Answer:
1) Hence, the period is 0.33 s.
2) The amplitude is 10 cm.
Explanation:
1) The period is given by:
![T = \frac{1}{f}](https://tex.z-dn.net/?f=%20T%20%3D%20%5Cfrac%7B1%7D%7Bf%7D%20)
Where:
f: is the frequency = 3 bob up and down each second = 3 s⁻¹ = 3 Hz
Hence, the period is 0.33 s.
2) The amplitude is the distance between the equilibrium position and the maximum position traveled by the spring. Since the spring is moving up and down over a distance of 20 cm, then the amplitude is:
Therefore, the amplitude is 10 cm.
I hope it helps you!
Answer:
yes
Explanation:
its not a good thing for the rest of your life but you have a PS4
Answer:
![d=1.84\ mm](https://tex.z-dn.net/?f=d%3D1.84%5C%20mm)
Explanation:
<u>Capacitance</u>
A two parallel-plate capacitor has a capacitance of
![\displaystyle C=\frac{\epsilon_o A}{d}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20C%3D%5Cfrac%7B%5Cepsilon_o%20A%7D%7Bd%7D)
where
![\epsilon_o=8.85\cdot 10^{-12}\ F/m](https://tex.z-dn.net/?f=%5Cepsilon_o%3D8.85%5Ccdot%2010%5E%7B-12%7D%5C%20F%2Fm)
A = area of the plates = ![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
d = separation of the plates
![\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%7B%5Cepsilon_o%20A%7D%7BC%7D%3D%5Cfrac%7B%5Cepsilon_o%20%5Cpi%20r%5E2%7D%7BC%7D)
We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by
![\displaystyle X_c=\frac{1}{wC}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_c%3D%5Cfrac%7B1%7D%7BwC%7D)
where w is the angular frequency
![w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s](https://tex.z-dn.net/?f=w%3D2%5Cpi%20f%3D2%5Cpi%20%5Ccdot%2036000%3D226194.67%5C%20rad%2Fs)
Solving for C
![\displaystyle C=\frac{1}{wX_c}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20C%3D%5Cfrac%7B1%7D%7BwX_c%7D)
The reactance can be found knowing the total impedance of the circuit:
![Z^2=R^2+X_c^2](https://tex.z-dn.net/?f=Z%5E2%3DR%5E2%2BX_c%5E2)
Where R is the resistance,
. Solving for Xc
![X_c^2=Z^2-R^2](https://tex.z-dn.net/?f=X_c%5E2%3DZ%5E2-R%5E2)
The magnitude of the impedance is computed as the ratio of the rms voltage and rms current
![\displaystyle Z=\frac{V}{I}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z%3D%5Cfrac%7BV%7D%7BI%7D)
The rms current is the peak current Ip divided by
, thus
![\displaystyle Z=\frac{\sqrt{2}V}{I_p}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z%3D%5Cfrac%7B%5Csqrt%7B2%7DV%7D%7BI_p%7D)
![I_p=0.65\ mA/1000=0.00065\ A](https://tex.z-dn.net/?f=I_p%3D0.65%5C%20mA%2F1000%3D0.00065%5C%20A)
Now collect formulas
![\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_c%5E2%3DZ%5E2-R%5E2%3D%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7DV%7D%7BI_p%7D%5Cright%29%5E2-R%5E2)
Or, equivalently
![\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_c%3D%5Csqrt%7B%5Cfrac%7B2V%5E2%7D%7BI_p%5E2%7D-R%5E2%7D)
![\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_c%3D%5Csqrt%7B%5Cfrac%7B2%5Ccdot%2018%5E2%7D%7B0.00065%5E2%7D-15000%5E2%7D)
![X_c=36176.34\ \Omega](https://tex.z-dn.net/?f=X_c%3D36176.34%5C%20%5COmega)
The capacitance is now
![\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F](https://tex.z-dn.net/?f=%5Cdisplaystyle%20C%3D%5Cfrac%7B1%7D%7B226194.67%5Ccdot%2036176.34%7D%3D1.22%5Ccdot%2010%5E%7B-10%7D%5C%20F)
The radius of the plates is
![r=18\ cm/2=9 \ cm = 0.09 \ m](https://tex.z-dn.net/?f=r%3D18%5C%20cm%2F2%3D9%20%5C%20cm%20%3D%200.09%20%5C%20m)
The separation between the plates is
![\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%7B8.85%5Ccdot%2010%5E%7B-12%7D%20%5Ccdot%20%5Cpi%5Ccdot%200.09%5E2%7D%7B1.22%5Ccdot%2010%5E%7B-10%7D%7D)
![d=0.00184\ m](https://tex.z-dn.net/?f=d%3D0.00184%5C%20m)
![\boxed{d=1.84\ mm}](https://tex.z-dn.net/?f=%5Cboxed%7Bd%3D1.84%5C%20mm%7D)
Answer:
yes
Explanation:
All parts of the body (muscles, brain, heart, and liver) need energy to work. This energy comes from the food we eat. Our bodies digest the food we eat by mixing it with fluids (acids and enzymes) in the stomach.