Why does a child in a 0utykc msc.bj gcw07g +,xm*7hewh 6;wagon seem to fall backward when you give the wagon a sharp pull7 g0 gu7*w+tmb kw,6hh scy.j cce;m0x forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts t; bix1(iuk6pg4 fex*m he truck an ;mgux41x6ki*ibf p(ed 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 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? Explaij9mrcctz(4xliybc-:n vtk(pq5m 7,; de* o* h n.

Only one force acts on an object. Can the object have zero(tb j cm59(t6ol:u/qikn0o 5ez4hyq i acceleration? Can it have z50bq546yk9ijtc/nhu t qo(:i m eloz(ero velocity? Explain.

When a golf ball is dropped to the pavemenyi c8zk3lb gu zn/ k;+,p4rv;ht, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what ex+4kb 38u;pz c/rlzyh, iv;n kgerts the force?

If you walk along a log floating on a lake, why does the log move zz6 d+3xe8,mvwmm ns1 in the opposite direcemv nzm36d +,18mzw xstion?

Why might your foot hurt if yo2 yx s kz0c7 jist44n:m2jam9zu kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate o8k z,z-sq kuu.ql mu,m8*q 7mquickly. (a) What is the origin of the force that causes you to stop? (b) Estim,m-mu8k l ,zu.*8u m7kqq oqzsate (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 teovk756l4np oj l 0hd5q3d+jrhe ceiling, 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 rvkod3 njlod+5el p076j hq54 stone or 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 great as that on a 1-kg rock.by.qec 2dtnr-6;6pa. :rpogog7)nxl Why then doesn’te.6xac;p g n pr67-gqd o:n).ly btr2o the heavier rock fall faster?

Would a spring scale 5g1qi9upbu4 u carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogrug4 iq9p1u u5bams?

You pull a box with a constanvmb:m ,4 -oym pffd-w0t 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 (wbp om4mdf-m: 0yv ,wf-ith 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 under the in(vh 8suk3 (r xcgo:b0dfluence 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 a: k(rghscv8ubx d(0o3 nd opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when yo jt- /-k3 ki/pykyiby3u are on the Moon with the force needed to lift it on Earth. Compare the f- ki /j ikyby-p/t3k3yorce needed to throw 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 war (Fig. 4–*fw2rf 1a1ykz 37) pulls with equal force z 1w ryf2*f1akon the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocer/ozhr 1au:tz2 y pke3(yx-)oxp0vk*hies. Describe 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 objec ryo3p/v -a*hux) zt0( z:2pk kh1oxeyt it is exerted.

When you stand still on the ground, how large a force does s3m,.h( ddzy04 1os )fhn(cgxlc w2k nthe ground exert on you? Why doesn’t t wh1s n420z(gxo (.mk3chnys)l,d fcdhis force make you rise up into the air?

Whiplash sometimes results from an automobile accident whb)o bj0pqf69nen the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is itj nbo96)0bqpf really?

A heavy crate rests on the bed of a flatbed truck. When the truck crak: iwydpr(x98h.fk/o /6)cq2b kkaccelerates, the crate remains where it is on the truck, so it, too, accelerates. What fo6okxr:kp fkc2yr.k/9d8qw hcb i()a/rce causes the crate to accelerate?

A block is given a push so foo2*jkfscjz b-(w 3)that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of it fcsfw(j -o j2o3k)z*bs acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yo a4j4d us,/) .kdmbazourself on an inclined planesdjmk do4.az4)ab, u/ ? Assume the mechanism functions properly, even at an angle.

  What force is needed to acceleryf// +,ys3.ol itxi4j fe3w n 8cu:wmeate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N ac4 k3(scaskuv2celerates 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 tdup(c kg32rf*8vl1j 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 74-x b ny)d urj(*rqsk$76-\mathrm{kg}$ 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 aj xux8ye b*tkxuok bl;( -tvc7608u/on 1100-kg car in 8.0 s if the car is traveling atxxbt kuy;6j7bxoe/ -ktlc8v8*u 0 u o( 95km/h? -  

  What average force is needed to accelerateup1,8lzxpe- b a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m e -8z,bpxlp 1ualong the barrel of a rifle?   

