A simple harmonic transverse wave is propagating along a string towards the left direction as shown in the figure. figure shows
1 answer:
Answer:
- Amplitude = 5 cm (Heights)
- Wavelength (λ) = 40 cm
- Wave speed (v) = 12 m/s (Approx)
- Time period (T) = 0.033 s (Approx)
- Maximum particle speed (V) = 9.43 m/s
Explanation:
1) Amplitude
Amplitude = 5 cm (Heights)
2) Wavelength (λ)
Wavelength (λ) = 40 cm
3) Wave speed
Wave speed (v) = √ t / μ
Wave speed (v) = √ 3.6 / [25x10⁻³]
Wave speed (v) = 12 m/s (Approx)
4) Time period (T)
Time period (T) = 1/f = (λ)/v
Time period (T) = 0.40m / 12
Time period (T) = 0.033 s (Approx)
5) Maximum particle speed (V)
Maximum particle speed (V) = Aw
Maximum particle speed (V) = [0.05x2x3.14] / 0.033
Maximum particle speed (V) = 9.43 m/s
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Answer: The force constant k is 10600 kg/s^2
Step by step:
Use the law of energy conservation. When the elevator hits the spring, it has a certain kinetic and a potential energy. When the elevator reaches the point of still stand the kinetic and potential energies have been transformed to work performed by the elevator in the form of friction (brake clamp) and loading the spring.
Let us define the vertical height axis as having two points: h=2m at the point of elevator hitting the spring, and h=0m at the point of stopping.
The total energy at the point h=2m is:
The total energy at the point h=0m is:
The two Energy values are to be equal (by law of energy conservation), which allows us to determine the only unknown, namely the force constant k: