During a medieval siege of a castle, the attacking army uses a trebuchet to hurl

Question

During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. If the trebuchet launches the stones with a velocity of +27.0 m/s at an angle of 56.0 degree find the following a) What is the maximum height of the launched stones? b) How long will the stones be in the air? c) What is the range (horizontal distance) that the stone will travel? d) A 85.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 15.0 m) and spun at a constant angular velocity of 13.2 rpm. Answer the following, show all work a. What is the angular velocity of the centrifuge in rad/s? b. What is the linear velocity of the astronaut at the outer edge of the centrifuge? c. What is the centripetal acceleration of the astronaut at the end of the centrifuge? d How many g's does the astronaut experience? e What is the centripetal force experienced by the astronaut? Give magnitude and direction f. Explain how and when the astronaut would experience a torque in this situation.

Explanation / Answer

1 a) hmax = u^2si^2theta/2g = 27^2sin^256/2*9.8

h max = 25.56 m

b) T = 2usin56/g = 2*27*sin56/9.8 = 4.57 sec

c) ranmge = 27cos56*T = 68.9 m

2 a) w = 13.2 rpm = 13.2*2*3.14/60 = 1.382 rad/sec

b) v = rw = 15*1.382 = 20.7 m/s

c) a = v^2/r = 28.63 m/s^2

d) a = 28.63/9.8 = 2.92 g

e) f = ma = 85*28.63 = 2433.6 N

f) T = r*f = 15*2433.6 = 3.65*10^4 Nm out wards

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