decelerates in 0.08 seconds after impact. The wooden brace holding the door shut on the inside will buckle if the net horizontal force applied to door is greater than 810,000N.

a) <20> What is horizontal velocity of the tree just before impacting the door?

b) <20> What is the horizontal deceleration of the tree as it impacts the door?

c) <20> What is the horizontal force of impact on the door?

d) <40> Soldiers on the inside of the door can help brace the door to keep it from breaking open. If each soldier can push on the door with a force 850N, how many soldiers are needed to keep the hordes of Mordor at bay?

Answer 1

a)

Ux = 27cos64 = 11.84 m/s

b)

ax = Ux/t = 11.84 / 0.08 = 148 m/s^2

c)

Fx = m ax = 5680 x 148 = 840357 N

d)

840357 - 810000 = 30357 N

n = 30357/850 = 35.7

= 36 soldiers atleast

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