Why does a child in a wagon seem to fall backward when you give(qcrktz9)r gd,le9uitl 9*o 7 the wagon a sharpo9*tz9gl79 eq)i cr t(kd,lur pull forward?

A box rests on the (fb pvv5f nja5 1 f4a7.h0p(p u7c4cpbxcrictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the trvcx(7f a15njcafb7p5.vp cu 4 ph40bpuck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces actingj0- m2mr9wksf5k4i bg on it? Explain.

Only one force acts on an object. Can the object have zero accelertsu,oh 1c /n4oif.-lk ation? Can it have zero velocity? Explain.ou fls,.nto 4/k -hic1

When a golf ball is dropped txj3v.:utqc+lgln-4m;bq a 6mo the pavement, it bounces back up. (a) Is a force needed to make x u:m;tj36 q+lm. 4 nabgclq-vit bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why doe8rno s/v(x +o;n.0 yzmlr*gets the log move in the oppositen lye/n0+ot; og r vs8*x(mr.z direction?

Why might your foot hurt if you kick a heavy txov79,pt ,ehdg6 ts5 desk or a wall?

  When you are running ga 7,q:4gyb xpand want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person rx a4:g bgp7,yqunning at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a1fn0- qsob/2xnx*u l)ui hb8a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone l xh/us0-f b a8b)u2i *xq1onnor above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as greatmg.*7*cgscad / h( yz eeogut5 rp; c+b,3mqw( as that on a 1-kg rock. Why then doesn’t the heav r sb/uzh+.gyc*e(m5w gmc ;ctpdg(q *e,a 7o3ier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale,,om/m:9 ( kz 7egthp:sizble had been calibrated (a) in pounds,:p:t 9egm/l ,e bz,o7k hzi(sm or (b) in kilograms?

You pull a box with a constant force across a frictionless table us;deo. x77 s2atyp/ oujing an attached rope held horizontally. If you now pull the rope with the same force at xa ts;edp27j/. ouy o7an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely d)1uyz.w mf (d:mm7* hpn ayp9hkfc53 under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doe9h1mfdyd(:) uynckmzap5 w.* 3 f 7phmsn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object g 14(6ds j-s xyfg4 wnbu5h2rowhen you are on the Moon with the force needed to lift it on Earth. Compare the force needed to thr d yh b gs4fr(gx4s2ju51o6wn-ow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of ouy/k 4uu l.l.pk8 rw(war (Fig. 4–37) pulls with equal force on the other team. What, then, deteo(wu/uykr8.4l ukp l. rmines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocerieutpw p9u2kgorta ss 36w35( sn f66el6s. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (bu os( st6earsp3n2t 66wu9p3lw5kg6f ) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how largev4 y9z1b tw 4n 5fb)eu )i9(xtsnq3gsl a force does the ground exert on you? Why doesn’t thi5s 1x t (g)9n 93bsiq4tyz)4ve nwlfubs force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the 63 tmlwrqyux)k7 7o :rvictim’s car is struck violently from the rear. Explain why the head of the v76ou:qr lr kxywt3m)7ictim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whe(q3otfrooo n:q8 5;yuzx*: pb n the truck accelerates, the crate remains where it poonf*b3: ;y 5orox(qzt :uq 8is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it sy7b d dajqol4ll okl 2ns;55.0lides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleratio.dal ;5b s5y2 o 7koqld4ll0jnn is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself oi1 sm cn9w9qodz n8l8;n an inclined plane? Assd8mi1oz9nswlc8n9 ; qume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a satlb) d)hxr v.wqn-y5 ,8aa 6j.f 8zwsled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike andt0h-h9v kxv ldk74dt+ rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope dhyuk(e+1ze( withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a vutk kbc-2q vd(0./i6tvh .pk $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if tzwfwm- dj9)jonv mb ge24j ,.3he car is traveling at 95km/h?v9 -o)2.f,jwgn zjj4 b m3mewd -  

  What average force is needed to accelerate a 7.00-gram pelle- fsj9i dipz61t from rest to 125m/s over a distance of 0.800 m along pizd s61j9i-fthe barrel of a rifle?   

