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3 years ago

All the formulas for Friction

Physics

1 answer:

notka56 [123]3 years ago

6 0

Answer:

f = \mu N

Explanation:

Newton’s 2nd Law

o Fnet = mass x acceleration = m * a

o If force is gravitational (Fg or weight↓),

 Weight = mass * gravitational acceleration

 Weight = m * g

Kinematic Equations (general)

o vf = v0 + at

o vf

= v0

+ 2ad

o d = v0t + ½ at2

Inclined Plane ( ) - F|| vs Ff

o F|| down plane (causing motion) = mg sin

o Ff up plane (friction force opposing motion) = mg cos

Friction

o Coefficient = Force of friction (Ff) (0 < <1)

Normal force (FN)

Ff = FN

Net Force (Fnet)

o Flat plane: Fnet = Fa – Ff = Fa – μmg

o Inclined plane: Fnet = F|| - Ff = mgsinθ = μmgcosθ

Pressure

o P = Applied force

area of application

o P = F/A (= mg/A when using a gravity or weight model)

Conversion

o cm2

x 10-4

= m2

o mm2

x 10-6

= m2

Units

o Force - Newtons

o Pressure - N/m2

or Pascals (Pa)

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series RC circuit is built with a 15 kΩ resistor and a parallel-plate capacitor with 18-cm-diameter electrodes. A 18 V, 36 kHz s

andre [41]

Answer:

$d=1.84\ mm$

Explanation:

<u>Capacitance</u>

A two parallel-plate capacitor has a capacitance of

$\displaystyle C=\frac{\epsilon_o A}{d}$

where

$\epsilon_o=8.85\cdot 10^{-12}\ F/m$

A = area of the plates = $\pi r^2$

d = separation of the plates

$\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}$

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

$\displaystyle X_c=\frac{1}{wC}$

where w is the angular frequency

$w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s$

Solving for C

$\displaystyle C=\frac{1}{wX_c}$

The reactance can be found knowing the total impedance of the circuit:

$Z^2=R^2+X_c^2$

Where R is the resistance, $R=15 K\Omega=15000\Omega$ . Solving for Xc

$X_c^2=Z^2-R^2$

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

$\displaystyle Z=\frac{V}{I}$

The rms current is the peak current Ip divided by $\sqrt{2}$ , thus

$\displaystyle Z=\frac{\sqrt{2}V}{I_p}$

$I_p=0.65\ mA/1000=0.00065\ A$

Now collect formulas

$\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2$

Or, equivalently

$\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}$

$\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}$

$X_c=36176.34\ \Omega$

The capacitance is now

$\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F$

The radius of the plates is

$r=18\ cm/2=9 \ cm = 0.09 \ m$

The separation between the plates is

$\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}$

$d=0.00184\ m$

$\boxed{d=1.84\ mm}$

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All the formulas for Friction​

All the formulas for Friction