Why does a child in a wagon seem to fall backward when you giv .0su 6qcnm wfw( 9bnht,o;w2ye the wagon a sharp f0 tw cb;w2 wn nohu9(6y,.mqspull forward?

A box rests on the (frictionless) bed of a truck. The truck driver sl uirqci73teq: 6v(*k tarts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the kl*3i6 :r(ieq vu7qct 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 acting on it? Ex,yn 3.7tuvaxzm2:c52hbkf 5f zmxx1 p plain.

Only one force acts on an object. Can the obj1jhos3 b :w ewr:*3qpmect have zero acceleration? Can it have zsemb o:w *pqjhw:3r13 ero velocity? Explain.

When a golf ball is dropped to thbs i+q0mor *g0e pavement, it bounces back up. (a) Is a force needed to make it bir+b so00 mqg*ounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppowf/sprfmnfc3ri908td5z .4 ml1m w m2site di z0md. mtfl23i84s/rfw19mpc rwmn f5 rection?

Why might your foot hu ht(+a:yxng+l rt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quic:t13et psf0ojncqxnsw //vfhz7 / +:ckly. (a) What is the origin of the forc 71e3 cnoc zvt wpq+s:/x0n:t/fsjh/fe that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a rd):owg9 9hl8s w0divsection 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 or above it? What ifh9lg:) 9wdsod8w0riv the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg,h: ,zjgvyse my, .ea5 rock is twice as great as that on a 1-kg rock. Why then doesn’t theh,zvgm y: ,es.,yja5 e heavier rock fall faster?

Would a spring scale carried to the Moonbqdz;-n e8(siiy 4ezxu; 2 lilb2n8f,q 2u-ux give accurate results if the scale had been calibrated (a) in pounds, or (b) (lz;by 2lie8z q u2qnxufui,42i;-sdx ben-8 in kilograms?

You pull a box with a cons+omoklr * q6 dhjg*.-stant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box6d**g-+. hos k qlojmr 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 under the inxvz g0 pi.b:7nfluence of gravity there is a net force mg exevxgn7:i0p z.b rted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) need9lq2,c*d,kdld1 efe ked to lift a 10-kg object when you are on the Moon with the force neel,ee91 ddkdq*kfl, 2 cded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, e-j- .xd vcduf5ach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determ5dv .fux--dj cines which team will win?

A person exerts an upward force of 40 N to hold a bag x fl c,pie)1b1rgl8r,of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magn1plxgc,ifbr) 1,e 8rlitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on tbhrgqz77(b , ihe ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the air,h7g7 bqz bir(?

Whiplash sometimes results from an tknn zv-40h5zautomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatih4v n 5kz0-znton. Is it really?

A heavy crate rests on the begntklu*oz0 w4gy:x:w dv* : r.d of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, acceleratewod::.gr4uv**g yw l :zkntx 0s. What force causes the crate to accelerate?

A block is given a push so that it slides ux /t;rn r:t2 dr mz,0py9gyu0pp a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the desce/ trnypm z2 ugrdy0t: p9x0;r,nt than on the ascent. Why?

What would your bathroom scale read if you weighed yoursk6y8imk 1 .l6 a;uecii3x6z:xdza /xxelf on an inclined plane? Assume the mechanism functions properly, even at ayu6a i.ki x63d/xkazxe8; x lzic1 m:6n angle.

  What force is needed to accelerate a child on a sled at 1.2gl:hj.l-(8 x rsvpjg,6. nyaz5m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30dan-ur)zk. , j$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mus9ey :1d 5gxifdt a rope 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 +ayxd*,95 ksrgy.n)v w;zj :oynqe;fh;yf;q $76-\mathrm{kg}$ 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 r5x 2b9 ;d)iqx1xi iqwhequired to stop an 1100-kg car in 8.0 s if the car is traveling at 95kmq x29w;iq5bdx1 ixi )h/h? -  

  What average force is needed to accelerate a 7.00-gram pell, bshycw 2h;9lngd.:b et from rest to 125m/s over a distance of 0.800 m along the barrel of dhln,;2gwych .9: bbs a rifle?   

