Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
A fundamental frequency of 60 Hz, attached mass of 1 kg., rod length of
0.3 m gives the mass of the part of the string as 3.245 × 10⁻³ kg.
Response:
- The mass of the string, m ≈ 3.245 × 10⁻³ kg
How can the mass of the part of the string be calculated?
The given parameters are;
Mass of the sphere, M = 1.00 kg
Length of the rod, L = 0.300 m
Angle the string makes with the rod, θ = 35°
The fundamental frequency of the standing wave in the portion of the
string above the rod, f₁ = 60.0 Hz
Required;
The mass of the portion of the string above the rod
Solution:
The fundamental frequency in a string is given as follows;
- [tex]f_1 = \mathbf{\dfrac{\sqrt{\dfrac{T}{m/l} } }{2 \cdot l}}[/tex]
Where;
T = The tension in the string
m = The mass of the string
l = The length of the string
- [tex]The \ tension \ in \ the \ string, \ T= \mathbf{\dfrac{M \cdot g}{sin(\theta)}}[/tex]
Which gives;
[tex]T= \mathbf{\dfrac{1 \times 9.81}{sin(35)}} \approx 17.1[/tex]
The tension in the string, T ≈ 17.1 N
- [tex]The \ length \ of \ the \ string, \ l=\mathbf{\dfrac{L}{cos(\theta)}}[/tex]
Therefore;
[tex]l=\dfrac{0.300}{cos \left(35^{\circ} \right)} \approx 0.366[/tex]
Therefore;
[tex]60.0 = \mathbf{\dfrac{\sqrt{\dfrac{17.1}{m/0.366} } }{2 \times 0.366}}[/tex]
Which gives;
[tex]m = \dfrac{17.1}{(60.0 \times 2 \times 0.366)^2} \times 0.366 \approx 3.245 \times 10^{-3}[/tex]
- The mass of the string, m ≈ 3.245 × 10⁻³ kg
Learn more about the fundamental frequency of an material here:
https://brainly.com/question/3776467
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.