In: Physics
A buoy bobs up and down, undergo- ing near simple harmonic motion. Which of the following statements are true about the buoy?
(a) The buoyancy force is a maximum when the buoy moves the
fastest.
(b) The buoyancy force is always a maximum when the
displacement of the buoy from equilibrium is greatest.
(c) The acceleration of the buoy is maximum when it’s speed is
zero.
(d) The acceleration of the buoy is zero when it’s speed is
zero.
(e) The time it takes the buoy’s velocity to go from a minimum to
maximum is the same amount of time it takes it’s acceleration to go
from a minimum to a maximum.
(a) FALSE.
The buoy moves the fastest when it is at equilibrium position. But the buoyancy force is maximum when the most amount of water is displaced by the buoy(archimedes principle). That happens when it is submerged to the maximum extent.
(b) TRUE
When the displacement of the buoy is maximum in the DOWNWARD direction, the buoy is submerged to its fullest extent. At this point, the buoyancy force is maximum.
(c) TRUE
In simple harmonic motion, the acceleration is maximum at the farthest displacement, at the point where the direction of motion changes. At this point, its speed is zero ( since the direction of motion is changing, the particle is momentarily at rest).
(d) FALSE
The acceleration of the buoy is maximum when the speed is zero, as explained in answer (c)
(e) TRUE
At the equilibrium position : speed is maximum, acceleration is minimum
At the maximum displacement position : speed is minimum, acceleration is maximum.
Time taken to go from equilibrium to maximum displacement is same as time taken to go from maximum diaplacement to equilibrium and is equal to T/4 (T being the time period of oscillation)