A hovercraft floats, with negligible friction, on a cushion of air slightly abov
ID: 1480837 • Letter: A
Question
A hovercraft floats, with negligible friction, on a cushion of air slightly above a smooth floor. The hovercraft is a disk with radius R=2 m and mass M=200 kg. A m=50 kg person runs toward the edge of the hovercraft at a speed of 8 m/s, then jumps on board at the hovercraft edge. Her twin of mass m also is stationed on the opposite side of the hovercraft as shown below.
A) Describe the subsequent motion using and justifying any conservation laws.
TOP VIEW OF HOVERCRAFT Person 1: mass m, Initial speed vo Hovercraft: Mass M, radius R Person 2: mass mExplanation / Answer
a) let w is the final angular velocity.
Apply conservation of angular momentum
initial angular momentum = final angular momentum
m*v*R = (I_disk + I_persons)*w
m*v*R = (0.5*M*R^2 + 2*m*R^2)*w
w = m*v*R/(0.5*M*R^2 + 2*m*R^2)
= 50*8*2/(0.5*200*2^2 + 2*50*2^2)
= 1 rad/s
b) K_before = 0.5*m*v^2
= 0.5*50*8^2
= 3200 J
K_after = 0.5*I*w^2'
= 0.5*(0.5*M*R^2 + 2*m*R^2)*w^2
= 0.5*(0.5*200*2^2 + 2*50*2^2)*1^2
= 400 J
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