A fisherman yanks a fish vertically out of the wat7y- :cbl29:j-wnqh* loy+(kzvirok rer with an acceleration of 2.+r oo qrk2j-zvkw l h9ln:c-y( *7iyb:5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mil171 lbaj7a3 s/rd mopee track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg )5)bkikg4 7bqq is to be designed so that the maximum acceleration is k7k bgqbq)i54 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When the elevator n c719qpn9uz3g2n +dnu rz j8zbegins to move, the scale briefly reads ozn293n1gpzcq n97u +n 8jdrzunly 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 24om2yor mon87125-kg elevator has a maximum strength of 21,750 N. What maximum upward acce 28oomny7r4om leration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg es/be,o nnq,2 including para,obnes2q /n, echute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground b5b) 1bn (jxsjzelow, he bends his knees so that his torso decelerates over an s bj)nbj1(z 5xapproximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the b..m+sre3lu nw qf ej);ox runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the othe3;m n.s rquw.+ jlef)er side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram foriqo/mc l5 tzj,l4pr 3- a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momenty.l, msq9k)t4 vdcmsbwel7 (( it is hit by the bat, and again (b) aftek lmedyvstmc ,4b7.(s(l9 wq) r it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A secorl fazwla74 86x16rd/iqg:ex nd 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your anie 8rxa r6fwag/z1ll7q x4:6d swer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontal)p;r vg5g9dyxf1*y ml ly between two buildings 10.0 m apart. The sag in the rope when she is at the)yrmf xypg*v1 l9;d5g midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from g 2 sn1;ymcprdk499jr another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.ubka yv/ +s7*,ox841v9: clmb iq+,ks uxjist0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctikr1wpo1 ;oxct2s6 qf(8kb dw *a 0gt3uca, as shown 6rw*xatq10(28 ;bptgoc w1 ds ou3kkfin Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is puk*)qw+ o 1z04usk 5gyldxk /zllling two cars of the same mass behind it, Fig. 4-47 . Determine tzx1ld0go su)l qk z/y+kk*w54he ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls s4wif:0r8 gts) jwsx: herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hers0)4is t : fwgsrjx:sw8elf slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, amndj- zdtp h .7q9 j0da;x7ld+ 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (masupa, 8rgajn7*p kk. 2ks $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surfaceujx ij ;l47i 0;dzu)uv are in contact with each other, as 4 0uv zxj);iiu;udj7l shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52phl7d.fr9c,s/ p/czy are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is relepz,fhpd ./rl7ycs/9 cased? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are c zhf(8 za:fg:donnected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each bo::df zaz(8 fhgx and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frict:sigqa uo k*k--5auf(ira)yjsb3 i:3ion between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is ruqg9), sjjri/equired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a trai 5+lexuw m2e wmj7qh(:oti7 e/zn+t6en accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if zjox teh/emqw6u+wn+ me2el :7t(75 iyou are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffil(ljl4m *m)o qmr2 +fd,j/7hu8 eajg byj4aq4cient of static friction betwe,4)uqeg *4a 2 dq rh+f/mj m 7(a8j4lbjlylmjoen the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pave iwz(sz p k*rn8a4 7;m hfp;gxd33bjd-ment is about 0.8. On how steep a hill (maximum angle) can you leave a j 3mxa;;kgwsp3df*(zrn7i- hdp8 z4 bcar parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -lkd7g io8 3ykr-8id/r4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a roughv)mw /gu vz+eege7m )* 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt po4fjz/x pbxd:v07 g1l*gjv1 surface have a very high coefficient of static friction.0*b/1o p4lgzdvjxj7gf 1vxp:

