Why does a child in a wagon seem to fall backward when you give th6fbh79 yw6;;je9r zka8a fa ,m 8epacue wagon a sharp pull ;jpfhfk6a bew ,9c 897yr6u;aa ze8 maforward?

A box rests on the (frictionless) bed 21g vmie -dp.hof a truck. The truck driver starts 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 ground beside the truck and (b) by Chris who is riding on the tru.h g mv-i12edpck

If the acceleration of an object is zero, are no forces acting on it? Exp3ahv(p )gq sx7q. aj4jka1ou3lain.

Only one force acts on an object. Can the object have zero acceleration? Can ii+nml gf (,-thn9plmi. yp7(dt have zero velocity? Explaipl( . ,p+m97hdni( tnfml-ygin.

When a golf ball is dropped to the paoj, vh (ekm0v6i,nye9vement, it bounces back up. (a) Is a force needed to make it bj6(ne9ym koe,v,hvi0 ounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, whtz 73rri4t*hqobi jioqo,7:d h 6q 7a2y does the log move in the opposite directhtrqz 3i7 6oaqooi4 , b:7*ir27qtj hdion?

Why might your foot hurt :bxutoiac;v5 -d )tt) if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicklfae-o)a ljkaxd ;*/w9i(; pqey. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximumojf;-q)(wxe9l*k /ai e ; apda rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fys5 /8.qg uupmine thread from the 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 stone or above it? What if the person gives a slow and steady pull? Explain m5ugs 8p.yq/u your answers.

The force of gravity on a 2-kg aou1li0 /ty85i rk 5kdrock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fal8k5toua50lrik1d y/ i l faster?

Would a spring scale carried to the Moon give accurate results if the scale rp+wq(z 6i1x p4b6kb*u0v avohad been calibrated (a) in pounds, orav+qzo41p(0wk*p 6i6bvrxbu (b) in kilograms?

You pull a box with a const; l-asxcajf :)vx5/, kfh dbx4dcm8,zant 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 box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Expldcm, vc sx;:,z l)xj 4 8d5a/abxhfk-fain.

When an object falls freely under the influence of gravity the3qnx-8w81d5 f z jn+rty6 uxqvre is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposit58vnj q+yn xurdq683t-1xfzw e force on the Earth. Why doesn’t the Earth move?

Compare the effort (or formt- a ;ov.veq9ce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the f .v;taemo v9-qorce needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, eachd fa)0llzr pw*mqj1 b *37xj-.ror,(ssu(ogr team in a tug of war (Fig. 4–37) pulls with equal force on 0mwjfl oxr1o(-gq(a . d)7r **ub,rjs3lr psz the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holds kqclm-qte9p k98r, wk 7bhervw( :23 a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it isw2 ewc qt-r99kle(p37brhv :mqkk8, s exerted, and (d) by what object it is exerted.

When you stand still on the/p.f1ego2k :kb x 1qwd ground, how large a force does the ground exert on you? Why doesn’t this fwpb:e x.q g21d/k1okforce make you rise up into the air?

Whiplash sometimes results from an automobile accident when the yqp2 -,5ocq ezvictim’s car is struck violently from the rear. Explain why the head of the victizo y,qpq e-c52m seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck .4b8x(2e 6u gybwmk4qi uakez8z,mu; accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes th yxuwm 8 zbgzk4b8auu 2;64,(kem. qeie crate to accelerate?

A block is given a push so that iu1x 3r 5ux/ i,ujbhgv*t slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on ,vxh /bjr3i x*g1 uuu5the descent than on the ascent. Why?

What would your bathroom scale read if you weighf:q4 q n oplnz;* k;cs-4v/(crkuz1xded yourself on an inclined plane? Assume the mechanism fzkvsr :d/ ufqn k( 4q-;4 *cx;1znplocunctions properly, even at an angle.

