A Skidding Stop — phryzby

solved Work

Q. A cyclist comes to a skidding stop in 10 m $x_{1} = 10$ m. During this process, the force on the cycle due to the road is 200 N $| F_{r} | = 200$ N and is directly opposed to the motion $F_{r} = - | F_{r} |$ . How much work does the road do on the cycle, in joules?

Inputs

distance

x_{1}

10.00 m

force

| F_{r} |

200 N

Outputs

work

W_{F,r}

How it's solved

Solved with Work

Given

$x_{1} = 10$ m
$| F_{r} | = 200$ N
$F_{r} = - | F_{r} |$ from “directly opposed to the motion”

Assumed

$x_{0} = 0$ m

Find $W_{F,r}$ .

Working

directly opposed to the motion $F_{r} = - | F_{r} |$
$F_{r} = - 200$
$F_{r} = −200$ N
change of position(skidding, x) $Δ x = x_{1} - x_{0}$
$Δ x = 10 - 0$
$Δ x = 10$ m
work of a steady force(cycle, skidding, x) $W_{F,r} = F_{r} \cdot Δ x$
$W_{F,r} = (−200) \cdot 10$
$W_{F,r} = −2000$ J

Conclusion

The road pushes against the way the cycle moves, so it takes energy out of the motion: the work is the force times the distance, with a minus sign.

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_skidding_stop do4  kind :numerical5  describes "A cyclist comes to a skidding stop in %{distance}. During this process, the force on the cycle due " \6            "to the road is %{force} and is directly opposed to the motion. %{work}, in joules?"7  given distance: "10 m"8  given force: "200 N"9  asks work: "How much work does the road do on the cycle"10end

solution.rb

1require_relative "../questions/a_skidding_stop"2require_relative "../science/work_energy_and_power/work"34solve :a_skidding_stop, using: Work do5  objects :cycle, :road6  axes :x7  cycle.goes(:skidding)89  take distance: cycle.final_position10  take force: cycle.force(by: road).magnitude1112  assume cycle.initial_position => "0 m"13  deduce_from "directly opposed to the motion", cycle.force(by: road).direction => -x1415  work = cycle.work(by: road)16  answer work:, in: "J"1718  conclusion "The road pushes against the way the cycle moves, so it takes energy out of the motion: " \19             "the work is the force times the distance, with a minus sign."20end

playground.rb

1require_relative "../solutions/a_skidding_stop"23play_with :a_skidding_stop do4  title "A Skidding Stop"5end

The laws it drew on

quantity	written	units	within	from
volume	$volume$	—	—	Vectors
mass	$m$	kg	0 … ∞	Vectors
speed	$speed$	—	—	Vectors
density	$density$	—	—	Vectors
number of moles	$n$	—	—	Vectors
angular frequency	${angular}_{frequency}$	—	—	Vectors
work	$W_{F}$	J	—	Vectors
current	$current$	—	—	Vectors
temperature	$temperature$	—	—	Vectors
pressure	$pressure$	—	—	Vectors
time	$t$	s	0 … 1e+05	Vectors
power	$power$	—	—	Vectors
total path length	$s$	—	—	Vectors
energy	$energy$	—	—	Vectors
gravitational potential	${gravitational}_{potential}$	—	—	Vectors
coefficient of friction	$μ$	—	—	Vectors
charge	$charge$	—	—	Vectors
acceleration	$a$	m/s²	—	Vectors
velocity	$v$	m/s	—	Vectors
displacement	$Δ x$	m	—	Vectors
angular velocity	${angular}_{velocity}$	—	—	Vectors
force	$F$	N	—	Vectors
angular momentum	${angular}_{momentum}$	—	—	Vectors
linear momentum	$p_{lin}$	—	—	Vectors
electric field	${electric}_{field}$	—	—	Vectors
average velocity	$v_{av}$	m/s	—	Vectors
magnetic moment	${magnetic}_{moment}$	—	—	Vectors
relative velocity	$v_{AB}$	—	—	Vectors
impulse	$impulse$	—	—	Vectors
first vector	$A$	—	0 … ∞	Vectors
second vector	$B$	—	0 … ∞	Vectors
angle between	$φ$	—	0 … 3.142	Vectors
resultant	$R$	—	0 … ∞	Vectors
resultant direction	$β$	—	0 … 3.142	Vectors
direction	$α$	—	-3.142 … 3.142	Vectors
x component	$A_{x}$	—	—	Vectors
y component	$A_{y}$	—	—	Vectors
position	$x$	m	—	Velocity
path length	$d$	m	—	Velocity
time taken	$Δ t$	s	0 … 1e+05	Velocity
average speed	$c_{av}$	m/s	—	Velocity
starting position	$x_{0}$	m	—	Velocity
final position	$x$	m	—	Velocity
change of velocity	$Δ v$	m/s	—	Acceleration
average acceleration	$a_{av}$	m/s²	—	Acceleration
starting velocity	$v_{0}$	m/s	—	Acceleration
final velocity	$v$	m/s	—	Acceleration
gravity	$g$	m/s²	—	UniformAcceleration
net force	$F_{net}$	N	—	NewtonsSecondLaw
weight	$W$	N	—	NewtonsSecondLaw
work by gravity	$W_{g}$	J	—	Work
net work	$W_{net}$	J	—	Work
displacement of cycle during skidding along x	$Δ x$	m	—
position of cycle at end of skidding along x	$x_{1}$	m	—
position of cycle at start of skidding along x	$x_{0}$	m	—
average velocity of cycle during skidding along x	$v_{av}$	m/s	—
time taken of skidding	$Δ t$	s	0 … 1e+05
average speed of cycle during skidding	$c_{av}$	m/s	—
path length of cycle during skidding	$d$	m	—
change of velocity of cycle during skidding along x	$Δ v$	m/s	—
velocity of cycle at end of skidding from ground along x	$v_{1}$	m/s	—
velocity of cycle at start of skidding from ground along x	$v_{0}$	m/s	—
average acceleration of cycle during skidding along x	$a_{av}$	m/s²	—
acceleration of cycle during skidding along x	$a$	m/s²	—
net force on cycle during skidding along x	$F_{net}$	N	—
mass of cycle	$m$	kg	0 … ∞
mass of road	$m_{r}$	kg	0 … ∞
weight on ground	$\| W_{g} \|$	N	—
weight on cycle	$\| W \|$	N	—
weight on road	$\| W_{r} \|$	N	—
force on cycle by road during skidding	$\| F_{r} \|$	N	—
force on cycle by road during skidding along x	$F_{r}$	N	—
work on cycle by road during skidding	$W_{F,r}$	J	—
net work on cycle during skidding	$W_{net}$	J	—
displacement of cycle during skidding	$\| Δ x \|$	m	—
position of cycle at end of skidding	$\| x_{1} \|$	m	—
position of cycle at start of skidding	$\| x_{0} \|$	m	—
average velocity of cycle during skidding	$\| v_{av} \|$	m/s	—
change of velocity of cycle during skidding	$\| Δ v \|$	m/s	—
velocity of cycle at end of skidding from ground	$\| v_{1} \|$	m/s	—
velocity of cycle at start of skidding from ground	$\| v_{0} \|$	m/s	—
average acceleration of cycle during skidding	$\| a_{av} \|$	m/s²	—
acceleration of cycle during skidding	$\| a \|$	m/s²	—
net force on cycle during skidding	$\| F_{net} \|$	N	—

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

starting position

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

final position

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

starting velocity

v \equiv v_{i} (end of motion)

final velocity

t \equiv Δ t_{m}

time

A = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}}

magnitude from components

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

a_{i} (part 1) = a_{i} (whole)

steady through its parts

m_{b} \neq 0

has mass?

R^{2} = A^{2} + B^{2} + 2 \cdot A \cdot B \cdot \cos φ

law of cosines

R \cdot \sin β = B \cdot \sin φ

law of sines

R \cdot \cos β = A + B \cdot \cos φ

along the first

A_{x} = A \cdot \cos α

resolved along x

A_{y} = A \cdot \sin α

resolved along y

Δ x = x_{1} - x_{0}

change of position(skidding, x)

v_{av} = \frac{Δ x}{Δ t}

displacement a time(skidding, x)

c_{av} = \frac{d}{Δ t}

path a time(skidding, x)

Δ v = v_{1} - v_{0}

velocity gained(skidding, x)

a_{av} = \frac{Δ v}{Δ t}

velocity gained a time(skidding, x)

v_{1} = v_{0} + a \cdot Δ t

velocity after a time(skidding, x)

x_{1} = x_{0} + v_{0} \cdot Δ t + \frac{a \cdot {Δ t}^{2}}{2}

position after a time(skidding, x)

{v_{1}}^{2} = {v_{0}}^{2} + 2 \cdot a \cdot (x_{1} - x_{0})

velocity after a distance(skidding, x)

x_{1} - x_{0} = \frac{(v_{1} + v_{0}) \cdot Δ t}{2}

mean of the velocities(skidding, x)

F_{net} = m \cdot a

second law(skidding, x)

F_{net} = F_{r} + 0

net force is the resultant(cycle, skidding, x)

W_{F,r} = F_{r} \cdot Δ x

work of a steady force(cycle, skidding, x)

W_{net} = F_{net} \cdot Δ x

work of the net force(cycle, skidding)

| Δ x | = \sqrt{{Δ x}^{2}}

magnitude from components(displacement of cycle during skidding)

| x_{1} | = \sqrt{{x_{1}}^{2}}

magnitude from components(position of cycle at end of skidding)

| x_{0} | = \sqrt{{x_{0}}^{2}}

magnitude from components(position of cycle at start of skidding)

| v_{av} | = \sqrt{{v_{av}}^{2}}

magnitude from components(average velocity of cycle during skidding)

| Δ v | = \sqrt{{Δ v}^{2}}

magnitude from components(change of velocity of cycle during skidding)

| v_{1} | = \sqrt{{v_{1}}^{2}}

magnitude from components(velocity of cycle at end of skidding from ground)

| v_{0} | = \sqrt{{v_{0}}^{2}}

magnitude from components(velocity of cycle at start of skidding from ground)

| a_{av} | = \sqrt{{a_{av}}^{2}}

magnitude from components(average acceleration of cycle during skidding)

| a | = \sqrt{a^{2}}

magnitude from components(acceleration of cycle during skidding)

| F_{net} | = \sqrt{{F_{net}}^{2}}

magnitude from components(net force on cycle during skidding)

| F_{r} | = \sqrt{{F_{r}}^{2}}

magnitude from components(force on cycle by road during skidding)

F_{r} = - | F_{r} |

directly opposed to the motion

m \neq 0

has mass?(cycle)

m_{r} \neq 0

has mass?(road)

F_{net} = 0

free of forces?(cycle, skidding)