Pulling the Heavier Body

Q. Two bodies A and B of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to B along the direction of the string. What is the tension in the string, in newtons? expects 200 N

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. Two bodies A and B of masses 10 kg $m_{A} = 10$ kg and 20 kg $m_{B} = 20$ kg respectively kept on a smooth, horizontal surface are tied to the ends $m_{AB} = m_{A} + m_{B}$ of a light string $a_{A} (t) = a_{AB} (p)$ . A horizontal force F = 600 N $| F_{ABp} (p) | = 600$ N is applied to B along the direction of the string $F_{ABp} (p) = | F_{ABp} (p) |$ . What is the tension in the string, in newtons?

The playground

Inputs

mass a

m_{A}

10 kg

mass b

m_{B}

20 kg

force

| F_{ABp} |

600 N

Outputs

tension

| F_{As} |

The solution

Solved with NewtonsSecondLaw

Given

$m_{A} = 10$ kg
$m_{B} = 20$ kg
$| F_{ABp} (p) | = 600$ N
$m_{AB} = m_{A} + m_{B}$ from “tied to the ends”
$a_{A} (t) = a_{AB} (p)$ from “a light string”
$F_{ABp} (p) = | F_{ABp} (p) |$ from “along the direction of the string”

Find $| F_{As} (t) |$ .

Working

along the direction of the string $F_{ABp} (p) = | F_{ABp} (p) |$
$F_{ABp} (p) = 600$
$F_{ABp} (p) = 600$ N
net force is the resultant(pair, pulled, x) $F_{net,AB} (p) = F_{ABp} (p) + 0$
$F_{net,AB} (p) = 600 + 0$
$F_{net,AB} (p) = 600$ N
tied to the ends $m_{AB} = m_{A} + m_{B}$
$m_{AB} = 10 + 20$
$m_{AB} = 30$ kg
second law(pulled, x) $F_{net,AB} (p) = m_{AB} \cdot a_{AB} (p)$
$600 = 30 \cdot a_{AB} (p)$
$a_{AB} (p) = 20$ m/s²
a light string $a_{A} (t) = a_{AB} (p)$
$a_{A} (t) = 20$
$a_{A} (t) = 20$ m/s²
second law(towed, x) $F_{net,A} (t) = m_{A} \cdot a_{A} (t)$
$F_{net,A} (t) = 10 \cdot 20$
$F_{net,A} (t) = 200$ N
net force is the resultant(body a, towed, x) $F_{net,A} (t) = F_{As} (t) + 0$
$200 = F_{As} (t) + 0$
$F_{As} (t) = 200$ N
magnitude from components(force on body a by string during towed) $| F_{As} (t) | = \sqrt{{F_{As} (t)}^{2}}$
$| F_{As} (t) | = \sqrt{200^{2}}$
$| F_{As} (t) | = 200$ N

Conclusion

Now the string has only the lighter body to drag along, so it needs to pull less hard to keep it moving with the other.

The Ruby

1require_relative "../physics"23question :pulling_the_heavier_body do4  kind :numerical5  describes "Two bodies A and B of masses %{mass_a} and %{mass_b} respectively kept on a smooth, horizontal " \6            "surface are tied to the ends of a light string. A horizontal force F = %{force} is applied to B " \7            "along the direction of the string. %{tension}, in newtons?"8  given mass_a: "10 kg"9  given mass_b: "20 kg"10  given force: "600 N"11  asks tension: "What is the tension in the string"12end

1require_relative "../questions/pulling_the_heavier_body"2require_relative "../science/laws_of_motion/newtons_second_law"34solve :pulling_the_heavier_body, using: NewtonsSecondLaw do5  objects :string, :puller, body_a: :A, body_b: :B, pair: :AB6  axes :x7  pair.goes(:pulled)8  body_a.goes(:towed)910  take mass_a: body_a.mass11  take mass_b: body_b.mass12  take force: pair.force(by: puller).magnitude1314  deduce_from "tied to the ends", pair.mass => body_a.mass + body_b.mass15  deduce_from "a light string", body_a.acceleration => pair.acceleration16  deduce_from "along the direction of the string", pair.force(by: puller).direction => x1718  tension = body_a.force(by: string).magnitude19  answer tension:, in: "N"2021  conclusion "Now the string has only the lighter body to drag along, so it needs to pull less hard to keep " \22             "it moving with the other."23end

