Answer:
Explanation:
Velocity of the ship is given as
the direction of the velocity of the ship is making an angle of 11 degree with the current
so we will have two components of the velocity
1) along the direction of the current
2) perpendicular to the direction of the current
so here we know that the component of the ship velocity along the direction of the current is given as
(a) 3.5 Hz
The angular frequency in a spring-mass system is given by
where
k is the spring constant
m is the mass
Here in this problem we have
k = 160 N/m
m = 0.340 kg
So the angular frequency is
And the frequency of the motion instead is given by:
(b) 0.021 m
The block is oscillating up and down together with the upper end of the spring. The block will lose contact with the spring when the direction of motion of the spring changes: this occurs when the spring is at maximum displacement, so at
x = A
where A is the amplitude of the motion.
The maximum displacement is given by Hook's law:
where
F is the force applied initially to the spring, so it is equal to the weight of the block:
k = 160 N/m is the spring constant
Solving for A, we find