Why does a child in a wagon seem to fall backward when you gl r-jlp:2e0,.g* tcjfr5 fu pgive the wagon a sharl.furp5 -,:jlc f2r0gjpet*g p pull forward?

A box rests on the (frictionless) bed of a truck. The truck e n;r2iory/d:* mp6f sngh8)wdriver 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 sw8mn* g nid:e/ ;6rohf2p )yrstanding 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 ijqdnk cy;*. m8t? Explain.

Only one force acts on an object. 3xc zvut7 g.;zCan the object have zero acceleration? Can it ha3c7 .gxv tu;zzve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (as0jrd(/aqzz7.2 e jk g5n- oplhx(q8s ) Is a force needed to make it bounce bacs.5- adgx8nsljjpe(qrz07/ (hqoz k 2k up? (b) If so, what exerts the force?

If you walk along a log floating on a82qeupl c;vxy3d/ 9z t lake, why does the log move in the opposite directi38 q/yvuc2e 9xt ;dpzlon?

Why might your foot hurt if you42pa 7lro7 qnw)87 -ostrqnz l kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec xm+) dbdm6-doelerate quickly. (a) What is the origin of the foxd)md-6d o+mbrce 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 ceiling6z0 y k,xqb lwidt6*d3, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). Ifbd y6t l3*0w,i qdk6xz 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 your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.6re /vj0-j hup+8ybw tz,zh u1 Why then doesn’t the heavier rock fall w6-p/h8je 10z hvuu +zb,rtj yfaster?

Would a spring scale carried to the Moon give accurate results irj*rgxo 1. kptl75 wa8f the scale had been ko a5tr*j8l7 prw xg.1calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using a/68 ko9( ve r+zd0etauf) hg(oe,gnphn 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 ke tve9+6 g,frp/aud(8(n g o0eh ohz)of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under b:n4v5w0 -t 4wmz ezkdthe influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the objectvtwnmz5wdbz k0e4:-4 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 you35g c/+svaog3luldgaui *9 q - are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally w/* 3aa ucls+gglgqdo-3u5vi 9ith a given speed on the Moon and on Earth.

According to Newton’s third law, fwz4ge+ )kx .adb +zfy. fz1s;each team in a tug of war (Fig. 4–37) pulls with equal force on thz eb;)x1d+sgfzaf+..k4z fw ye other team. What, then, determines which team will win?

A person exerts an upward f5e*qt io,,gf v*xym/corce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s th,y5/ei o fcgm,**vxqt ird law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on6j1gawi+mi6dr sr0 ezt+4 z9fne*ia kq- k47j the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into tsd94iea*n k zz6+jmgiq -w 4r0+eka fr17j t6ihe air?

Whiplash sometimes results from an automobile accident when the +xzb/.ugpayk( 3g a 0nvictim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this yb+(/0az ng gpx3a. uksituation. Is it really?

A heavy crate rests on qzq917vaov5cthe bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate avqvq1z5c 97o to accelerate?

A block is given a push so that it slides up a ramp. A7jnmf z +3s0ihfter the block reaches its highest point, it slides back down but the magnitude of its a73fz nimhs0j+cceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wtt joq9h8*kurm7mqv wz,f(+/ eighed yourself on an inclined plane? Assume the met7uqm j+9vwot hm z,kq* fr/(8chanism functions properly, even at an angle.

