A Skidding Stop — phryzby

Q. A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 200 N and is directly opposed to the motion. How much work does the road do on the cycle, in joules? expects -2000 J

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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?

The playground

Inputs

distance

x_{1}

10.00 m

force

| F_{r} |

200 N

Outputs

work

W_{F,r}

The solution

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 Ruby

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

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

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

The laws

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)