1require_relative "../solutions/pulling_the_heavier_body"23play_with :pulling_the_heavier_body do4  title "Pulling the Heavier Body"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	$work$	—	—	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
displacement of pair during pulled along x	$Δ x_{AB} (p)$	m	—
position of pair at end of pulled along x	$x_{AB} (p₁)$	m	—
position of pair at start of pulled along x	$x_{AB} (p₀)$	m	—
displacement of body a during towed along x	$Δ x_{A} (t)$	m	—
position of body a at end of towed along x	$x_{A} (t₁)$	m	—
position of body a at start of towed along x	$x_{A} (t₀)$	m	—
average velocity of pair during pulled along x	$v_{av,AB} (p)$	m/s	—
time taken of pulled	$Δ t_{p}$	s	0 … 1e+05
average velocity of body a during towed along x	$v_{av,A} (t)$	m/s	—
time taken of towed	$Δ t_{t}$	s	0 … 1e+05
average speed of pair during pulled	$c_{av,AB} (p)$	m/s	—
path length of pair during pulled	$d_{AB} (p)$	m	—
average speed of body a during towed	$c_{av,A} (t)$	m/s	—
path length of body a during towed	$d_{A} (t)$	m	—
change of velocity of pair during pulled along x	$Δ v_{AB} (p)$	m/s	—
velocity of pair at end of pulled from ground along x	$v_{AB} (p₁)$	m/s	—
velocity of pair at start of pulled from ground along x	$v_{AB} (p₀)$	m/s	—
change of velocity of body a during towed along x	$Δ v_{A} (t)$	m/s	—
velocity of body a at end of towed from ground along x	$v_{A} (t₁)$	m/s	—
velocity of body a at start of towed from ground along x	$v_{A} (t₀)$	m/s	—
average acceleration of pair during pulled along x	$a_{av,AB} (p)$	m/s²	—
average acceleration of body a during towed along x	$a_{av,A} (t)$	m/s²	—
acceleration of pair during pulled along x	$a_{AB} (p)$	m/s²	—
acceleration of body a during towed along x	$a_{A} (t)$	m/s²	—
net force on pair during pulled along x	$F_{net,AB} (p)$	N	—
mass of pair	$m_{AB}$	kg	0 … ∞
net force on body a during towed along x	$F_{net,A} (t)$	N	—
mass of body a	$m_{A}$	kg	0 … ∞
mass of string	$m_{s}$	kg	0 … ∞
mass of puller	$m_{p}$	kg	0 … ∞
mass of body b	$m_{B}$	kg	0 … ∞
weight on ground	$\| W_{g} \|$	N	—
weight on string	$\| W_{s} \|$	N	—
weight on puller	$\| W_{p} \|$	N	—
weight on body a	$\| W_{A} \|$	N	—
weight on body b	$\| W_{B} \|$	N	—
weight on pair	$\| W_{AB} \|$	N	—
force on body a by string during towed	$\| F_{As} (t) \|$	N	—
force on body a by string during towed along x	$F_{As} (t)$	N	—
force on pair by puller during pulled	$\| F_{ABp} (p) \|$	N	—
force on pair by puller during pulled along x	$F_{ABp} (p)$	N	—
displacement of pair during pulled	$\| Δ x_{AB} (p) \|$	m	—
position of pair at end of pulled	$\| x_{AB} (p₁) \|$	m	—
position of pair at start of pulled	$\| x_{AB} (p₀) \|$	m	—
displacement of body a during towed	$\| Δ x_{A} (t) \|$	m	—
position of body a at end of towed	$\| x_{A} (t₁) \|$	m	—
position of body a at start of towed	$\| x_{A} (t₀) \|$	m	—
average velocity of pair during pulled	$\| v_{av,AB} (p) \|$	m/s	—
average velocity of body a during towed	$\| v_{av,A} (t) \|$	m/s	—
change of velocity of pair during pulled	$\| Δ v_{AB} (p) \|$	m/s	—
velocity of pair at end of pulled from ground	$\| v_{AB} (p₁) \|$	m/s	—
velocity of pair at start of pulled from ground	$\| v_{AB} (p₀) \|$	m/s	—
change of velocity of body a during towed	$\| Δ v_{A} (t) \|$	m/s	—
velocity of body a at end of towed from ground	$\| v_{A} (t₁) \|$	m/s	—
velocity of body a at start of towed from ground	$\| v_{A} (t₀) \|$	m/s	—
average acceleration of pair during pulled	$\| a_{av,AB} (p) \|$	m/s²	—
average acceleration of body a during towed	$\| a_{av,A} (t) \|$	m/s²	—
acceleration of pair during pulled	$\| a_{AB} (p) \|$	m/s²	—
acceleration of body a during towed	$\| a_{A} (t) \|$	m/s²	—
net force on pair during pulled	$\| F_{net,AB} (p) \|$	N	—
net force on body a during towed	$\| F_{net,A} (t) \|$	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_{AB} (p) = x_{AB} (p₁) - x_{AB} (p₀)

