Answer:
259 Hz or 269 Hz
Explanation:
Beat: This is the phenomenon obtained when two notes of nearly equal frequency are sounded together. The S.I unit of beat is Hertz (Hz).
From the question,
Beat = f₂-f₁................ Equation 1
Note: The frequency of the other instrument is either f₁ or f₂.
If the unknown instrument's frequency is f₁,
Then,
f₁ = f₂-beat............ equation 2
Given: f₂ = 264 Hz, Beat = 5 Hz
Substitute into equation 2
f₁ = 264-5
f₁ = 259 Hz.
But if the unknown frequency is f₂,
Then,
f₂ = f₁+Beat................. Equation 3
f₂ = 264+5
f₂ = 269 Hz.
Hence the beat could be 259 Hz or 269 Hz
Steel paper clip because it can be moved by the magnet and it is lighter than the iron nail
Moving fan has rotational kinetic energy
Non moving fan has no energy since it is in rest
Answer:
The answer is given below
Explanation:
u is the initial velocity, v is the final velocity. Given that:
![m_1=0.6kg,u_1=-5m/s(moving \ west),m_2=0.8kg,u_2=2m/s,k=1200N/m](https://tex.z-dn.net/?f=m_1%3D0.6kg%2Cu_1%3D-5m%2Fs%28moving%20%5C%20west%29%2Cm_2%3D0.8kg%2Cu_2%3D2m%2Fs%2Ck%3D1200N%2Fm)
a)
The final velocity of cart 1 after collision is given as:
![v_1=(\frac{m_1-m_2}{m_1+m_2})u_1+\frac{2m_2}{m_1+m_2}u_2\\ Substituting:\\v_1=\frac{0.6-0.8}{0.6+0.8} (-5)+\frac{2*0.8}{0.6+0.8}(2)= 5/7+16/7=3\ m/s](https://tex.z-dn.net/?f=v_1%3D%28%5Cfrac%7Bm_1-m_2%7D%7Bm_1%2Bm_2%7D%29u_1%2B%5Cfrac%7B2m_2%7D%7Bm_1%2Bm_2%7Du_2%5C%5C%20%20Substituting%3A%5C%5Cv_1%3D%5Cfrac%7B0.6-0.8%7D%7B0.6%2B0.8%7D%20%28-5%29%2B%5Cfrac%7B2%2A0.8%7D%7B0.6%2B0.8%7D%282%29%3D%205%2F7%2B16%2F7%3D3%5C%20m%2Fs)
The final velocity of cart 2 after collision is given as:
![v_2=(\frac{m_2-m_1}{m_1+m_2})u_2+\frac{2m_1}{m_1+m_2}u_1\\ Substituting:\\v_1=\frac{0.8-0.6}{0.6+0.8} (2)+\frac{2*0.6}{0.6+0.8}(-5)= 2/7-30/7=-4\ m/s](https://tex.z-dn.net/?f=v_2%3D%28%5Cfrac%7Bm_2-m_1%7D%7Bm_1%2Bm_2%7D%29u_2%2B%5Cfrac%7B2m_1%7D%7Bm_1%2Bm_2%7Du_1%5C%5C%20%20Substituting%3A%5C%5Cv_1%3D%5Cfrac%7B0.8-0.6%7D%7B0.6%2B0.8%7D%20%282%29%2B%5Cfrac%7B2%2A0.6%7D%7B0.6%2B0.8%7D%28-5%29%3D%202%2F7-30%2F7%3D-4%5C%20m%2Fs)
b) Using the law of conservation of energy:
![\frac{1}{2}m_1u_1+ \frac{1}{2}m_2u_2=\frac{1}{2}m_1v_1+\frac{1}{2}m_2v_2+\frac{1}{2}kx^2\\x=\sqrt{\frac{m_1u_1+m_2u_2-m_1v_1-m_2v_2}{k}}\\ Substituting\ gives:\\x=\sqrt{\frac{0.6*(-5)^2+0.8*2^2-(0.6*3^2)-(0.8*(-4)^2)}{1200}}=\sqrt{0}=0\ cm](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm_1u_1%2B%20%5Cfrac%7B1%7D%7B2%7Dm_2u_2%3D%5Cfrac%7B1%7D%7B2%7Dm_1v_1%2B%5Cfrac%7B1%7D%7B2%7Dm_2v_2%2B%5Cfrac%7B1%7D%7B2%7Dkx%5E2%5C%5Cx%3D%5Csqrt%7B%5Cfrac%7Bm_1u_1%2Bm_2u_2-m_1v_1-m_2v_2%7D%7Bk%7D%7D%5C%5C%20Substituting%5C%20gives%3A%5C%5Cx%3D%5Csqrt%7B%5Cfrac%7B0.6%2A%28-5%29%5E2%2B0.8%2A2%5E2-%280.6%2A3%5E2%29-%280.8%2A%28-4%29%5E2%29%7D%7B1200%7D%7D%3D%5Csqrt%7B0%7D%3D0%5C%20cm)
Option(a) the mass of cart 2 is twice that of the mass of cart 1 is the right answer.
The mass of cart 2 is twice that of the mass of cart 1 is correct about the mass of cart 2.
Let's demonstrate the issue using variables:
Let,
m1=mass of cart 1
m2=mass of cart 2
v1 = velocity of cart 1 before collision
v2 = velocity of cart 2 before collision
v' = velocity of the carts after collision
Using the conservation of momentum for perfectly inelastic collisions:
m1v1 + m2v2 = (m1 + m2)v'
v2 = 0 because it is stationary
v' = 1/3*v1
m1v1 = (m1+m2)(1/3)(v1)
m1 = 1/3*m1 + 1/3*m2
1/3*m2 = m1 - 1/3*m1
1/3*m2 = 2/3*m1
m2 = 2m1
From this we can conclude that the mass of cart 2 is twice that of the mass of cart 1.
To learn more about inelastic collision visit:
brainly.com/question/14521843
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