what is the minimum horizontal force f needed to make the box start moving in
Problem 1
CE Predict/Explicate You button ii identical bricks across a table-
peak with constant speed, $v,$ every bit shown in FlGURE $6-29 .$ In case $1,$ you
place the bricks cease to cease; in case $2,$ you stack the bricks one on
acme of the other. (a) Is the force of kinetic friction in case 1 greater
than, less than, or equal to the force of kinetic friction in case two ?
(b) Choose the best explanation from among the following:
\begin{equation}
\begin{array}{l}{\text { I. The normal force in instance } 2 \text { is larger, and hence the bricks press }} \\ {\text { down more firmly against the tabletop. }} \\ {\text { II. The normal forcefulness is the aforementioned in the 2 cases, and friction is }} \\ {\text { independent of area. }}\\{\text { III. Case } 1 \text { has more surface surface area in contact with the tabletop, and }} \\ {\text { this leads to more than friction. }}\end{array}
\cease{equation}
Nicholas M.
Numerade Educator
Trouble 2
CE Predict/Explain Two drivers traveling side-by-side at the
same speed suddenly see a deer in the road ahead of them and begin
braking. Driver 1 stops by locking up his brakes and screeching to a
halt; driver ii stops by applying her brakes just to the verge of locking, so that the wheels continue to turn until her comes to a complete stop.(a) All other factors being equal, is the stopping altitude of
driver 1 greater than, less than, or equal to the stopping altitude of driver 2$?$ (b) Cull the best explanation from amidst the following:
\begin{equation}
\begin{array}{50}{\text { I. Locking upwardly the brakes gives the greatest possible braking force. }} \\ {\text { Ii. The same tires on the aforementioned route result in the aforementioned strength of }} \\ {\text { friction. }} \\ {\text { 3. Locked-up brakes pb to sliding (kinetic) friction, which is }} \\ {\text { less than rolling (static) friction. }}\cease{array}
\end{equation}
Nicholas Yard.
Numerade Educator
Problem 3
A 1.viii -kg block slides on a horizontal surface with a speed of $5=0.80 \mathrm{thousand} / \mathrm{s}$ and an acceleration of magnitude $a=ii.viii \mathrm{m} / \mathrm{south}^{2},$ as shown in FIGURE $half-dozen-30$ . (a) What is the coefficient of kinetic friction between the block and the surface? (b) When the speed of
the block slows to 0.xl $\mathrm{m} / \mathrm{due south}$ , is the magnitude of the acceleration
greater than. less than, or equal to 2.eight $\mathrm{m} / \mathrm{s}^{two}$ ? Explicate.
Ramsey Southward.
Numerade Educator
Problem 4
A child goes down a playground slide with an acceleration of i.26 $\mathrm{thousand} / \mathrm{s}^{2} .$ Detect the coefficient of kinetic friction between the
child and the slide if the slide is inclined at an bending of $33.0^{\circ}$ below
the horizontal.
Ramsey S.
Numerade Educator
Trouble v
What is the minimum horizontal
strength $F$ needed to
brand the box start
moving in FIGURE
$6-31 ?$ The coefficients of kinetic
and static friction
betwixt the box and the flooring are 0.27 and $0.38,$ respectively.
Keshav Southward.
Numerade Educator
Trouble half-dozen
What is the minimum horizontal force $F$ needed
to brand the box start moving in Figure $6-32$ ? The coefficients of kinetic
and static friction
between the box and the floor are 0.24 and $0.41,$ respectively.
Ramsey S.
Numerade Educator
Problem 7
CE The three identical boxes shown in Figure $vi-33$ remain at rest. on a rough, horizontal surface, even though they are acted on by
two unlike forces, $\overline{\mathbf{F}}_{ane}$ and $\mathbf{F}_{two}$ . All of the forces labeled $\mathbf{F}_{one}$ have the aforementioned magnitude; all of the forces labeled $\overline{\mathbf{F}}_{2}$ are identical to
one some other. Rank the boxes in lodge of increasing magnitude of
the force of static friction betwixt them and the surface. Betoken
ties where appropriate.
Nicholas Grand.
Numerade Educator
Problem 8
To move a large crate beyond a rough flooring, you push on it with a forcefulness $F$ at an angle of $21^{\circ}$ beneath the horizontal, as shown in Effigy
$six-34$ . Find the strength necessary to showtime the crate moving, given that
the mass of the crate is 32 $\mathrm{kg}$ and the coefficient of static friction
betwixt the crate and the floor is 0.57
Nicholas K.
Numerade Educator
Problem 9
Predict/Calculate $\mathrm{A} 37$ -kg crate is placed on an inclined ramp.
When the angle the ramp makes with the horizontal is increased
to $23^{\circ},$ the crate begins to slide downward. (a) What is the coefficient of static friction between the crate and the ramp? (b) At what
bending does the crate begin to slide if its mass is doubled?
Nicholas One thousand.
Numerade Educator
Problem ten
Coffee To Become A person places a cup of coffee on the roof of his car
while he dashes dorsum into the business firm for a forgotten particular. When he
returns to the automobile, he hops in and takes off with the coffee cup even so
on the roof. (a) If the coefficient of static friction between the coffee cup and the roof of the car is $0.24,$ what is the maximum acceleration the motorcar tin have without causing the cup to slide? lgnore
the furnishings of air resistance. (b) What is the smallest amount of
time in which the person can advance the car from residuum to 15 $\mathrm{thou} / \mathrm{s}$
and still keep the coffee loving cup on the roof?
Nicholas Chiliad.
Numerade Educator
Problem xi
A mug rests On an inclined
surface, as shown
in FlGURE $six-35$ .
(a) What is the
magnitude of the
frictional strength
exerted on the
mug? (b) What
is the minimum
coefficient of static friction required to proceed the mug from sliding?
Problem 12
Predict/Calculate Force Times Distance At the local hockey rink,
a puck with a mass of 0.12 $\mathrm{kg}$ is given an initial speed of $v=5.iii \mathrm{m} / \mathrm{south}$ .
(a) If the coefficient of kinetic friction between the water ice and the puck
is $0.xi,$ what distance $d$ does the puck slide before coming to rest?
(b) If the mass of the puck is doubled, does the frictional force $F$
exerted on the puck increment, decrease, or stay the same? Explain.
(c) Does the stopping distance of the puck increase, decrease, or
stay the aforementioned when its mass is doubled? Explain. (d) For the state of affairs considered in part (a), prove that $F d=\frac{1}{2} m v^{2} .$ (In Chapter 7
we will encounter $\frac{i}{2} m v^{two}$ is the kinetic energy of an object.)
Nicholas M.
Numerade Educator
Problem 13
Predict/Calculate The coefficient of kinetic friction between
the tires of your car and the roadway is $\mu$ . (a) If your initial speed is
$v$ and you lock your tires during braking, how far do yous skid? Give
your reply in terms of $v, \mu,$ and $m,$ the mass of your car. (b) If you
double your speed, what happens to the stopping distance? (c) What
is the stopping distance for a a truck with twice the mass of your car,
assuming the same initial speed and coefficient of kinetic friction?
Nicholas M.
Numerade Educator
Problem 14
CE A certain spring has a forcefulness constant $k$ . (a) If this spring is cutting
in half, does the resulting one-half spring accept a forcefulness constant that
is greater than, less than, or equal to $k$ (b) If two of the original
full-length springs are connected finish to end, does the resulting
double spring accept a forcefulness abiding that is greater than, less than,
or equal to $m ?$
Nicholas G.
Numerade Educator
Problem 15
CE A certain spring has a force constant $m$ . (a) If 2 such identical springs are connected in parallel to each other, as shown in
role (a) of Effigy $6-36$ , does the resulting double leap accept an
effective strength constant that is greater than, less than, or equal
to $grand ?$ Explicate. (b) If ii of the original springs are connected equally
shown in function $($ b) of Figure $6-36,$ does the resulting double spring
have an effective forcefulness constant that is greater than, less than, or
equal to $one thousand$ ? Explain.
Nicholas M.
Numerade Educator
Problem 16
Pulling up on a rope, you lift a vii.27 -kg bucket of h2o from a well
with an acceleration of 1.24 $\mathrm{m} / \mathrm{s}^{2} .$ What is the tension in the rope?
Nicholas Thou.
Numerade Educator
Problem 17
When a 9.09 -kg mass is placed on acme of a vertical spring, the
spring compresses iv.18 $\mathrm{cm} .$ Find the force constant of the bound.
Nicholas M.
Numerade Educator
Trouble 18
Predict/Calculate A backpack total of books weighing 52.0 $\mathrm{N}$
rests on a table in a physics laboratory classroom. A bound with a
forcefulness constant of 150 $\mathrm{N} / \mathrm{m}$ is attached to the backpack and pulled horizontally, as indicated in $\mathrm{Figure} 6-37$ (a) If the spring is pulled until it stretches 2.00 $\mathrm{cm}$ and the pack remains at residual, what is the force of friction exerted on the backpack by the table? (b) Does
your reply to function (a) modify if the mass of the backpack is doubled? Explain.
Nicholas M.
Numerade Educator
Problem 19
Ii springs, with strength constants $k_{1}=150 \mathrm{North} / \mathrm{thou}$ and $k_{2}=250 \mathrm{Northward} / \mathrm{m},$ are
continued in series, as shown in FlGURE
$6-38 .$ When a mass $m=0.xc \mathrm{kg}$ is fastened to the springs, what is the corporeality of stretch, $10$ ?
Nicholas M.
Numerade Educator
Problem xx
Predict/Calculate Illinois Jones is
beingness pulled from a snake pit with a rope
that breaks if the tension in information technology exceeds 755
N. (a) If Illinois Jones has a mass of 70.0
kg and the ophidian pit is 3.40 $\mathrm{thousand}$ deep, what
is the minimum time that is required to
pull our intrepid explorer from the pit?
(b) Explain why the rope breaks if Jones
is pulled from the pit in less fourth dimension than that calculated in office (a).
Nicholas M.
Numerade Educator
Problem 21
Predict/Summate A jump
with a strength abiding of 120 $\mathrm{N} /$
$\mathrm{m}$ is used to push a 0.27 -kg cake
of wood against a wall, equally shown
in Figure $half dozen-39$ . (a) Find the minimum pinch of the spring
needed to go on the cake from
falling, given that the coefficient of static friction between
the block and the wall is 0.46 .
(b) Does your reply to office (a)
change if the mass of the block
of wood is doubled? Explain.
Nicholas Thousand.
Numerade Educator
Trouble 22
A spring is suspended vertically from the ceiling of a room.
When a mass is attached to the bottom of the bound, the amount
of stretch is recorded. A plot of stretch versus mass is given in
FlGURE $vi-40 .$ Use the data given in the plot to determine the forcefulness
constant of the leap.
Nicholas M.
Numerade Educator
Problem 23
Mechanical Advantage The pulley organization shown in Figure $6-41$ is used to lift a
$m=67-$ kg crate. Note that ane chain
connects the upper pulley to the ceiling
and a second chain connects the lower
caster to the crate. Assuming the masses
of the chains, pulleys, and ropes are negligible, determine (a) the force $F$ required to lift the crate with constant speed,
(b) the tension in the upper chain, and
(c) the tension in the lower chain.
Donald A.
Numerade Educator
Trouble 24
Pulling the cord on a bow back with a forcefulness of $28.7 \mathrm{lb},$ an archer
prepares to shoot an arrow. If the archer pulls in the eye of the
string, and the angle between the two halves is $138^{\circ},$ what is the
tension in the string?
Nicholas M.
Numerade Educator
Problem 25
In Effigy $vi-42$ we see two blocks connected past a cord and tied to
prepares to shoot an arrow. If the archer pulls in the center of the
string, and the angle betwixt the two halves is $138^{\circ},$ what is the
tension in the string?
Nicholas Thou.
Numerade Educator
Problem 26
BIO Traction After a skiing blow, your leg is in a cast and supported in a traction device, as shown in FIGURE $six-43 .$ Observe the magnitude of the strength $\mathbf{F}$ exerted by the leg on the pocket-size caster. (By
Newton's third law, the small pulley exerts an equal and opposite
force on the leg.) Allow the mass $m$ be 2.27 $\mathrm{kg}$ .
Nicholas M.
Numerade Educator
Problem 27
2 blocks are connected by a cord, every bit shown in FIGURE half-dozen-44.
The smooth inclined surface makes an angle of $42^{\circ}$ with the horizontal, and the block on the incline has a mass of 6.7 $\mathrm{kg}$ . Find the
mass of the hanging block that will cause the system to exist in equilibrium. The caster is assumed to be platonic.)
Nicholas M.
Numerade Educator
Trouble 28
Predict/Calculate The system shown in $\mathrm{Effigy} 6-45$ consists of ii
pulleys and two blocks. The pulleys each take a mass of 2.0 $\mathrm{kg}$ ,
the block on the left has a mass of 16 $\mathrm{kg}$ , and the block on the right
has a mass $m$ . The system is in equilibrium, and the cord is massless.
(a) Is the mass $m$ greater than, less than, or equal to 16 $\mathrm{kg}$ ? Explain.
(b) Determine the mass $m$ .
Nicholas Chiliad.
Numerade Educator
Problem 29
CE Predict/Explain (a) Referring to the hanging planter in
Example $half-dozen-10,$ which of the 3 graphs $(A, B,$ or $C)$ in FIGURE $6-46$
shows an accurate plot of the tensions $T_{one}$ and $T_{2}$ as a function
of the angle $\theta$ (b) Choose the all-time explanation from amid the
post-obit:
\begin{equation}
\begin{array}{fifty}{\text { I. The 2 tensions must be equal at some bending between } \theta=0} \\ {\text { and } \theta=90^{\circ} .} \\ {\text { II. } T_{2} \text { is greater than } T_{1} \text { at all angles, and is equal to } thousand m \text { at } \theta=xc^{\circ} \text { . }} \\ {\text { Three. } T_{two} \text { is less than } T_{one} \text { at all angles, and is equal to } 0 \text { at } \theta=xc^{\circ} \text { . }}\end{array}
\end{equation}
Nicholas Thousand.
Numerade Educator
Problem 30
B1O Spiderweb Forces An orb-weaver spider sits in her spider web that is
supported by iii radial strands, as shown in Figure$half-dozen-47 .$ Assume
that simply the radial strands contribute to supporting the weight of
the spider. If the mass of the spider is $five.two \times ten^{-4} \mathrm{kg}$ , and the radial
strands are all under the aforementioned tension, discover the magnitude of the
tension, $T .$
Nicholas M.
Numerade Educator
Problem 31
A 0.fifteen -kg ball is placed in a shallow wedge with
an opening angle
of $120^{\circ},$ as shown
in FIGURE $half dozen-48 .$ For
each contact bespeak
between the wedge
and the ball, determine the force
exerted on the ball. Assume the organization is frictionless.
Nicholas One thousand.
Numerade Educator
Problem 32
Predict/Calculate A picture hangs on the wall suspended by
two strings, as shown in FisuRE $six-49$ . The tension in string 1 is one.7 $\mathrm{N}$ .
(a) Is the tension in string 2 greater than, less than, or equal to
1.7 $\mathrm{N} ?$ Explain. (b) Verify your answer to function (a) by calculating
the tension in cord $2 .$ (c) What is the weight of the picture?
Nicholas Chiliad.
Numerade Educator
Problem 33
Predict/Calculate Yous want to nail a ane.six -kg lath onto the wall
of a befouled. To position the board before nailing, you push it confronting
the wall with a horizontal force $\overrightarrow{\mathbf{F}}$ to keep it from sliding to the ground (Effigy $6-fifty )$ . (a) If the coefficient of static friction between
the board and the wall is $0.79,$ what is the least force you tin can apply
and however concord the board in place? (b) What happens to the force of
static friction if you push against the wall with a force greater than
that found in part (a)?
Nicholas M.
Numerade Educator
Problem 34
BIO The Russell Traction System To immobilize a fractured
femur (the thigh bone), doctors often utilize the Russell traction system illustrated in FIGURE $6-51 .$ Notice that one force is
applied directly to the knee joint, $\overrightarrow{\mathbf{F}}_{1},$ while ii other forces, $\overrightarrow{\mathbf{F}}_{2}$ and
$\overrightarrow{\mathbf{F}}_{3}$ are applied to the human foot. The latter two forces combine to give
a force $\overline{\mathbf{F}}_{two}+\mathbf{F}_{three}$ that is transmitted through the lower leg to
the articulatio genus. The event is that the knee experiences the total forcefulness
$\overrightarrow{\mathbf{F}}_{\text { total }}=\overrightarrow{\mathbf{F}}_{1}+\overrightarrow{\mathbf{F}}_{2}+\overrightarrow{\mathbf{F}}_{iii}$ . The goal of this traction system is to
have $\overrightarrow{\mathbf{F}}_{\text { total }}$ directly in line with the fractured femur, at an angle
of $xx.0^{\circ}$ higher up the horizontal. Observe (a) the bending $\theta$ required to
produce this alignment of $\overrightarrow{\mathbf{F}}_{\text { total }}$ and $(\mathbf{b})$ the magnitude of the
strength, $\overrightarrow{\mathbf{F}}_{\text { total }}$ that is applied to the femur in this case. (Presume the
pulleys are ideal.)
Nicholas K.
Numerade Educator
Problem 35
CE In Example $6-13$ (Connected Blocks), suppose $m_{1}$ and $m_{2}$ are
both increased by a cistron of 2 . (a) Does the acceleration of the
blocks increase, decrease, or stay the aforementioned? (b) Does the tension in
the cord increment, decrease, or stay the same?
Nicholas Chiliad.
Numerade Educator
Problem 36
CE Predict/Explain Suppose $m_{1}$ and $m_{2}$ in Example $6-14$
(Atwood's Motorcar) are both increased by 1 kg. Does the acceleration of the blocks increase, decrease, or stay the same? (b) Cull
the all-time caption from among the following:
\begin{equation}
\begin{assortment}{l}{\text { I. The cyberspace forcefulness acting on the blocks is the same, only the total }} \\ {\text { mass that must be accelerated is greater. }} \\ {\text { Two. The difference in the masses is the same, and this is what de- }} \\ {\text { termines the net forcefulness on the system. }} \\ {\text { III. The strength exerted on each cake is greater, leading to an in- }} \\ {\text { creased acceleration. }}\end{array}
\end{equation}
Nicholas M.
Numerade Educator
Problem 37
CE Three boxes of masses $thousand, 2 yard,$ and 3$1000$ are continued as shown
in FIGURE$6-52 .$ A strength is applied to accelerate the boxes toward the
right. (a) Rank the tensions in the ropes, $T_{i}, T_{ii}$ , and $T_{iii}$ , from smallest to largest, when the boxes are in movement and there is no friction
between the boxes and the horizontal surface, (b) Rank the tensions in the ropes, from smallest to largest, when the boxes are in
motion and in that location is a coefficient of kinetic friction $\mu_{\mathrm{thou}}$ between the
boxes and the horizontal surface.
Nicholas Chiliad.
Numerade Educator
Trouble 38
Find the acceleration of the masses shown in FlGURE $6-53,$ given
that $m_{1}=1.0 \mathrm{kg}, m_{ii}=ii.0 \mathrm{kg},$ and $m_{3}=three.0 \mathrm{kg}$ . Assume the table
is frictionless and the masses move freely.
Nicholas M.
Numerade Educator
Problem 39
Predict/Summate (a) If the hanging mass $m_{iii}$ in Effigy $half dozen-53$ is
decreased, will the acceleration of the organization increase, decrease,
or stay the same? Explain. (b) Discover the acceleration of the system
given that $m_{one}=ane.0 \mathrm{kg}, m_{2}=2.0 \mathrm{kg},$ and $m_{three}=0.l \mathrm{kg}$
Nicholas K.
Numerade Educator
Problem 40
Two blocks are continued past a cord, as shown in FlGURE $6-54$
The shine inclined surface makes an angle of $35^{\circ}$ with the horizontal, and the block on the incline has a mass of 5.7 $\mathrm{kg}$ . The mass
of the hanging cake is $m=3.2 \mathrm{kg}$ . Find (a) the management and
(b) the magnitude of the hanging cake'southward acceleration.
Nicholas Thou.
Numerade Educator
Problem 41
Predict/Calculate $\mathrm{A} 3.50-\mathrm{kg}$ cake on a smooth tabletop is
fastened by a cord to a hanging block of mass two.80 $\mathrm{kg}$ , as shown
in $\mathrm{FIGURE}{vi-55}$ . The blocks are released from residue and allowed to
motility freely, (a) Is the tension in the string greater than, less than,
or equal to the weight of the hanging mass? Notice (b) the acceleration of the blocks and (c) the tension in the string.
Nicholas M.
Numerade Educator
Trouble 42
Predict/Calculate $\mathrm{A} seven.7$ -N force pulls horizontallyona $1.6-\mathrm{kg}$ block
that slides on a smooth horizontal surface. This block is connected
by a horizontal string to 2nd block of mass $m_{2}=0.83 \mathrm{kg}$ on the
aforementioned surface. (a) What is the acceleration of the blocks? (b) What is
the tension in the string $?(\mathrm{c})$ If the mass of block 1 is increased, does
the tension in the string increase, decrease, or stay the aforementioned?
Nicholas K.
Numerade Educator
Problem 43
Predict/Calculate $\mathrm{A} vii.7$ -Northward force pulls horizontally on a 1.6 -kg block
of the 2 blocks in FlGURE $6-56$ (a). Presume the top block slides
without friction on the horizontal surface. (b) If the $12-\mathrm{N}$ block
in Effigy $6-56$ (a) is replaced with a 12 -N strength pulling downward,
as in Figure $vi-56(b)$ is the acceleration of the sliding block greater than, less than, or equal to the acceleration calculated in function (a)?
Explain. (c) Summate the acceleration of the block in Figure $six-56$
(b), bold it slides without friction.
Nicholas M.
Numerade Educator
Trouble 44
CE A automobile drives with constant speed on an elliptical rail, as shown
in Effigy $6-57$ . Rank the points $A, B,$ and $C$ in guild of increasing
likelihood that the car might skid. Indicate ties where appropriate.
Nicholas M.
Numerade Educator
Problem 45
CE A puck fastened to a string undergoes circular move on an air
tabular array. If the string breaks at the indicate indicated in FIGURE $6-58,$ is the
subsequent motion of the puck best described by path $\mathrm{A}, \mathrm{B}, \mathrm{C},$ or D?
Nicholas M.
Numerade Educator
Problem 46
BIO Bubble Net Fishing Humpback whales sometimes catch fish
by swimming rapidly in a circle, blowing a drape of bubbles that
confuses a school of fish and traps it in a small area, where the
whales tin easily catch and eat them. Suppose a $28,000$ -kg hump-
back whale swims at 2.2 $\mathrm{m} / \mathrm{s}$ in a circle of radius 8.5 $\mathrm{m} .$ What centripetal forcefulness must the whale generate?
Nicholas Grand.
Numerade Educator
Problem 47
When yous take your 1900 -kg automobile out for a spin, you go around
a corner of radius 53 $\mathrm{thousand}$ with a speed of 13 $\mathrm{m} / \mathrm{southward}$ . The coefficient of
static friction between the car and the road is 0.88 . Bold your
car doesn't skid, what is the force exerted on it by static friction?
Nicholas M.
Numerade Educator
Problem 48
BIO A Human Centrifuge To examination the effects of high dispatch on
the human body, the National Helmsmanship and Infinite Administration (NASA) constructed a large centrifuge at the Manned Spacecraft
Center in Houston. In this device, astronauts were placed in a capsule
that moved in a circular path with a radius of xv $\mathrm{one thousand} .$ If the astronauts
in this centrifuge experienced a centripetal acceleration ix.0 times
that of gravity, what was the linear speed of the capsule?
Nicholas M.
Numerade Educator
Problem 49
A motorcar goes around a curve on a road that is banked at an angle of
$21.5^{\circ} .$ Fifty-fifty though the route is slick, the car will stay on the road
without any friction between its tires and the road when its speed
is nineteen.viii $\mathrm{chiliad} / \mathrm{south} .$ What is the radius of the curve?
Nicholas M.
Numerade Educator
Problem 50
Clearview Screen Large ships oft have circular structures in
their windshields, as shown in Figure $6-59 .$ What is their purpose? Called clearview screens, they consist of a glass disk that
is rotated at high speed by a motor (in the center of the circumvolve) to
disperse rain and spray. If the screen has a diameter of 0.39 $\mathrm{m}$ and
rotates at 1700 $\mathrm{rpm}$ , the speed at the rim of the screen is 35 $\mathrm{k} / \mathrm{s}$ .
What is the centripetal dispatch at the rim of the screen? (A
large centripetal dispatch keeps liquid from remaining on the
screen. For comparison, call back that the acceleration due to gravity is ix.81 $\mathrm{1000} / \mathrm{southward}^{2}$ .
Nicholas Chiliad.
Numerade Educator
Problem 51
Predict/Calculate (a) As yous ride on a Ferris wheel, your
apparent weight is dissimilar at the summit than at the bottom.
Explain. (b) Calculate your apparent weight at the summit and bot-
tom of a Ferris wheel, given that the radius of the bicycle is $7.2 \mathrm{m},$ it
completes one revolution every 28 $\mathrm{s}$ and your mass is 55 $\mathrm{kg}$ .
Nicholas M.
Numerade Educator
Problem 52
Driving in your automobile with a constant speed of $v=22 \mathrm{m} / \mathrm{south},$ y'all
encounter a bump in the road that has a round cross section, equally
indicated in FIGURE $6-60 .$ If the radius of curvature of the crash-land is
$r=52 \mathrm{m},$ find the apparent weight of a $67-\mathrm{kg}$ person in your automobile as
you pass over the top of the bump.
Nicholas K.
Numerade Educator
Trouble 53
CE If you weigh yourself on a bathroom scale at the equator, is
the reading you get greater than, less than, or equal to the reading
yous go if you weigh yourself at the North Pole?
Nicholas M.
Numerade Educator
Problem 54
CE BIO Maneuvering a Jet Humans lose consciousness if exposed
to prolonged accelerations of more nearly 7$g .$ This is of business concern to jet fighter pilots, who may experience centripetal accelerations of this magnitude when making high-speed turns. Suppose nosotros would like to decrease the centripetal acceleration of a jet.
Rank the post-obit changes in flight path in guild of how effective they are in decreasing the centripetal dispatch, starting
with the least effective: A, subtract the turning radius by a factor
of two; $B$ , subtract the speed past a cistron of three; or $C,$ increase the
turning radius by a factor of four.
Nicholas One thousand.
Numerade Educator
Problem 55
CE BIO Gravitropism As plants grow, they tend to align their
stems and roots along the direction of the gravitational field. This
tendency, which is related to differential concentrations of plant
hormones known as auxins, is referred to as gravitropism. Every bit an illustration of gravitropism, experiments show that seedings placed in
pots on the rim of a rotating turntable do not grow in the vertical
direction. Do y'all wait their stems to tilt inward- toward the axis
of rotation-or outward- away from the axis of rotation?
Nicholas M.
Numerade Educator
Problem 56
BIO Homo-Powered Centrifuge Ane of the hazards of prolonged
weightlessness on long space missions is bone and muscle loss. To
combat this trouble, NASA is studying a man-powered centrifuge, like the 1 shown in Figure $6-61 .$ In this device, one astronaut pedals a suspended, bike-like contraption, while a second
astronaut rides standing up in a similarly suspended platform. If
the continuing astronaut moves with a speed of 2.7 $\mathrm{m} / \mathrm{s}$ at a distance
of 2.9 $\mathrm{m}$ from the center of the device, what is the astronaut'due south
centripetal dispatch? Give your reply equally a multiple of $thou,$ the
acceleration due to gravity on the surface of the Earth.
Nicholas M.
Numerade Educator
Problem 57
Predict/Calculate $\mathrm{A} 9.three$ -kg box slides across the floor of an lift with a coefficient of kinetic friction equal to 0.38 (a) What is
the strength of kinetic friction acting on the box when the elevator is at
rest? (b) If the elevator moves upward with constant acceleration, is
the forcefulness of kinetic friction acting on the box greater than, less than,
or equal to the value found in role (a)? Explain. (c) Determine the
force of kinetic friction interim on the sliding box when the lift
moves upward with a constant acceleration of 1.4 $\mathrm{m} / \mathrm{south}^{2}$ .
Nicholas K.
Numerade Educator
Problem 58
A child goes downwards a playground slide that is inclined at an bending
of $26.5^{\circ}$ below the horizontal. Detect the acceleration of the child
given that the coefficient of kinetic friction between the kid and
the slide is $0.315 .$
Nicholas M.
Numerade Educator
Problem 59
Spin-Dry Dragonflies Some dragonflies splash downwardly onto the
surface of a lake to clean themselves. After this dunking, the dragonflies proceeds altitude, and and then spin rapidly at about 1000 rpm
to spray the water off their bodies. When the dragonflies do this
"spin-dry," they tuck themselves into a "brawl." If they spin with a
linear speed of two.3 $\mathrm{thou} / \mathrm{s}$ , and curlicue into a brawl with a radius of $1.one \mathrm{cm},$
what is the centripetal acceleration they produce?
Nicholas Thousand.
Numerade Educator
Trouble 60
The da Vinci Code Leonardo da Vinci $(1452-1519)$ is credited
with being the offset to perform quantitative experiments on friction, though his results weren't known until centuries later, due in
office to the hugger-mugger code (mirror writing) he used in his notebooks.
Leonardo would identify a block of wood on an inclined airplane and
measure the angle at which the block begins to slide. He reports
that the coefficient of static friction was 0.25 in his experiments.
At what angle did Leonardo'south blocks begin to slide?
Nicholas Thousand.
Numerade Educator
Problem 61
A iv.five -kg sled is pulled
with constant speed across
a crude, horizontal surface
with diverse amounts of
weight added to the sled.
Data showing the required
force for several different
amounts of added weight
are given in the tabular array.
Plot the data and determine the coefficient of kinetic friction between the sled and the horizontal surface.
Nicholas Thousand.
Numerade Educator
Problem 62
A 0.045 -kg golf ball hangs past a cord from the rearview mirror
of a car, as shown in FIGURE $6-63 .$ The auto accelerates in the forward
direction with a magnitude of 2.1 $\mathrm{m} / \mathrm{southward}^{2}$ . (a) What bending $\theta$ does
the string brand with the vertical? (b) What is the tension in the
string?
Nicholas Thousand.
Numerade Educator
Problem 63
A physics textbook weighing 22 $\mathrm{N}$ rests on a desk-bound. The coefficient of static friction between the volume and the desk is $\mu_{\mathrm{s}}=0.threescore \mathrm{j}$
the coefficient of kinetic friction is $\mu_{\mathrm{1000}}=0.40$ . You push horizontally on the book with a forcefulness that gradually increases from 0
to $15 \mathrm{N},$ and so slowly decreases to $v.0 \mathrm{N},$ as indicated in the
tabular array below. For each value of the applied force given in the table,
requite the magnitude of the force of friction and country whether the
volume is accelerating, decelerating, at rest, or moving with constant speed.
Nicholas M.
Numerade Educator
Problem 64
Predict/Calculate The blocks shown in FIGURE $half-dozen-64$ are at rest.
(a) Find the frictional force exerted on block $A$ given that the mass
of block $A$ is 8.82 $\mathrm{kg}$ , the mass of cake $\mathrm{B}$ is $2.33 \mathrm{kg},$ and the coefficient of static friction betwixt block A and the surface on which it
restsis $0.320 .$ (b) If the mass of block $A$ is doubled, does the frictional
force exerted on it increment, decrease, or stay the aforementioned? Explain.
Nicholas Thousand.
Numerade Educator
Problem 65
A Conical Pendulum $\mathrm{A} 0.075-\mathrm{kg}$ toy aeroplane is tied to the ceiling
with a string. When the plane's motor is started, information technology moves with a
constant speed of 4.47 $\mathrm{m} / \mathrm{s}$ in a horizontal circle of radius $1.28 \mathrm{m},$ equally
illustrated in FIGURE $6-6.65$ . Find (a) the angle the string makes with
the vertical and (b) the tension in the string.
Nicholas M.
