An elevator is rising up a vertical shaft in a skyscraper. Between the 12th and 20th floors, it travels at a constant speed. Dur
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Answer:
<em>A = 6.9 cm</em>
Explanation:
<u>Simple Harmonic Motion</u>
A mass-spring system is a common example of a simple harmonic motion device since it keeps oscillating when the spring is stretched back and forth.
If a mass m is attached to a spring of constant k and they are set to oscillate, the angular frequency of the motion is
The equation for the motion of the object is written as a sinusoid:
Where A is the amplitude.
The instantaneous speed is computed as the derivative of the distance
And the maximum speed is
Solving for the amplitude
Computing w
Calculating A
This is a classic example of conservation of energy. Assuming that there are no losses due to friction with air we'll proceed by saying that the total energy mus be conserved.
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
Solving for h gives us:
It doesn't depend on mass!
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
Solving for h gives us:
It doesn't depend on mass!