A fisherman yanks a fish 5 kr)gze-k3:9e8qqz +dpyu 4ted ht0dvertically out of the water with an acceleration of 2.r54:hkqtg-pdu z3k+y t )dd80e9ez e q5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track (4qga;tju)wztre;c *4: 02 $\mathrm{~m}$) 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 ) is to be designed so that the maximum 1 cb ammzn4e/u3q 4c)d8x:ntb acceleration is 0.0680 g . What are the maximum and minimum forces the moton3mxdu bc4c8tbaz: n4e/mq 1 )r 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 dflmqwh+4 f-.e9o nk) motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elk -)hnoq el+ dm.9wf4fevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stretc6 a067c 7sg n(t4 xktl(itegngth of 21,750 N. What maximum ux0 ite(( 477a6ccnts gttk6lgpward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleh) tgblt8 whj7 b4q7.nration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth 7l74ht bj g .8htwqnb)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-egckn 9hci.)r sn7 1b7m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance o9 h i1.n cbcekrg7)sn7f 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 re.* sew +c-jdshlx 4k7ists on a table. A rope tied to the box runs vertically upward over a7shex w*-4idkl + .scj 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 other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dingrgny 3/x)9 lh(aa8mxt bl/; agram for 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 basebaue;l0axe-6y/rw: yxk ll (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flr/k yu:ax;wxee0 6y -lying toward the outfield.

A 650-N force acts in a northwesterly direction. A second h;;gds6,alnw.p.qg fd x4vp* 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answ ldvs ;4; ,d. q.6ahgfwgnp*xper with a vector diagram.

  Arlene is to walk across a "high wire7tncj y vt3b6rv4 .jn;" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10jtj vn ;t367b4 .vncyr.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 massl ew k4tb+ ec7o;sc0;dvr*a/aj ess cord from 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.xz+62x oc s,px0$-\mathrm{kg}$ 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 Bas/7u47onpbrzb 4c me5s e, Antarctica, as shown in Figsp5/ 47bu 4m erncb7oz. 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 pulling two cars of the same mass behin/w8g c(eknl 2g :n en*(ej;rwgd it, Fig. 4-47 . Deter/(*(l :gk e;ecew gnjgnrn28 wmine the 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 herv-v ltplkm:2ha3z /th8 wv/2eka t)vtb. b n4.self upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to kbt tevav2l.p l 3k)m8v/42zv bwh.th/:-atn raise herself 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, a 6y02,n:xew abq2b f(kx;v p8rh5$-\mathrm{kg}$ 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 (mass7rvs :jiw+xy - $ 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 hjyrma52vmk 6* o38y q mhr/4 mc:0klbvorizontal surface are in contact with each other, as shown in F mykjvhmb 5rvalmk04o8m:2yqr6 3 c/* ig. 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. 4-52 are each in8vkg)t m.g*a7 ,i tntditially 1.80 m above the ground, and tig7. m)gank ,8t*d vtthe massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [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 connected by a heavy cord of mal-muh a hx1*(hss 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53ahh(1mhl- *xu. 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 frictionr585+ljdpw1r8r0ni+ oat x(w ud *;ci: gomlf 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 require9 ay7ln,jzvg0+ )f vybd 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 stave,pc5:6y;vya 3)i t:tryi 3iq. dbynnding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist betw3dyitqbp: 6cn:, eayyr ) 3;yiitvv.5een your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficieg;nkndt;q2*wn rdvn;5rg.i 6 nt of static friction bd *n .;gvwrq n;;n26trki5ngdetween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber 99oze 7w1xigv(zl ;paand normal street pavement is about 0.8. On how steep a hill (maximum ang (;zwea7zpx1gliov99le) can you leave a car 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 l ltd34 sm u1kds85k2m -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 reili3 9al.4uol f0 uls.l6a ufg o.:vk1st on a rough 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 surface have a very high coefficient zz i-y n85.)qhmczdw5oq h 5mz-.n 8)ydwcziz5f static friction.