change of position(pulled, x)

Δ x_{A} (t) = x_{A} (t₁) - x_{A} (t₀)

change of position(towed, x)

v_{av,AB} (p) = \frac{Δ x_{AB} (p)}{Δ t_{p}}

displacement a time(pulled, x)

v_{av,A} (t) = \frac{Δ x_{A} (t)}{Δ t_{t}}

displacement a time(towed, x)

c_{av,AB} (p) = \frac{d_{AB} (p)}{Δ t_{p}}

path a time(pulled, x)

c_{av,A} (t) = \frac{d_{A} (t)}{Δ t_{t}}

path a time(towed, x)

Δ v_{AB} (p) = v_{AB} (p₁) - v_{AB} (p₀)

velocity gained(pulled, x)

Δ v_{A} (t) = v_{A} (t₁) - v_{A} (t₀)

velocity gained(towed, x)

a_{av,AB} (p) = \frac{Δ v_{AB} (p)}{Δ t_{p}}

velocity gained a time(pulled, x)

a_{av,A} (t) = \frac{Δ v_{A} (t)}{Δ t_{t}}

velocity gained a time(towed, x)

v_{AB} (p₁) = v_{AB} (p₀) + a_{AB} (p) \cdot Δ t_{p}

velocity after a time(pulled, x)

v_{A} (t₁) = v_{A} (t₀) + a_{A} (t) \cdot Δ t_{t}

velocity after a time(towed, x)

x_{AB} (p₁) = x_{AB} (p₀) + v_{AB} (p₀) \cdot Δ t_{p} + \frac{a_{AB} (p) \cdot {Δ t_{p}}^{2}}{2}

position after a time(pulled, x)

x_{A} (t₁) = x_{A} (t₀) + v_{A} (t₀) \cdot Δ t_{t} + \frac{a_{A} (t) \cdot {Δ t_{t}}^{2}}{2}

position after a time(towed, x)

{v_{AB} (p₁)}^{2} = {v_{AB} (p₀)}^{2} + 2 \cdot a_{AB} (p) \cdot (x_{AB} (p₁) - x_{AB} (p₀))

velocity after a distance(pulled, x)

{v_{A} (t₁)}^{2} = {v_{A} (t₀)}^{2} + 2 \cdot a_{A} (t) \cdot (x_{A} (t₁) - x_{A} (t₀))

velocity after a distance(towed, x)

x_{AB} (p₁) - x_{AB} (p₀) = \frac{(v_{AB} (p₁) + v_{AB} (p₀)) \cdot Δ t_{p}}{2}

mean of the velocities(pulled, x)

x_{A} (t₁) - x_{A} (t₀) = \frac{(v_{A} (t₁) + v_{A} (t₀)) \cdot Δ t_{t}}{2}

mean of the velocities(towed, x)

F_{net,AB} (p) = m_{AB} \cdot a_{AB} (p)

second law(pulled, x)

