a certain machine changes a large input force into a smaller output force. how will the machine affect the distance over which t
1 answer:
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Answer:
2 seconds
Explanation:
The frequency of a wave is related to its wavelength and speed by the equation
where
f is the frequency
v is the speed of the wave
is the wavelength
For the wave in this problem,
v = 2 m/s
So the frequency is
The period of a wave is equal to the reciprocal of the frequency, so for this wave:
This means that the wave takes 4 seconds to complete one full cycle.
Therefore, the time taken for the wave to go from a point with displacement +A to a point with displacement -A is half the period, therefore for this wave:
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
. So we can write
that we can solve to find an expression for v:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
that we can solve to find an expression for v: