Why does a child in a wagon seem to fall backg x*cwfg i+)k: a7v)laward when you give the wagon a sharp pull forward)) 7:gc w k*fia+lvaxg?

A box rests on the (frictionless) bed of a truck. The trutwg .; :d ,s5 0uzgv7pbz*jzobck driver starts the truck and accelerates forward. The box immediately puz; bgj .z,so*tvb7 wd0:zg5starts 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 ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object istx;bdwtca )6xfh4ek f/hdd:h4y+ :n- zero, are no forces acting on it? Explain.

Only one force acts on an mpkoc i8f7b)/ object. Can the object have zero acceleration? Can it have zero velocity? Explaincb /kio 87)pfm.

When a golf ball is dropwd;s vpfm jkyut491 *2u6t8: tikud2fped to the pavement, it bounces back up. (a) Is a force needed to make it bounce backu tduyt*2sw:d9 2;4u6jfi1tk8m vpfk up? (b) If so, what exerts the force?

If you walk along a log floating on a lae7f iwnl h8y-19o,pxb -r.jud 96lyw xke, why does the log move in the opposite dw -b-7h.yr196ox pjliwul fey9 8xd,nirection?

Why might your foot hurt if you kick a heavy deskccup 33gxxg 2wdr-y7 z udo/8. or a wall?

  When you are running and want to stop quickly, you must decele6g mvmc zxd)-9ds7crda/v54 erate quickly. (a) What is the origin ofg6vs 5 m7d rc/a z9x)-dved4cm the force 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 ceilio )q6 2l5v,qbh5tjh nyng, and a 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 or above it? What if the person gives a slow and steady pull? 6h55 l),jv ont yq2hqbExplain your answers.

The force of gravity on a 2-kg rock is twice as great as tgc642 cdld/lo8 o)9grjvn vgclz0) n/hat on a 1-kg rock. Why then doesn’t the heavier ro8c cd9colv2ggnvr4jz d/ g6 /)0l)nolck fall faster?

Would a spring scalej;4von 4x 1tt clu0,dnar7:cn carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogramstnc;d jr 4nvu:ocaxt n7 ,l104?

You pull a box with a constant force across a frictiebc 9,vmn):igx43s o uf24 ckjonless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with thg2se 4xu3fm:kb cc ov4),j ni9e 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 under the influence of e ;u.tir oy9ijk/ 5-++ wpusnigravity there is a net force mg exerted on it by the Earth. Yet b/ii ru;kn+y is-9e.wpju5+t oy 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) needed to lift a 10-kg object when you8p3z7ix +uaku are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally wiu8p+3a iu kz7xth a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fi5pxl612q:w ye -smeefg. 4–37) pulls with equal force on the other t1xe:l 6 yqs ef5p-emw2eam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descr vg4s8k4k7oz gibe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object48o4zkg skv g7 it is exerted.

When you stand still on the ground, how large a forc)t ims v5g+ii;u s:5sf*dw f/ie does the ground exert on you? Why doesn’t thisdv/igmssfiui*i:5wt)f 5;s+ force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vi5z( pip 9 -kw3/faanqmctim’s car is stru/iz3ka 9na5qpm -fw(p ck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When tmwvi m /k4 ooj xefs.a:6250dbhe truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What fo5 :o/wsvm a20jeiodx46fm.bkrce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches ch;s,1aei)rm/gr-v)z)y zdy its highest point, it slides back down but the magnitude of its acceleration is less on the rvs;mr-ze) g/,)1)ziacyh dydescent than on the ascent. Why?

What would your bathroom sca rikt65:0x)b 6y :pvzuxbn;i nle read if you weighed yourself on an inclined plane? Assume the mechanism functionu06rtn)p:z b65i : iknbv x;xys properly, even at an angle.

  What force is needed to accelerate a cdixvj*9ck e ;7hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerhw) 3a*msm/gl3 zl2w sbhxk37ates a bike and 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 withstand if it is used to accelerate aigl mq iq.3-.iw5 dru; 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of e btcxboctf v,4 5;-+. qi.sbqnc)jy1a $76-\mathrm{kg}$ 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 requi/pbsz 5smf+ax2(e* tsred to stop an 1100-kg car in 8.0 s if the car is traveling at 95km* +t(bpsz/ae ssf25mx /h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125tbr6/(4pm efv)l(g hb m/s ov(vr(gtbhp/ e46 bl)fmer a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an a1/y tm(d+ i0 *behdmxvcceleration of 2.5vm/ h(bdi+0 *mtedyx1 $\mathrm{~m} / \mathrm{s}^{2}$ 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 os z4:q9:a 7xwrntue 3xwfb:+,tn;t acan cover a quarter-mile 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 ) is to be designed so that the maximum acceleration iy0tykm c-3/a xri hx20s 0.0680 g . What are the maximum and minimum forces the motor should exert on the su0max/r yh 0ty-c2 kxi3pporting 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 fwxnc yzq:/xp2f y.;(elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the ely.f( 2xfn;zwp /:yxqcevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-k o pp761rniwh5l,3ir rg elevator has a maximum strength of 21,750 N. What maximum upward accele ,p1 ni35rpr7wh ol6irration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fal3..tf)*)m op /bdsu dnn yab3bling sky divers (mass 132 kg including parachute) when the upwardbus) . bfm/3n. pn)tyaddb o*3 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 os(yu4,i( -s7r fcvfp qf a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his ( s-(qcvisryp 7f,4fu 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 box runs vertica7b(yascf 1 dfw0tb. 5j :yuonqnz e0/7lly upward over a pulley and a weight is hung 7 0u75f/nyjb0:tnowz (1s.cbqyda effrom 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 dii+c(bbgz no6 y09zi(sagram 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 baseball (a) at 98hgx/ yjwao;/ p4iaythe moment it is hit by the bat, and again (b) after it has left the bat an948 japyai/xho;g /yw d is flying toward the outfield.

A 650-N force acts in a northwp zw7*ivuf72fm5ce j: esterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer w u5j 2ifzw7cf*mev:7pith a vector diagram.

  Arlene is to walk across a "high wire" strung p22 vwrawg, l,a)7ks dhorizontally between two buildings 10.0 m apart. The sag in the rope w,aa 7wsv2k2rd pw ,gl)hen she is at the 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 hang a7)fasumf w+de*l/2gm*)h6t5 qwlhling by a massless 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 12izl(j/j ; sb5wbe9xlm fo/ ;t4.0$-\mathrm{kg}$ 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 McM q6:.6 o*ins+jgbgn8y(oaziroz id / :urdo Base, Antarctica, as shown in Fig. 4-46. The sum ofo yo z8iosndg *:q /giz: 6.r+abi(j6n 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 behind itrd 4iy5g/pd;h / tu gi 61x3ksppj*4ri, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive ad i6hrutiyg45x /p/*1 gkp rip4 ;jds3nd 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 herself upward using the bucket-pulley apparatus shown;j0e 4wrsxxc , in Fig. 4-48. (a) How hard must she pull downward to raise herself slow 0jw;r,e4xcxs ly 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 b/yoj-gq awv1-2pk,v) .9dqapb zg os4egan, a 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 (mass h fa/ ,rpm/ (f6t gyp3j awde8)0l*mio$ 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 hori)mjv,fe ( s*c1:kedd7u c kf059rlcsezontal surface are in contact with each other, as shown in Fig. 4-51. A forc9fe k1l esdjfck7ur )5v * emsc,dc(0:e $\overrightarrow{\mathbf{F}}$ 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 initially 1p3b ux*p -(zx ,:5iudua 5sfih.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height doedaf5pui ix3:zus*p , bh(ux-5s 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 cowvzi0e2 gft.;3ohm f4 /ecd:ord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cordm fcvw/;42to zgeef .o0:ih 3d, 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 kineticzzy; */)0kzz -lkog oy friction 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 required tzabfm l pl3v079pn4tjk ;e r;(o 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 train accdvhs +7mlj5b ucq(:a0 elerating at 0.20g. What minimum coefficient of static friction must exist between your feet and th7dbvsh a qujm5 +(:lc0e floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta2 teb* h+zccqjisly/s78mp55tic friction betwe ms2tsl/7pcy5jh qc58bez+* ien the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal s;j7zo+s p-z ihtreet pavement is about 0.8. On how steep a hill (maximum angle) jh7+zos-ip; zcan 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 decelerateq q/zkb6 ps:f: at -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 rest on a roje zsof1q.;s;6x 36x; bewf .oarnc 0nugh 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 ;7k) hnr;4sl rbb7uc vvery high coefficient of static frl;rrbv74; s k 7nbh)cuiction.