Numerade Educator
Trouble 66
A tugboat tows a clomp at abiding speed with a 3500 -kg cablevision,
as shown in Effigy $6-66 .$ If the angle the cable makes with the horizontal where information technology attaches to the clomp and the tugboat is $22^{\circ}$ , find
the force the cable exerts on the clomp in the forward management.
Nicholas M.
Numerade Educator
Problem 67
Predict/Calculate Ii blocks, stacked one on top of the
other, can movement without friction on the horizontal surface
shown in Effigy $6-67 .$ The surface between the two blocks is
rough, however, with a coefficient of static friction equal to
0.47 (a) If a horizontal force $F$
is applied to the five.0 -kg bottom
block, what is the maximum
value $F$ can have before the
2.0 - kg superlative block begins to sideslip? (b) If the mass of the tiptop cake
is increased, does the maximum value of $F$ increase, subtract, or
stay the aforementioned? Explain.
Nicholas Thou.
Numerade Educator
Problem 68
Predict/Calculate In a daring rescue by helicopter, 2 men
with a combined mass of 172 kg are lifted to condom. (a) If the helicopter lifts the men straight up with constant dispatch, is the tension in the rescue cable greater than, less than, or equal to the combined weight of the men? Explain. (b) Determine the tension in the
cable if the men are lifted with a abiding acceleration of 1.10 $\mathrm{m} / \mathrm{s}^{ii}$ .
Nicholas M.
Numerade Educator
Problem 69
Predict/Calculate A light jump with a force constant of
thirteen $\mathrm{N} / \mathrm{k}$ is connected to a wall and to a ane.2 -kg toy bulldozer, as shown
in FIGURE $6-68 .$ When the electric motor in the bulldozer is turned
on, information technology stretches the spring for a distance of 0.45 $\mathrm{thou}$ before its tread
begins to sideslip on the floor. (a) Which coefficient of friction (static
or kinetic) can be determined from this information? Explicate.
(b) What is the numerical value of this coefficient of friction?
Nicholas M.
Numerade Educator
Problem seventy
Predict/Calculate
The blocks in FIGURE $6-69$
have an acceleration of magnitude
$a=ane.1 \mathrm{m} / \mathrm{due south}^{2} .$ (a) Is the
tension in the string
greater than, less than,
or equal to $(1.5 \mathrm{kg}) \times$
(9.81 $\mathrm{yard} / \mathrm{due south}^{ii} ) ?$ Explain.
(b) What is the tension
in the string connecting
the blocks? (c) What is the magnitude of the forcefulness of kinetic friction
acting on the upper block? (d) What is the coefficient of kinetic friction between the upper block and the horizontal surface?
Nicholas One thousand.
Numerade Educator
Problem 71
Predict/Calculate Playing a Violin The tension in a violin cord is
two.7.N. When pushed down confronting the neck of the violin, the string
makes an angle of $4.ane^{\circ}$ with the horizontal. (a) With what forcefulness
must you push down on the string to bring it into contact with the
cervix? (b) If the angle were less than 4.1' , would the required forcefulness
exist greater than, less than, or the same as in part (a)? Explicate.
Nicholas M.
Numerade Educator
Trouble 72
Predict/Calculate $\mathrm{A} ix.8$ -kg monkey hangs from a rope, as
shown in FIGURE $6-seventy .$ The tension on the left side of the rope is $T_{1}$
and the tension on the right side is $T_{2}$ . (a) Which tension is largest
in magnitude, or are they the same? Explicate. (b) Decide the
tensions $T_{i}$ and $T_{2}$
Nicholas Grand.
Numerade Educator
Trouble 73
Equally your aeroplane circles an airport, information technology moves in a horizontal circle of
radius 2300 $\mathrm{m}$ with a speed of 390 $\mathrm{km} / \mathrm{h}$ . If the lift of the airplane's
wings is perpendicular to the wings, at what angle should the
aeroplane exist banked so that it doesn't tend to slip sideways?
Nicholas Chiliad.
Numerade Educator
Problem 74
At a playground, a $22-\mathrm{kg}$
child sits on a spinning
merry-go-circular, as shown
from above in FlGURE $6-71$ .
The merry-go-round completes one revolution every
$6.2 \mathrm{due south},$ and the child sits at
a radius of $r=1.4 \mathrm{g} .$ (a)
What is the force of static
friction interim on the
kid? (b) What is the minimum coefficient of static
friction between the child
and the merry-go-round to
keep the child from slipping?
Nicholas M.
Numerade Educator
Trouble 75
A 2.0 -kg box rests on a plank
that is inclined at an angle of
$65^{\circ}$ to a higher place the horizontal. The
upper end of the box is fastened
to a jump with a strength constant
of $360 \mathrm{N} / \mathrm{m},$ equally shown in FIGURE
$6-72$ . If the coefficient of static
friction between the box and
the plank is $0.22,$ what is the
maximum amount the leap
tin can be stretched and the box
remain at remainder?
Nicholas M.
Numerade Educator
Problem 76
A wood block of mass $m$ rests on a larger wood block of
mass $Chiliad$ that rests on a wooden table. The coefficients of static
and kinetic friction betwixt all surfaces are $\mu_{\mathrm{s}}$ and $\mu_{\mathrm{k}}$ , respectively. What is the minimum horizontal strength, $F$ , practical to
the lower block that volition crusade it to slide out from under the
upper block?
Nicholas M.
Numerade Educator
Problem 77
A hockey puck of mass $grand$ is attached to a cord that passes through a pigsty in the center of a table, as shown in Effigy $6-73$ . The hockey puck moves in a circle of radius $r$ Tied to the other end of
the string, and hanging vertically beneath the tabular array, is a mass $M .$
Bold the tabletop is perfectly smoothen, what speed must the
hockey puck have if the mass $M$ is to remain at remainder?