A fisherman yanks a fish vertqt3:1i*0-bu yno8ezudxpt q 1ically out of the water with an acceleration of 2.:x-pid 1tb3 *nqztuoq8eu1 0y5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tracd26 enyj/,)he 1ulxz,kccn3 sk (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 thv ((6bsr3t mh*cnm9 nyy( kg7ph/jta5e maximum acceleration is 0.0680 g . What are the maximum and minimum forces the *3s ytnr pma/ g96bthh 75 v(mncj(y(kmotor 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 epn ;tz*/b (77d1(ev lk,qq/xb ukwt xklevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accele7q1k* vkzqwt;7/xb nk(/ (pdlu,bxte ration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengo1cm4n8vhr d-1gd u5yth of 21,750 N. Whatc4o 1d5-g 8 muyvdrh1n maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers p.d93dvx tl* n(mass 132 kg including parachute) when t *xddv.l3 9tpnhe 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 9xj4k8 mrpphz2d.7f dhouse 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. Ip.j pd79z4mkd2 rh8x ff 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 box runs v9n*inxa-t hkk1hxx96 ertically upward over a pulley and a weight is hun i *k9h-ah 61xtk9xnxng 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 diagrd,lt i x91udb+am 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 the moment it is hit b *vc r(t9wi0pmy the bat, and aga9i v0*(cwmr ptin (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwe9g4fupk2rv j 43;0v2 jebld vesterly 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 with a vector diagram.u l0j2 b4fvr3vjgde9v; p42ek

  Arlene is to walk across a "high wire" strung9n fr7 :flyq3ghbf7m; f)l f3z horizontally between two buildings 10.0 m apart. The sag im;nlf 9fz7b7 ff yql):r33f ghn the rope when 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 hanging by a m /yl5po ncao.:assless 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.k rf. vf6y* j 8+ztpqyleg)9c60$-\mathrm{kg}$ 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 un)m7 3 zzqx (mu,rdcos5it to a new location at McMurdo Base, Antarctica, as shown in Fm5crxz 7) sd3(zqom,u ig. 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 tw;8l ym/bfp 2(mgz;kse o cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive lb; yzfgsk8 m p/me2(;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 hers.r fabd(h7 hn+elf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pul.dhh+rba (n7 fl downward to 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 beganm2w*v ghxbx hsqskw16um 7-lmev*qo9//tm0 +, 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 d0ub-jvqdb 1 +(mass $ 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 surfarwu wa a9rx1-zv0+wf) j8tv:qce are in contact with each other, as show:0 +a1frr v)w9vtw- 8qxauwjzn 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. 4-52 are each initially 1.80 m ajx)v,z- yrgfnwj6 2 o4bove the ground, and the massless frictionless pulnfv gyjj-2o w64)xrz, ley 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 frict3ao 9n (e2dkkpionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the (dkkn2apoe9 3 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 o mfgw 1/as,b1ywfc+*vf kinetic 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 tom w3kh)46/ 78r8im 4 dbnus2hq fezutu 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 n6l+rh tlje5 :on a train accelerating at 0.20g. What minimum coefficient of static 65nlr +e:lhtj friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sv:s hnm 8o/-yj8oasr/ tatic friction between the tires and the ground is 0.80?r//8-:8nomoss yh jav   

  The coefficient of static friction bwfkl 4yggy,,c w 6.hu4etween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? , ukc4 . gygfwwh4y6l,  $^{/circ}$

  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 -94sjh*er rt r 5d.:vxq4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 r .yavec2ty 83nss.y6 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 3 leyi:+i :bsxhigh coefficient of static friction:ly:e +x3bii s.