F_{net,A} (t) = m_{A} \cdot a_{A} (t)

second law(towed, x)

F_{net,A} (t) = F_{As} (t) + 0

net force is the resultant(body a, towed, x)

F_{net,AB} (p) = F_{ABp} (p) + 0

net force is the resultant(pair, pulled, x)

| Δ x_{AB} (p) | = \sqrt{{Δ x_{AB} (p)}^{2}}

magnitude from components(displacement of pair during pulled)

| x_{AB} (p₁) | = \sqrt{{x_{AB} (p₁)}^{2}}

magnitude from components(position of pair at end of pulled)

| x_{AB} (p₀) | = \sqrt{{x_{AB} (p₀)}^{2}}

magnitude from components(position of pair at start of pulled)

| Δ x_{A} (t) | = \sqrt{{Δ x_{A} (t)}^{2}}

magnitude from components(displacement of body a during towed)

| x_{A} (t₁) | = \sqrt{{x_{A} (t₁)}^{2}}

magnitude from components(position of body a at end of towed)

| x_{A} (t₀) | = \sqrt{{x_{A} (t₀)}^{2}}

magnitude from components(position of body a at start of towed)

| v_{av,AB} (p) | = \sqrt{{v_{av,AB} (p)}^{2}}

magnitude from components(average velocity of pair during pulled)

| v_{av,A} (t) | = \sqrt{{v_{av,A} (t)}^{2}}

magnitude from components(average velocity of body a during towed)

| Δ v_{AB} (p) | = \sqrt{{Δ v_{AB} (p)}^{2}}

magnitude from components(change of velocity of pair during pulled)

| v_{AB} (p₁) | = \sqrt{{v_{AB} (p₁)}^{2}}

magnitude from components(velocity of pair at end of pulled from ground)

| v_{AB} (p₀) | = \sqrt{{v_{AB} (p₀)}^{2}}

magnitude from components(velocity of pair at start of pulled from ground)

| Δ v_{A} (t) | = \sqrt{{Δ v_{A} (t)}^{2}}

magnitude from components(change of velocity of body a during towed)

| v_{A} (t₁) | = \sqrt{{v_{A} (t₁)}^{2}}

magnitude from components(velocity of body a at end of towed from ground)

| v_{A} (t₀) | = \sqrt{{v_{A} (t₀)}^{2}}

magnitude from components(velocity of body a at start of towed from ground)

| a_{av,AB} (p) | = \sqrt{{a_{av,AB} (p)}^{2}}

magnitude from components(average acceleration of pair during pulled)

| a_{av,A} (t) | = \sqrt{{a_{av,A} (t)}^{2}}

magnitude from components(average acceleration of body a during towed)

| a_{AB} (p) | = \sqrt{{a_{AB} (p)}^{2}}

magnitude from components(acceleration of pair during pulled)

| a_{A} (t) | = \sqrt{{a_{A} (t)}^{2}}

magnitude from components(acceleration of body a during towed)

| F_{net,AB} (p) | = \sqrt{{F_{net,AB} (p)}^{2}}

magnitude from components(net force on pair during pulled)

| F_{net,A} (t) | = \sqrt{{F_{net,A} (t)}^{2}}

magnitude from components(net force on body a during towed)

| F_{As} (t) | = \sqrt{{F_{As} (t)}^{2}}

magnitude from components(force on body a by string during towed)

| F_{ABp} (p) | = \sqrt{{F_{ABp} (p)}^{2}}

magnitude from components(force on pair by puller during pulled)

m_{AB} = m_{A} + m_{B}

tied to the ends

a_{A} (t) = a_{AB} (p)

a light string

F_{ABp} (p) = | F_{ABp} (p) |

along the direction of the string

m_{s} \neq 0

has mass?(string)

m_{p} \neq 0

has mass?(puller)

m_{A} \neq 0

has mass?(body a)

m_{B} \neq 0

has mass?(body b)

m_{AB} \neq 0

has mass?(pair)

F_{net,A} (t) = 0

free of forces?(body a, towed)

F_{net,AB} (p) = 0

free of forces?(pair, pulled)