A Beating Heart — phryzby

solved PeriodicMotion

Q. On an average, a human heart is found to beat 75 $N = 75$ times in 1 min $Δ t = 1$ min. What is its frequency, in hertz?

Inputs

beats

N

time

Δ t

1 min

Outputs

frequency

ν

How it's solved

Solved with PeriodicMotion

Given

$N = 75$
$Δ t = 1$ min

Find $ν$ .

Working

$Δ t = 1$ min $= 60$ s
frequency is repetitions a second(beating) $ν = \frac{N}{Δ t}$
$ν = \frac{75}{60}$
$ν = 1.25$ Hz
$ν \approx 1.25$ Hzto 3 significant figures

Conclusion

Frequency counts the beats in each second, so the beats in a minute are shared out over its sixty seconds.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :a_beating_heart do4  kind :numerical5  describes "On an average, a human heart is found to beat %{beats} times in %{time}. %{frequency}, in hertz?"6  given beats: "75"7  given time: "1 min"8  asks frequency: "What is its frequency"9end

solution.rb

1require_relative "../questions/a_beating_heart"2require_relative "../science/oscillations/periodic_motion"34solve :a_beating_heart, using: PeriodicMotion do5  objects :heart6  heart.goes(:beating)78  take beats: heart.repetitions9  take time: beating.time_taken1011  frequency = heart.frequency12  answer frequency:, in: "Hz", figures: 31314  conclusion "Frequency counts the beats in each second, so the beats in a minute are shared out over " \15             "its sixty seconds."16end

playground.rb

1require_relative "../solutions/a_beating_heart"23play_with :a_beating_heart do4  title "A Beating Heart"5end

The laws it drew on

quantity	written	units	within	from
position	$x$	m	—	Velocity
displacement	$Δ x$	m	—	Velocity
path length	$d$	m	—	Velocity
time taken	$Δ t$	s	0 … 1e+05	Velocity
average velocity	$v_{av}$	m/s	—	Velocity
average speed	$c_{av}$	m/s	—	Velocity
starting position	$x_{0}$	m	—	Velocity
final position	$x$	m	—	Velocity
repetitions	$N$	—	—	PeriodicMotion
frequency	$ν$	Hz	0 … ∞	PeriodicMotion
period	$T$	s	—	PeriodicMotion
displacement of heart during beating	$Δ x$	m	—
position of heart at end of beating	$x_{1}$	m	—
position of heart at start of beating	$x_{0}$	m	—
average velocity of heart during beating	$v_{av}$	m/s	—
time taken of beating	$Δ t$	s	0 … 1e+05
average speed of heart during beating	$c_{av}$	m/s	—
path length of heart during beating	$d$	m	—
frequency of heart	$ν$	Hz	0 … ∞
repetitions of heart during beating	$N$	—	—
period of ground	$T_{g}$	s	—
frequency of ground	$ν_{g}$	Hz	0 … ∞
period of heart	$T$	s	—

x_{0} \equiv x_{i} (start of motion)

starting position

x \equiv x_{i} (end of motion)

final position

d_{i} (whole) = d_{i} (part 1) + d_{i} (part 2)

path in parts

Δ t_{w} = Δ t_{p} + Δ t_{p}

time in parts

T_{b} = \frac{1}{ν_{b}}

period is the time of one

Δ x = x_{1} - x_{0}

change of position(beating)

v_{av} = \frac{Δ x}{Δ t}

displacement a time(beating)

c_{av} = \frac{d}{Δ t}

path a time(beating)

ν = \frac{N}{Δ t}

frequency is repetitions a second(beating)

T_{g} = \frac{1}{ν_{g}}

period is the time of one(ground)

T = \frac{1}{ν}

period is the time of one(heart)