Nicholas Chiliad.
Numerade Educator
Problem 78
Predict/Calculate A popular ride at entertainment parks is
illustrated in FlGURE $6-74 .$ In this ride, people sit in a swing that is
suspended from a rotating arm. Riders are at a altitude of 12 $\mathrm{thou}$
from the centrality of rotation and move with a speed of 25 $\mathrm{mi} / \mathrm{h}$ .
(a) Find the centripetal acceleration of the riders. (b) Discover the
angle $\theta$ the supporting wires make with the vertical. (c) If you
observe a ride similar that in Figure $six-74,$ or every bit shown in the photo on
page 178 , y'all will discover that all the swings are at the same angle $\theta$
to the vertical, regardless of the weight of the rider. Explicate.
Nicholas M.
Numerade Educator
Problem 79
A Conveyor Belt $A$ box is placed on a conveyor belt that moves
with a constant speed of 1.25 $\mathrm{m} / \mathrm{s}$ . The coefficient of kinetic friction between the box and the belt is $0.780 .$ (a) How much time
does it accept for the box to cease sliding relative to the belt? (b) How
far does the box motion in this time?
Nicholas Yard.
Numerade Educator
Problem 80
As part of a circus act, a person drives a motorcycle with
constant speed $v$ around the
inside of a vertical track of radius
$r,$ as indicated in Effigy $6-75.$
If the combined mass of the
motorcycle and rider is $m,$ notice
the norcycle and passenger is $k,$ notice
motorcycle by the track at the
points (a) $A,($ b) $B,$ and (c) $C .$
Nicholas M.
Numerade Educator
Problem 81
On the direct-line segment Two in Figure $6-76$ (b) we see that
increasing the applied mass from 20 $\mathrm{thousand}$ to 25 $\mathrm{yard}$ results in a reduction of the finish-to-terminate distance from 42 $\mathrm{mm}$ to 24 $\mathrm{mm} .$ What is the force abiding in $\mathrm{N} / \mathrm{m}$ on segment II?
\begin{equation}
\begin{assortment}{ll}{\text { A. } 0.28 \mathrm{N} / \mathrm{thousand}} & {\text { B. } 0.37 \mathrm{Due north} / \mathrm{m}} \\ {\text { C. } 2.vii \mathrm{N} / \mathrm{thousand}} & {\text { D. } 3.6 \mathrm{N} / \mathrm{one thousand}}\end{array}
\end{equation}
Nicholas M.
Numerade Educator
Trouble 82
Rank the straight segments $1,11,$ and lII in lodge of increasing
"stiffness" of the nasal strips.
Nicholas M.
Numerade Educator
Problem 83
In use on a typical human olfactory organ, the stop-to-finish distance is measured to exist 30 $\mathrm{mm}$ . What force does the strip exert on the nasal
passages in this situation?
\begin{equation}
\begin{assortment}{ll}{\text { A. } 0.23 \mathrm{N}} & {\text { B. } 0.69 \mathrm{N}} \\ {\text { C. } nine.0 \mathrm{N}} & {\text { D. } 2 \mathrm{N}}\stop{array}
\end{equation}
Nicholas K.
Numerade Educator
Problem 84
Predict/Calculate REFERRING TO Instance $vi-3$ Suppose the coefficients of static and kinetic friction betwixt the crate and the truck
bed are 0.415 and $0.382,$ respectively. (a) Does the crate begin to
slide at a tilt angle that is greater than, less than, or equal to $23.2^{\circ}$ ?
(b) Verify your answer to role (a) by determining the angle at
which the crate begins to slide. (c) Find the length of fourth dimension it takes
for the crate to slide a distance of 2.75 $\mathrm{thousand}$ when the tilt bending has
the value found in function (b).
Nicholas M.
Numerade Educator
Trouble 85
Predict/Calculate REFERRING TO Case $half-dozen-3$ The crate begins to
slide when the tilt angle is $17.5^{\circ} .$ When the crate reaches the bot-
tom of the flatbed, later sliding a distance of $2.75 \mathrm{one thousand},$ its speed is
3.11 $\mathrm{m} / \mathrm{due south} .$ Detect (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the crate and the flatbed.
Nicholas Thousand.
Numerade Educator
Problem 86
REFERRING TO EXAMPLE $6-13$ Suppose that the mass on the frictionless tabletop has the value $m_{1}=2.45 \mathrm{kg}$ . (a) Find the value of
$m_{2}$ that gives an acceleration of two.85 $\mathrm{m} / \mathrm{s}^{2} .$ (b) What is the corresponding tension, $T$ , in the string? (c) Calculate the ratio $T / m_{ii} yard$
and testify that it is less than $1,$ as expected.
Nicholas Grand.
Numerade Educator
Problem 87
REFERRING TO Example $6-15$ (a) At what speed will the force of static
friction exerted on the car past the road be equal to half the weight
of the car? The mass of the car is $grand=1200 \mathrm{kg},$ the radius of the
corner is $r=45 \mathrm{1000},$ and the coefficient of static friction between the
tires and the route is $\mu_{ten}=0.82 .$ (b) Suppose that the mass of the car
is now doubled, and that it moves with a speed that again makes
the force of static friction equal to half the car'due south weight. Is this new
speed greater than, less than, or equal to the speed in role (a)?
Nicholas M.
Numerade Educator
Source: https://www.numerade.com/books/chapter/applications-of-newtons-laws/
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