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinmby (cs709cgsetic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4hb9y7 k1 p1 a:d5a syvs6otjp4-32 (Example 4-20) how large a mass would box A have to have to prevent any mb saykpvp1 ty5ho:d1 6ja97s4otion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will cqpq9;+b * ld,r1f5vgkv, pe fit go, given that the coefficient of kinetic f5+1 qlrkpc;e gvvf*9 fpqdb, ,riction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , ax/yldc r n2ub1a5qs g(4o(c2+3fw ddcre in contact and at rest on a horizontal surface (Fig. 4-54). A 65 d2w1scx+(l2o 3 qc/gy(rb4dcduan f20$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefgon :k:81+sh4t 5b az.eak 9ekgcdi:uficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelera+e: k5.ab h1sik g:ugkn8d9tcza:4oete and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in/m tp ck5g-lu (0 8kmyuq*jbl0 your driveway, which has an incline of m 80/clqk*5ty m kj(-0uplgub 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide w1qmu d* g9n z(yrcj9l;ith a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilte .pz4.a)q oq- laf.yufi ljc9x/ 3nb0hd at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3. (kxkvyr)2s j:0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches thlrp-pli-0dnl 0vzp5 s7 lu3.ue top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by someone pushg9n(8a1jw gcna zpdo 8uoyx5-w;,4bcing on it with a force directed upward at 2 zcn58gcy pw;ga x-bn4u(8a o,djo91w8$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become danr cyyat s4m;(*lz7 5uxgerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with asy ;yxrulz75 4*(atcm pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping hvpq8qz9v ;/cx mni5 d;0whxyl(jx3( distance for an automobile traveling at speed v is equal3 qv(h/;d5l n jxxchi9mqv 0x zpy;(8w to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dashq1miwgy4 (bh/ when the driver decelerates f4 1(q/bywgi hmrom 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given l/junoiw -elhr.7 9m+: x 0qwsan initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are f gbm2*mm nw 3r hv,df;9qhx19filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero ;13 w*hfrgmnqd9bf mxm9,h2v speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient o,(p7yb;-p tr.kegzgc f kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast downoc)g*q0xc(bg u* ;ybp a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplifir9c c.5w5xeh nh+eu ,ted model of a mammalian heart, at each pulse approximately nc xe5ct rue95. h+,hw20 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surz/y03k z;g4n5fuc+nrh a ks.9wky: pr viving an automobile crash if the deceleration is no more than 30 " g 's."kp9/syfrn+ku cgk.:;zzhran 453y w0 Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by anin urvu1(zz4) earthquake is a , and if an object is (4ru)1uiznvz going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the 0:n 5 omeivs1f5zz gu -):cbfkscene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate)kov e05:s- f5:cfm1 izbu ngz the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 w fpi-af6a;zaz 0lc)w7i m4:om traveled along the road, the elevation change is 1 m). How fasiiw: ;clm )pa azf-640zawo7 ft is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from theud39f/9tqq2oj 4 md6q b nyk1e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forceq nfm9t 1j9u4qbded/2k6oy3q of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wa;p44cgd6t(vpw ;qw hhere the effective coefficient of frictigva qh;t4;d(pwp wc64on is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is workkt;zv gz+* -ftdm9cf3hw50 aeing on the redesign of a hilly portion of a city. An important consideration is 9dg0 kzw+ft-ma3 z c5*hetv;f how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch fromx8p)s s:cg;n ae4.ujdu*7 n(nd . cedx a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig.n*8.pddxc :(;n ena4 uxud)gj sse7 c. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be s lxmd n-y7)1ajeveral ramps connecting different parts of the 71n-xam l)ydj store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift thetdzx : 3 wy*cuhi6o54n piano (mass M ) using the pul cto3 inyuz6 wh*5:4dxley apparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accev q9e a90dy3+vm fhyk5lerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraind v 20. 9wff,w5gzupjgt chair, an engineer considers the followingfvgd,f9pwgzu 0 2. wj5 set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian trajnr rnz392gos2e2 8coin has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of sim0wdcwtj26 -n rilar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming t- c wjrn2tw0d6hat the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " n ;ugno9eg 6jqfq14c0q:qc4 u10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 9hv7a6bu ywx 4 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers w14zwoik0 *i efho are roped together are ascending an ice field inclined at i1kwz0ofie 4* 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.