  What force is needed t4 mbhpf.oa.t0eh - 7zto accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider6* xxp6hb+ lfwv/g cp7 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 accelerat50 -7tm4 p)padh;szcaleurpz 94vi 4p e a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a qt1h6q67jmc dk65 focj1r *wm $76-\mathrm{kg}$ 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 84un7/op ,jvzoqvl: p6ybs/yto stop an 1100-kg car in 8.0 s if the car is traveling at 95k:onv q8 bjylp pzvs y4,6o//u7m/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest todics.mv cs ofrq91hv5*8j; *g 125m/s over a distance of 0.r qm**dsf sjc.8;91vgoc vi h5800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically ouw p+lmq1ro0;dt of the water with an acceleration of 2.5rl;qpwom1d0 + $\mathrm{~m} / \mathrm{s}^{2}$ 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-m( kki2woq vw7u20kml5ile 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 tglyty51 ip+o. he maximum acceleration is 0.0680 g . Whyiy1 .oglp +5tat are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator.z*7hjw5en u6 rf.6 qu2njx*ft When the elevator begins to move, the scale briefly reads only 0.75 of the 7ntxfru jw56 unfq6 ezjh2*. *person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum streni ;,h7h ql9hmr-8ya6apdt i 7tgth of 21,750 N. What maximum upward acceleration can it give thr6 7t ,;l mqhaphh t9di8-y7iae elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f s87*:mbe( 8;zkdv jr-wkvle balling sky divers (mass 132 kg including parwzl-;vk m88kej7 (r: ed v*bbsachute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of anuo+,.e )sr oz house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance ooz +so.,)ur enf 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 restk3nv ,idj5,jb/fxhd; s on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging o ;dvxhj,n3k5, /dfb jin the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pv .,*4 6 4 nrdgisfdf,ylk r9kpps-f.dlayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram ofnucvs( k r7 x,9niz,+25mx ixi a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying towardnnik,i i5 cur2m,(xvs+z 7x9 x the outfield.

A 650-N force acts in a northwesterly direio.7jnu 8rag q8zdd4b,per7 /ction. A second 650-N force must be exerted ze7n8,uo874 j rqi/bgdrad p. in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire"upc(lwek.cn+ c :q1- -g-woavtiz2m8 strung horizontally between two buildings 10.cz8u:getqwc(npwl a+-v-.iko-2 cm1 0 m apart. The sag in 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 massless cord from anothe0nmrrwyr:jo538dv2 +x/z almr 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+5vkw s;o(qc i bp.ra+.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 McMurdo Base3a44u pqusk5q4pnm w ., Antarctica, as shown in Fig. 4-46. The sum of thesu4mq5wn4 pp3kau.4q 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 it, Fi g289.4asl : ugiwqmtjg. 4-47 . Determine the ratio of the tension in the coupling between the locogjmu2 : awlq948ig.ts motive 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 herself upward using the bucket-pulley apparatus.8ibu0plia /)u0 ivzeljaq405c czp+ hpm3w 5 shown in Fig. 4-48. (a) How h paec. lc l0iu8+ 3ju/)v4zzh50pba ip 0qim5ward must she pull 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 begabqn*d q jgz1/9n, 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 gdzd 0 vk9;rq*(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 friction:ixy qy- (rv2e vgl(8;gbu z)yless horizontal surface are in contact with each other, as showg:ziub -gxy;8veq) v(rlyy (2n 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 aboucxm((z k0;nao;8a c;) rko hive the ground, and the massless frictionless pulom;kico8ahuk 0nr cz;x;a()( 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 pz(me80asx zj:denx m5+k/6r a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the c086msa(n/dxez: j rm5p+xke zord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction bet8dz(g2hc.s nd ween 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 to siv* 0tlb5v0o:kdfd-o.x*j (ia ws ak5tart 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 accek5mu9b a*wx -jlerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are nojbu9am5w -xk*t to slide?   

  What is the maximum acceleration:/q4vavv 8uvp cl 4sp/opy -4u a car can undergo if the coefficient of static friction between the tires and the ground is 0.8vp:4v u4qoyu/ ac4-/lpv sv8p 0?   