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 kinetic friction for a 9-9tbw se glfr85j 0,bt27 fpvokc gj0$ 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. 4-32 (Example 4-20) how lars.j+ rw;cgvnfk2f i;9ge a mass would box A have to have to prevent any motion from occurring? Assume kfgw2is ;rf .+9j v;cn$\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that 1m9ul/ -ib ajtv/7tbfit slides across the floor. How far will it go, given that the coefficient of kinetic friction ifi- / bj79b1/latvumt s 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 , are in contact and at be3a:cjx+ad daz;0j* rest on a horizontal sj* addb ca:z3 +0aj;exurface (Fig. 4-54). A 620$-\mathrm{N}$ 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 cr1 1pt) .ox,ftskt:hsk9 -mzox ate. The coefficient 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 decelerate ano)o9-k.t xmhzkt sxft:,p1s 1d still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whic n.i)u4takz.cm s-xp 8h has an incline ..4ukim-tsxc pz a)n 8of 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 wi8up namj9 ybzj zn;(9xay7a48th 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(3w yn-4jijbti kbuc*ay:8/ m lies on a plane tilted 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 ofm b:2atn6q knea u56u+ 3.0 $\mathrm{~m} / \mathrm{s}$ 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 the top of the steepest hill with aswsl t :l,d9jc01 :eec 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 k.sitk ro4- b;qy2ukni(g,i 7 rough wall by someone pushing on it with a force dir(ok;7kr b .qu- iyig,4itn2ksected upward at 28$^{\circ}$ 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 kl2p- olac5j wpz*22kroofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof w* jkloklw c zp2p2a2-5ith a 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 distance f,)vx aahi:ac dcnt06 3p)zi6hor an automobile traveling at speed v is equal tz )a6)i:h3cp0dh6tc ax avi, no $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 dashboaa2y5wxe8:qa eun6v9s/ 7qx -x ri.board of a car slides forward on the dash when the driver dece2n-6 axy5 xs9qqbv7w./aor e euax:8 ilerates from 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 mwh)y8x u/kcxs(c d(e8 is given an 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 convey 3/h-gml)ht7 w+xo ma1m9b 6z+rcxkqzor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero 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 rw+xh-3 zozm9clk6 +mh7gxma q/ b1 )teach 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 of kinetic friction between kyo13fk b jf8 av+cm 7jn;u0k7$m_{1}$ 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 down e4-ifa 1epv ri7zx8*v 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 simplified model lhg 2n3ksaedz*kpq2fti q42v9od-, * /9t nvpof a mammalian heart, at each pulse approximately 20 g of vna*f*k9v4e9t,/nl2 sphdi o2z- p2 dgktqq 3blood 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 surviving an automobile coqvd7 rlc 32ow ;dcf(:rash if the deceleration is no more than 30 " g 's." Calculatlocw v:2q(doc f7 ;rd3e 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 an earthquake is a , and k16b+o.hfi tj if an object is going to "h6.jtio+ bh 1fkold 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 w zx-3jrk-7; ,mnrvjlthe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before lwr,3jnvmx;z k7r j-- colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling downd qb4h-7h wjim9n2 ;se a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after sd ;nh 79hwbij q-4e2mtraveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from thez2 9m;kx1o odkfx47ul top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the averaglz749u 1;ofkxxmd2 o ke force of air resistance?   

  A cyclist is coastinho9q;eetmm, 6tyy) upe( 0hk2g at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction 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 emergie6eh y0;p(h mut)2 9qtekyo ,mng?   

  A city planner is work3p (entj)zvk i *0kn0uing on the redesign of a hilly portion of a city. An important consideration is 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 t0v0ek z*n) j kn3i(up21$ \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 experimp 9pz*zlbzpga,3fbw bu+9 :6oents, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle ofp fz, a 3zogbzp69l9w+:b*ubp 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 , vg*-)2 y4p3hhnmno get /ddlbp7mp4 are to be several ramps connecting different parts of the *ngpn htdp l7by,2 )-me/4 dovg4p3mhstore.
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 nt an5 u(b bk 1hzz)lsf )fkbs2gg5*k55eeded to lift the piano (mass M ) using the pull2)sbb* kb5lhaf 5uzn 1fkgt 5gk(5zs)ey 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 accec (423lusl2w(s,xriqh dj/wpno8 1 jr lerating 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 proces r z,8ky xff:z w341l7/ yjh(unotd6qgs for a child-restraint chair, an engineer considers the following senqzy (h:y738luxd61 j/,gz4trfok wf t 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 t9 8i( n-tkbq6drh)s dgrain 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 Kareb8 9se*4t*jxvxoa/ non, use safety ropes of similar 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 ajas ob8env* x *4/o9xtbout 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that 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 qv8p;vjnefg fn+,8c b*2wp o8g7cga 7using a " 10-1 $\mathrm{~b}$ 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 reah6ciy5sq9. m qch a maximum speed of 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 who are roped together are ascending an ice fieldgh 8)x hk9: n6wc)ey3 aggq,lj inclined at 21.hgwn, c x6:lgke) 8a) gqh93jy0$^{\circ}$ 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.