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3 years ago

Two skaters stand facing each other. One skater's mass is 60 kg, and the other's

Physics

1 answer:

jeyben [28]3 years ago

3 0

Answer:

v' = 2.4 m/s

Explanation:

Given that,

Mass of one skater, m = 60 kg

Mass of the other's skater, m' = 60 kg

The two skaters push off each other. After the push, the smaller skater has a velocity of 3.0 m/s.

When there is no external force acting on a system, the momentum remains conserved. It means initial momentum is equal to the final momentum. Let v' is the velocity of the larger skater.

mv = m'v'

$v'=\dfrac{mv}{m'}\\\\v'=\dfrac{60\times 3}{75}\\\\v'=2.4\ m/s$

So, the velocity of the larger skater is 2.4 m/s.

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A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red

Alik [6]

Answer:

Speed of physicist car is 0.036c or 1.08 x 10⁷ m/s .

Explanation:

Doppler Effect is defined as the change in frequency or wavelength of the wave as the source or/and observer moving away or towards each other.

In this case, the Doppler effect equation in terms of wavelength is :

$\lambda_{s} = \lambda_{o}\sqrt{\frac{1-\frac{v}{c} }{1+\frac{v}{c} } }$ ......(1)

Here $\lambda_{s}$ is source wavelength, $\lambda_{o}$ is observed wavelength, v is speed of the observer and c is the speed of light.

Given :

Source wavelength, $\lambda_{s}$ = 660 nm = 660 x 10⁻⁹ m

Observed wavelength, $\lambda_{0}$ = 555 nm = 555 x 10⁻⁹ m

Substitute these values in the equation (1).

$555\times10^{-9} } = 660\times10^{-9} \sqrt{\frac{1-\frac{v}{c} }{1+\frac{v}{c} } }$

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3 years ago

A resonant circuit using a 286-nFnF capacitor is to resonate at 18.0 kHzkHz. The air-core inductor is to be a solenoid with clos

lukranit [14]

Answer:

The inductor contains $N = 523962.32$ loops

Explanation:

From the question we are told that

The capacitance of the capacitor is $C = 286nF = 286 * 10^{-9} \ F$

The resonance frequency is $f = 18.0 kHz = 18*10^{3} Hz$

The diameter is $d = 1.1 mm = \frac{1.1 }{1000} = 0.00011 \ m$

The of the air-core inductor is $l = 12 \ m$

The permeability of free space is $\mu_o = 4 \pi *10^{-7} \ T \cdot m/A$

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This inductance can also be mathematically represented as

$L = \frac{1}{w^2}$

Where $w$ is the angular speed mathematically given as

$w = 2 \pi f$

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Now equating the both formulas for inductance

$\frac{\mu_o * N^2 \pi d^2}{4 l} = \frac{1}{4 \pi ^2 f^2}$

making N the subject of the formula

$N = \sqrt{\frac{1}{(2 \pi f)^2} * \frac{4 * l }{\mu_o * \pi d^2 C} }$

$N = \frac{1}{2 \pi f} * \frac{2}{d} * \sqrt{\frac{l}{\pi * \mu_o * C} }$

Substituting value

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