  The coefficient of sta*ip mz ma43ht*tic friction between hard rubber and normal street pavement is about 0.8. On 3 h z*tmi*apm4how steep a hill (maximum angle) 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 a+ gwre+2 gtgdie0hr)9 t -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 roughey gr7u +88b +e7uzzqi 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 az:w+fgn6 oxm 2n qw-6bn asphalt surface have a very high coefficient of st6n+g2- zw o m:nbqxw6fatic 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 9jf.asl2hu:5agn( 9 ,ee bauy 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) how large a mass would box A hazcw69 m6)4ge:dcdj3pdze; rv ve to have to prevent any motion from occurring? Assudcvwzdjc6er)9mg3dp e6 ; 4 :zme $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides ac-7+b t-cn7 ccvy1qe jcross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 qcc+n etjbc1-y - 77vc$\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a 7n q pf5:,marehorizontal surface (Fig. 4-54). A efa 57mnrp,: q 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 coefficient z 12rbxs9 zzltp /w6 w(/,bfxmof static friction between the crate and the bed of the truck is 0.75. Wf xxt6b9r,/z2p/zwsmlz wb1( hat 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 w dqt,e05us.ty orry about parking your car in your driveway, which has an inclinet0s.5,ytqu de 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 slide d4vq v b+c3kv0with 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 a.dj*et1+l/anl gc.:6 t gz;obcm :sflt an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3r kz)nzj(ey 5xdz5p6 l .ezn3+.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 steep(m/tytg*v d(p(w 5towest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall hb5 j( r17jonbov0m5sby someone pushing on it with a force directed u hj1rvj5n5ms b( o7ob0pward 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 can become dangerous projec9wfiqpm+ clol3l 63uk z86*dg tiles as they melt. Consider a chunk of snow at th6kpwi 3c+mz3l8qf6o9 gd* ulle 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 mini ;baz v,bqt3 (,qubif2mum stopping distance for an automobile traveling at speed v is equal bbb,3q;, af tuv(q2z ito $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 dashhjs ;4nwo i.7 lu42bybboard of a car slides forward on the dash when the driver de lhs74;ou 24i bnjb.wycelerates 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 tw*e78gaqg3n;vf*8 )ut d 8syvbui4 ginitial 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 wsutd/hw; b8 ity;gjcylz- .-+ loa5+are filled to the packing station 11.0 m away. The belt is initially c zt-+l;twj.laiw+d;-u5yby / h o8sgstationary 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 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 wzhy7v)t,it-z j8bh sz6+w v. $m_{1}$ 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 coflab8x( lr61 cx 3ug.aast 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 mode hyks. /,1*tutj ml:bal of a mammalian heart, at each pulse approximately 20 g of blood is accelerated f*tyu1j/,bms. hkl a t:rom 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 deceler pl5 whz: c)urow:;.l7 tjow+uation is no more than 30 " g 's." Calculate the force on a 7 lt.l)oz:ruwh7;opw: u w+5jc0$-\mathrm{kg}$ 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 z/ hrvtz)9gvcazq+08an9l/ y a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with8zvt+ ha/gc/99 rzavy q ln)0z 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 accident involving two cars,eeg3p)7k6 . 7svfbhde measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate t 7)hepkvsef7g .e3bd6 he initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for eachh cami)qptl u8a k4 r:pd8ue35h2hj. * 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after trr5).4hp2:3ua t8 uhda pcjhemi lq *8kaveling 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 Leaningjt9 p7yszkdv1) i y/ 1ivn;b9p Tower of Pisa and falls 55 m before re p9vbpdn)vs kji1 yy;iz/97 t1aching 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 but enters j(qsh qi d gakk;:8**da muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch withouqd8s *:ig(qk; jdh*kat 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 zo q1ang+ai7 );tkv+h 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 partg kq +anavt+71 i)h;zoicular 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 exper 90u*usn3 zt7usowl+.+etqaaiments, dangles her watch from a thin piece of string while the jetliner she is in .7aon l +ewu93+ *tqssuz0utatakes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a sukt+0vu2nq bw2rz ci/dv5 jx./permarket, there are to be several ramps connecting different parts of the sw/vdx. zk2q520cnivr/+ubj t tore.
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,y fvhng4vp/ l3p5(c3* yr xcn piano (mass M ) using the pulley appara35h*yl fv, yxrg/ n4cvc(pn3ptus 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 9qsyfs hb rm/ 7k+9c.stwcr8 ;at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the folc0sm uo r/i(8blowing se 0 scubo/(m8irt 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 train has a mfobi/6anw /ktf.,t/ oass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety v*t:pu z)nbuq im8 cdbr. olig sx(01.+rd4/iropes 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 t)t:1.(lv rpzsdu. i8q0 b+b *nro4i miu/xcgdhe rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boatf o6(h i13*ijn2,eq1jypiqr: t n2dih is using 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 reach af pg0rj7 0 4wc(yrft:b 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 goj30yu za f//an ice field inclined at 20g 3oj/y/f auz1.0$^{\circ}$ 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.