When you stretch a spring 13 cm past its natural length, it exerts a force of 21 N. What is the spring constant of this spring?
2 answers:
Answer:
Explanation:
From Hooke's law,
Substistuting the values, you can ignore the minus sign, since it is there to state that the force is always in the opposite direction of the deformation, and has no influence otherwise, and your constant is
Answer:
Spring constant, k = 161.5 N-m
Explanation:
It is given that,
Force on spring, F = 21 N
The spring is stretched 13 cm past its natural length i.e. x = 0.13 m
The Hooke's law gives the relationship between the force and the compression in the spring. Mathematically, it can be written as :
k is spring constant
-ve sign shows the direction of force is opposite
So,
k = 161.5 N-m
Hence, this is the required solution.
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(a)
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k is the wave number
is the angular frequency
t is the time
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A = 3.0 mm = 0.003 m is the amplitude
is the wave number
is the period, so the angular frequency is
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(b) 0.094 m/s
For a transverse wave, the transverse speed is equal to the derivative of the displacement of the wave, so in this case:
So the maximum transverse wave occurs when the cosine term is equal to 1, therefore the maximum transverse speed must be
where
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(c) 5.24 mm/s
The wave speed is given by
where
f is the frequency of the wave
is the wavelength
The frequency can be found from the angular frequency:
While the wavelength can be found from the wave number:
Therefore, the wave speed is