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:/f f/su jf,7h 5yorkg $ 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 c d x5vr8zouq9f*r f39+ plp mk yf7q/-r25smv4-20) how large a mass would box A have to have to prevent any motz7c y/5xv5rkufp m-fm9v2qfd9l8 r q*so+pr3ion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far of)aspv0lk go6(h (l0 will it go, given that o0hl (f)l0vs( poa6g kthe coefficient of kinetic friction 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 , are in contact ane(4o 7)fd +kr)faeqgmd at rest on a horizontal surface (Fig.(o 47fdrakme+)e)f qg 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 crate. The coy eic-7k1c+k vu0hnf. efficient of static friction between the crate10cku+i kfnh c7y-. ve and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry abxu k)tkrov)l ejl)kq u ct *7*5bx:;,eod+1gbout parking your car in your driveway, which has an incline ofkb7lox*t)* rc) vq otx bl )kud5ug;+,e 1ekj: 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 slidoj +;o;z s)czc +ftesr*; q6xw;mojkd,i 0ho3e 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 Fihke)v u6w( 8cug. 4-55 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 oz983ml )skm kcf 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 a sp;v2ohr8xjgi25pn2 i1/abrce eed 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 xewk;sb, 9rp/ g(us* zft*yf8uu)2abplace against a rough wall by someone pushing on it with a fo)ap(*ubr9fu;zx/ g, bu 8f*ke 2yss wtrce directed 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 roofs ca6sf na* w ulghms7o;d w;sdp6)4y 6,udn become dangerous projectiles as they melt. Consid sw hnouypdwaf s7;gs64m;,d *l6d )6uer a chunk of snow at the ridge of a roof with 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 :0b(ucxk: 04w awxihx2 g+dcq stopping distance for an automobile traveling at speed v a(xkq+du0x:i 2:x0h wcw4gbc is equal 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 tht5r:k 0lavv nu 9u6p/ie dash when the driver decelerau la0 :np/6r5t 9kvviutes 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 in42 tuufg4tux - .badt7 n3* u:lt1gbotitial 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 filled to thejwch np9lzk :fb5+6)yfl : e8q 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 m wyz lc9l bf+n: e65jh8)fp:qkinimum 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 kine rkb3c7d-1z ,elsn6z vtic 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 zd90gdrnu;;( cuddul0h6 8 oxdown 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, a:hde0q x4g-u qt each pulse approximately 20 g of bl-0: hgqq4dux eood 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 crash if the decc7y v c+3 vgu952dronyeleration is no more than 30 " g 's." Calculate the force on adrcc3v+5 2yv7 og yu9n 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 lqg*bix s9l dtu1h,lnn2i 2m,w q/ .d: a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictioit92lx q. u:d l,glsi,h2mndw/ bq*1 nn 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 acjkh 6 -c3+ vt6gcjb 4 mru9(9wkbjmi6qcident 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 theu649( c v tg+b3kj6-kcjhwm mbrq96ji pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling 4.o)3tv h uvaxdown a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road,3toaxv h4u. )v the elevation change is 1 m). How 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 Tower of Pisa and falls5g3 a9xb3o u+cgrz qb4 55 m before reaching the ground with a speed of What was xob g q39 cb3gr5ua4z+the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy str)m+dpld 1 b g*8bxld/xetch where the effective coeffici)*8g/xdxpl+ d1bb d mlent 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 emerging?   

  A city planner is working on the redesign of a hilly portion of a city. Azvr4(bnp: j: 9ucgc5x j*q h(dn 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 d:*45 gcrpuzj (hq:vcxn(b 9j , 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 from a thin pi0s*. szqejx7qo +:( ogc0gue bece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices thb7osg*eeuoq+xj0 0qsc. gz( : at 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 tq:r d.0aljun1 52; figo/sbzto be several ramps connecting different part.01zan2s5:fj;dutb g il qro/s of the 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 the piano (mass M ) using the pw6g;w qk 4nf,),gcbf utyo/cl*to71u ulley apparatus showocg)lo /t qf7*fw6g , kn1yutuw;c 4b,n 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 a 8f7cl(jl6drl t 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 ao )52p61 xvqxlmq v0m :x/nlvz child-restraint chair, an engineer considers the following set of conditionslxqpvm x 5mx6z v:v)l0n/ 1o2q:
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 metxqd 8a-5y d*ck 6hi d((kr2grmric 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 safetf3kzagm4;7)k7 ywnw3)t g g dgy 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? y37)4)3w;dwtkan g 7fmzgg g kWhich climber is more likely to be hurt?

A fisherman in a boat is using a "*u-2oacz4vq aq7ob72yuf( c g 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 edi wloa;+j(3x(y -a ubuilding 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 ascending an ice field inf7f0,k u pa7oc:hu+i pgxy3;hclineykochip+73 xfgf ph,u7u:;0ad at 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.