Question

In: Physics

A buoy bobs up and down, undergo- ing near simple harmonic motion. Which of the following...

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.

Solutions

Expert Solution

(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)


Related Solutions

Which of the following statements are correct? A. All oscillatory motion is Simple Harmonic Motion. B....
Which of the following statements are correct? A. All oscillatory motion is Simple Harmonic Motion. B. Simple Harmonic motion is a special case of oscillatory motion. C. Oscillatory motion is a special case of Simple Harmonic motion. D. Oscillatory motion cannot be Simple Harmonic motion Which of the following statements is correct? A. In simple harmonic motion, kinetic energy is constant. B. In simple harmonic motion, potential energy is constant. C. In simple harmonic motion, the sum of kinetic and...
Write a discussion and conclusion for simple harmonic motion.
Write a discussion and conclusion for simple harmonic motion.
particle is in simple harmonic motion along the x axis. The amplitude of the motion is...
particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = −1 2x1, the kinetic and potential energies are: A. K = 5 J and U = 3J B. K = 5 J and U...
A spring-mass system undergoes simple harmonic motion. Which of the following statements are True/False? The kinetic...
A spring-mass system undergoes simple harmonic motion. Which of the following statements are True/False? The kinetic energy is maximum at the point of zero displacement. (True or False) The potential energy is maximum at the point of maximum displacement. (True or False) The force exerted by the spring is zero at the point of maximum displacement. (True or False ) The acceleration is greatest at the point of zero displacement. (True or False ) If the amplitude of the oscillations...
A particle executes simple harmonic motion, such that at a given time, it is at ?A/3...
A particle executes simple harmonic motion, such that at a given time, it is at ?A/3 moving in towards equilibrium. 0.7seconds later, it is at x=0.9A moving towards equilibrium. Find the angular frequency of the particle, if it passes through equilibrium once between the two occurrences. Repeat the above, with the particle passing through equilibrium 5times between the two occurrences.
We have a simple harmonic motion that is described by the equation: ? (?) = 0.82cos...
We have a simple harmonic motion that is described by the equation: ? (?) = 0.82cos (0.4? + 0.2) Determine the equation of v (t) and a (t).
Find the solution of the following simple harmonic motion: . A 24-lb weight stretches a spring...
Find the solution of the following simple harmonic motion: . A 24-lb weight stretches a spring 8 ft. Initially the weight released from 2ft above equilibrium position with upward velocity 2 ft/sec. Find the equation of motion x(t).
An object attached to a spring vibrates with simple harmonic motion as described by the figure...
An object attached to a spring vibrates with simple harmonic motion as described by the figure below. (a) For this motion, find the amplitude.   (b) For this motion, find the period. (c) For this motion, find the angular frequency.  (d) For this motion, find the maximum speed  (e) For this motion, find the maximum acceleration.  (f) For this motion, find an equation for its position x in terms of a sine function. 
In simple harmonic motion, what happens to the velocity as the acceleration is maximum and vice...
In simple harmonic motion, what happens to the velocity as the acceleration is maximum and vice versa what happens to the acceleration as velocity is maximum. Explain in details on how you arrive at your conclusion.
A 323 g object is attached to a spring and executes simple harmonic motion with a...
A 323 g object is attached to a spring and executes simple harmonic motion with a period of 0.210 s. If the total energy of the system is 6.70 J. (a) Find the maximum speed of the object. m/s (b) Find the force constant of the spring. N/m (c) Find the amplitude of the motion. mA 323 g object is attached to a spring and executes simple harmonic motion with a period of 0.210 s. If the total energy of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT