A small raft rests on the surface of the sea. There is a heavy swell that causes
ID: 2107011 • Letter: A
Question
A small raft rests on the surface of the sea. There is a heavy swell that causes the raft to rise and fall with a motion that is approximately simple harmonic with a displacement in meters by the expression given where t is time in seconds. There is a shipwrecked sailor on the raft who has a mass of 70kg.
Expression: y=1.5cos[(pi*t)/4]
What is the period of the oscillations in seconds?
What is the displacement in meters at t=1.8 seconds?
What is the displacement of the raft when the contact force between the sailor and the raft is at its min value?
What is the displacement of the raft and sailor in meters when the magnitude of the contact force between him and the raft is equal to his body weight?
Explanation / Answer
period of oscillation= (2*pi)/(pi/4)=8 s (pi/4 is the angular frequency)
disp. at t=1.8 s =1.5cos(pi*1.8/4)=0.234
The contanct force between the sailor and the raft is maximum at the highest position because the acceleration is acting downwards
disp.=+1.5
When the raft is in 0 acceleration the contact force will be equal to the body weight...
The raft has 0 acceleration at the central position of s.h.m ...
So disp=0
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