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 frictg 79cfyo:ybhwmjp;a bf8,2: nion 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. 4-32 (Example 4-20) h/ -3xzil,6dlss59ww x4i ptglow large a mass would box A have to have to prevenwg5dwls x3 / 9iizxp-l46,ts lt any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wil/su013b roa :gwg hal3l it go, given that the coefficient ofs1rbwogh/a g: 3a0u 3l kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7oc9uwj: n8k,2 jtwp r-5 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4:p jo-tcn r8 9,kuwwj2-54). 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 4u5*4:agvbdjah pe,1 xncqu 8 a heavy crate. 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 and still avoid hav1auc*:jh, d8bgep x n4av4q 5uing the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drivewt3ennt1+0ii qay, which has an i q0t3ti1+e nnincline of 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 slidn4t4 4kgi0slo e with 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 tilted at an r3;mgsg x )rhy0hm9)bangle $\theta=22.0^{\circ}$ 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 fo/eddj .j94k8ont3v of 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 ddz e,d(g.7pdthe 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 pqj,)izb fm beeu :9718qj,bbslace against a rough wall by someone pushing on it with a force directed upward at ib9eqj8bqb ,u)mfb e1j7z,:s 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 roofs can become dangerous projectiles as tp d.othyvmn(4z:63 mr8 jz 0kmhey melt. Consider a chunk of snow at the ridge of a roof with a pitch of nrmpk.v0:zh(jmtdm 8463 oyz$ 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 for an automobile travel7et 0fcdcc) o;ing at speed v is equa ;coc70)eftdcl 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 foax*9ddn, ls a- 77svxjrward on the dash when the driver l*d,j7sdx7s ana v9- xdecelerates 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 m is given an ini;e zf3( 5bd7z7pfjybq tial 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 areikp jo -zj71(c filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit z j17kpij(c- ois 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 of kinetic friction between .fr qu6a2tnxwcdw54+ $m_{1}$ 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 (includingzo53 zd,dl b5ltmq7)l.h7w tr the bicycle) can coast down 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 of a mammalian heart, at each pulse approximat gg/ldj5 lryle/*d/1 1psp fq5ely deqdlsf15rjg/l * pp/l /g15y 20 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 chancen )/bob1tttrr*9q4p r of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calcularto4tt)pr*91/q br n bte 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 , ancgk tirx(xb-8w g)*i: d if an object is going to "hold its place" on the ground, show that the coefficg*r:cx k8tiw gb i)(x-ient 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 scene of an jd75srl jsjjw+r*,kwp /t( v: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 tl5+ kv/jjpwjs,:(rr*wt7sj dhe pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that7 xcovd ;(clg6 for each 4 m traveled along the road, the elevation change is 1 m). Howgdl(ovx c c;67 fast 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 the top of the Leaning Toweevdo1+ds6oh ti66yk /r of Pisa and falls 55 m before ro/ohv1+d k66 yts6e ideaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s bj w832-wc yffnut enters a muddy stretch where the effective coefficient of fyfw -32nw f8jcriction 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 working on the ad/v*,vs,wrv 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 hillsvasrw,vv, d*/ 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 experim1kb22;rx nre9a4.6m;3skv o r svugptents, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She noti9 kr2movuprbvrx 3s24 .;1ge6;ta snkces 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 several ramps u:y)4wmbb5 n-+bhv sz connecting different parts of the st-w4b 5us bmn +zyhb)v:ore.
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 ihzvqk0-.*l s us needed to lift the piano (mass M ) using the pulley apparatusvuhz* l-sq0k. 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 accelerating adv 6 1:klkiniyv+k3 0ct 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-restraint chair, an engineer considers twv4 z+z mv9fu)he following set o w+fmz)u 94zvvf 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 train has a mass of 660 metric tons (660,0 ; )7hb8 zkuuyk2go2+i*zwxkp00 $\mathrm{~kg}$) . 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.jgvu+qbje st/ay8i 9i91e *,jcyp-f and Karen, 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 about 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 beiesbegy-c, u8q*j1pf+vjt 9yj . 9a/i hurt?

A fisherman in a boat is using a "e*1 unzybk e*0 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 bui zd.4 v:hy-gc 2b8 3/rxhg t6roz3ipzilding is allowed to reach 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 asceufrbtybw,x240m .zhl bit) ;d i 5axd7ehp3)0nding an ice field inclined ad;ewm bi2 pzy i0t )xurhxhl0.54,tf3 abdb)7t 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.