What a Force Is Made Of

Q. What is a force made of, when it moves a mass m through l in t?

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The web of concepts

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Q. What is a force made of, when it moves a mass $m$ through $l$ in $t$ ?

The playground

Inputs

mass in kilograms

m

length

l

3.00 m

time

t

1.50 s

Outputs

speed

v

2.0 m/s

acceleration

a

1.333

force

F

2.667

The solution

Solved with Dimensions

Given

$m$ , $l$ , $t$ yours to vary

Find $v$ , $a$ , $F$ .

Working

average speed $v = \frac{l}{t}$
$v = \frac{3}{1.5}$
$v = 2.0 m/s$
average acceleration $a = \frac{v}{t}$
$a = \frac{2}{1.5}$
$a = 1.33333333$ m/s²
newtons second law $F = m \cdot a$
$F = 2 \cdot 1.33333333$
$F = 2.66666667$ N

Conclusion

A mass times an acceleration, and an acceleration is a length over a time over a time again: [F] = [M L T⁻²]. Whatever the numbers, a force is always built that way.

The Ruby

1require_relative "../physics"23question :what_a_force_is_made_of do4  describes "%{force}, when it moves a mass %{mass} through %{length} in %{time}?"5  given :mass6  given :length7  given :time8  asks force: "What is a force made of"9end

1require_relative "../questions/what_a_force_is_made_of"2require_relative "../science/units_and_measurement/dimensions"34solve :what_a_force_is_made_of, using: Dimensions do5  take mass: :m, length: :l, time: :t6  find_value :v7  find_value :a8  take force: :F9  find_value :force1011  conclusion "A mass times an acceleration, and an acceleration is a length over a time over a " \12             "time again: [F] = [M L T⁻²]. Whatever the numbers, a force is always built that way."13end

1require_relative "../solutions/what_a_force_is_made_of"23play_with :what_a_force_is_made_of do4  title "What a Force Is Made Of"56  input :m, 0.1..10.0, step: 0.1, default: 2.0, as: "mass in kilograms"7  input :l, 0.1..10.0, in: "m", step: 0.1, default: 3.0, as: "length"8  input :t, 0.1..5.0,  in: "s", step: 0.1, default: 1.5, as: "time"910  output :v, in: "m/s"11  output :a12  output :F13end

The laws

quantity	written	units	within	from
speed of light	$c$	m/s	—	Units
avogadro constant	$N_{A}$	mol⁻¹	—	Units
length	$l$	m	0 … ∞	Units
mass	$m$	kg	—	Units
time	$t$	s	0 … ∞	Units
electric current	$I$	A	—	Units
temperature	$T$	K	—	Units
amount of substance	$n$	mol	—	Units
luminous intensity	$I_{v}$	cd	—	Units
arc length	$s$	m	—	Units
radius	$r$	m	0 … ∞	Units
plane angle	$θ$	—	—	Units
area	$A$	m²	—	Units
solid angle	$Ω$	—	—	Units
light time	$t_{light}$	s	—	Units
light distance	$d_{light}$	m	—	Units
number of entities	$N$	—	—	Units
baseline	$B$	m	—	Units
distance away	$D$	m	—	Units
parallax angle	$θ_{p}$	—	—	Units
pi	$π$	—	0 … ∞	Dimensions
gravitational constant	$G$	N m² kg⁻²	—	Dimensions
volume	$V$	m³	—	Dimensions
speed	$v$	m/s	—	Dimensions
acceleration	$a$	m/s²	—	Dimensions
force	$F$	N	—	Dimensions
density	$ρ$	kg/m³	—	Dimensions
work	$W$	J	—	Dimensions
surface area	$S$	m²	—	Dimensions
height	$h$	m	—	Dimensions
breadth	$b$	m	—	Dimensions
cylinder surface area	$S_{c}$	m²	—	Dimensions
volume of a slab	$V_{s}$	m³	—	Dimensions
relative density	$ρ_{rel}$	—	—	Dimensions
density of water	$ρ_{w}$	kg/m³	—	Dimensions
linear magnification	$m_{l}$	—	—	Dimensions
image length	$l_{i}$	m	—	Dimensions
object length	$l_{o}$	m	—	Dimensions
image area	$A_{i}$	m²	—	Dimensions
object area	$A_{o}$	m²	—	Dimensions
volume of them all	$V_{N}$	m³	—	Dimensions
molar volume	$V_{m}$	m³	—	Dimensions
room to spare	$R_{V}$	—	—	Dimensions

θ = \frac{s}{r}

arc over radius

Ω = \frac{A}{r^{2}}

area over radius squared

d_{light} = c \cdot t_{light}

distance at light speed

N = n \cdot N_{A}

entities in moles

θ_{p} = \frac{B}{D}

baseline over distance

V = l^{3}

volume of a cube

v = \frac{l}{t}

average speed

a = \frac{v}{t}

average acceleration

F = m \cdot a

newtons second law

ρ = \frac{m}{V}

mass per volume

W = F \cdot l

force through a distance

S = 6 \cdot l^{2}

surface of a cube

V = \frac{4 \cdot π \cdot r^{3}}{3}

volume of a sphere

S_{c} = 2 \cdot π \cdot r \cdot (r + h)

surface of a cylinder

A = l \cdot b

area of a rectangle

V_{s} = l \cdot b \cdot h

volume from three sides

ρ_{rel} = \frac{ρ}{ρ_{w}}

density against water

m_{l} = \frac{l_{i}}{l_{o}}

lengths magnified

{m_{l}}^{2} = \frac{A_{i}}{A_{o}}

areas magnified

V_{N} = N \cdot V

atoms side by side

R_{V} = \frac{V_{m}}{V_{N}}

molar over atomic volume