Pressure is proportional to kinetic energy per unit volume, while temperature is proportional to kinetic energy per particle. ... A gas can be at high temperature and low pressure if it has low number density; likewise, a gas can be at low temperature and high pressure if it has high number density.
The formula for resonant frequency is:
![f_0=\frac{1}{2\pi\sqrt{LC} }](https://tex.z-dn.net/?f=f_0%3D%5Cfrac%7B1%7D%7B2%5Cpi%5Csqrt%7BLC%7D%20%7D)
Given information:
![f_{0\text{,small}}=500 \text{ kHz}\\f_{0\text{,large}}=1650 \text{ kHz}\\L=3.83\text{ } \mu \text{H}](https://tex.z-dn.net/?f=f_%7B0%5Ctext%7B%2Csmall%7D%7D%3D500%20%5Ctext%7B%20kHz%7D%5C%5Cf_%7B0%5Ctext%7B%2Clarge%7D%7D%3D1650%20%5Ctext%7B%20kHz%7D%5C%5CL%3D3.83%5Ctext%7B%20%7D%20%5Cmu%20%5Ctext%7BH%7D)
Plug in the given values to find one value of capacitance:
![500 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.645*10^{-8} \text{ F}=26.45 \text{ nF}](https://tex.z-dn.net/?f=500%20%5Ctext%7B%20kHz%7D%3D%5Cfrac%7B1%7D%7B2%5Cpi%5Csqrt%7BC%283.83%5Ctext%7B%20%7D%20%5Cmu%20%5Ctext%7BH%7D%29%7D%20%7D%5C%5CC%3D2.645%2A10%5E%7B-8%7D%20%5Ctext%7B%20F%7D%3D26.45%20%5Ctext%7B%20nF%7D)
Plug in the given values to find the other value of capacitance:
![1650 \text{ kHz}=\frac{1}{2\pi\sqrt{C(3.83\text{ } \mu \text{H})} }\\C=2.429*10^{-8} \text{ F}=2.429 \text{ nF}](https://tex.z-dn.net/?f=1650%20%5Ctext%7B%20kHz%7D%3D%5Cfrac%7B1%7D%7B2%5Cpi%5Csqrt%7BC%283.83%5Ctext%7B%20%7D%20%5Cmu%20%5Ctext%7BH%7D%29%7D%20%7D%5C%5CC%3D2.429%2A10%5E%7B-8%7D%20%5Ctext%7B%20F%7D%3D2.429%20%5Ctext%7B%20nF%7D)
This gives a range of 2.429 nF to 26.45 nF.
With significant figures taken into account, the range of capacitance is 2.43 nF to 30 nF.
Use kinematic equation:
vf² = vo² + 2g(xf - xo)
vf = final velocity = 10 m/s
vo = initial velocity = 0 m/s (i.e. at rest)
g = 9.81 m/s²
xf - xo = distance traveled = d
*rearrange equation to solve for d
(vf² - vo²)/(2g) = d
d = ((10 m/s)² - (0 m/s)²)/(2*9.81 m/s²)
d = (100 m²/s²)/(2*9.81 m/s²)
d = 5.097 m