  What force is needed to s;oj6fe 1b+q)r, 4 umwahudv-accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rl.bmo+; e uyx(co,aw8bdi1 o3 ider 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 a7vu8yu wk l1)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 awsm b,xn6b;i8 $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car il 1+i+sq7tz,; yazboyn 8.0 s if the car is traveling atsl+y;bo y z1i+tza7 ,q 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellugh-.-v5 39u7qt dr5t tmkifhf (zaz4et from rest to 125m/s over a distance oqzr 9u- gi3a 5 ft m7zvhkth(dft.u4-5f 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleraf vm k3577eepu3zvm2stion of 2.5 2k5v73 e 7vzus empmf3$\mathrm{~m} / \mathrm{s}^{2}$ 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 quarfcsxqrp3.f8 h yc z4+rf5/tk8ter-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 ;85cl6hlsg;vqr7ydx 1npo 4lkgkw6 8maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supp konxh6lc;;q5g4 1s7rpldk gv 8w8yl6orting 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 bathr pde v/-kgp-huge (40xoom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular4gxe p-he(/ kd- vup0g weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting 67dwde ;5zh sckn*+f )uxobe- a 2125-kg elevator has a maximum strength of 21,750 N. What makd *z;eouxf) 7+ bw5e6csdnh-ximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includl8zs 6c9 nf3adt7o-qding parachute) when the upward force of air resistance is equan 68s ld3-cdtf 97qozal 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+f-2(m qunbto roof of a house 3.9-m high. When he strikes the ground below, he benoq-n 2(t+f mbuds his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically ( gg 79n1lhmdm2u;r yzupward 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 tl dgy(mumgh29;71z rnhe 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 dia:;tw(grwl ni e0vh 2ilc,ft8 ;gram 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 by the ba:oiiz)0d46b x z5lnxst, and again (b) after it has l0 :zxdi56s bxonlzi )4eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A seiy qb76dxz,h9cond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illudb qy7x,h9 zi6strate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally bt/5k.e ox l:wmetween two buildings 10.0 m apart. The sag in the rox /:w.ktleo5mpe 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 0q b/; 9bs+cbnadda8agsh 5c2 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 1jh;ft) d l--f6cq moh04.0$-\mathrm{kg}$ 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 l g +jlh2de;u8cocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. +l;2dh8u j egcThe 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 pulj7eeczwwx ;: )t: b.vzling two cars of the same mass behind it, Fig. 4-47 . e.w etwb ;z7x:j:vc) zDetermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulleyxp */bo*r3.t 8txrq di apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slox3 bri./p8 qdtr*ot* xwly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a )96h rpy-x;-sc, kahdg yz8tc 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 blockq0;qfcylxy/*0mtf1 y (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 surface are in cony:fa,dxm l q0cd28 ;mttact with each other, as shownq2,;: fmdx lda0cty m8 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 above the grouna/g9seyz(* w bd, and the massless frictionless pulley is 4.8 m above the gwz(ya*be gs9/round. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy co tdg.i5pmbm2,rd of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shownmtdi.,pb 2g m5 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 fric.djq.ia nbifixk77o pb u94qh eq.9,0tion 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 to startlfdo,6 t)5x 3 jnay5sq 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 accele 88t/md3tvkcu4ev ; hirating at 0.20g. What minimum coefficiekvh4emtcv ud8;3/8tint of static 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 coeffifqzpt8;8p kc1xfm2 kqhk1 e1(j/ or v2cient of static friction between the tires1hkjqe xcp1z8f m8v2p oqt2fk(/r1k; and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal st k)r*2)8xnbz5 3r( ey-ldfxyo 1bfiva n*raq8reet pavement is about 0.8. Onr5 k) 8ze qldrab8 vrai2n)x*3byy1nf(o-f*x how 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 at -4.80. 6uwxp8y g7 d8q 5cx*qi2yxrg $\mathrm{~m} / \mathrm{s}^{2}$ 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 * + dn)vboyl)ja 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 wi8y3oazr-5)/* l c .wod sbmggjth an asphalt surface have a very high coefficient of/o b*-zaj.) l5o8cyw3sm gdgr static friction.

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

  The coefficient of kinetic friction for a )a.usoo;sgujv s07o :u .afa :$ 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 wiq;w;r)8jxpt / 00xzeii3f czould box A have to have to prevent any motion from oc;ti0xj/ix83f ziwp qc)0;r e zcurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slof43s n;hg()1tpmn3,cc nkkr ides across the floor. How far will it go, given that the coefficient of kinetic fr(p;h 41n fcc ,3gnms3otkk rn)iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg0f : )w+xaz3gtdwrrg2 and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 620 3+r:arzfd )0xgw2t gw$-\mathrm{N}$ 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 coefficien3 -4: jpvv3wgb7ntm t1/jt*-hl ko cfy -kgwr:t of static friction between the m*jw- bo tv/fk3t tg:k y-nw7-r 4:cv3j1lgph crate 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 about parking your 7senicri0:fvyp/t . o1u o8* ib0sga8car in your driveway, which has an inr0v gy0b*s/7881e i.osuoanc :ifip tcline 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 us,cwi;nk3 ,eslide 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 ;v r+/3ftfh+w wdoqs 9z4z-zd0crlf- 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 spes nc;8 e5( hxsa5a*wvked 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 reachesn u3r85m/xlm;n fi3 oxlb(i.oc .q:iu the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushin,hb1p+vv*cluyndpov67 o*g4:w-ml, 4ff njlg on it with umhpfy7,bnd*gpv6nv :c *l -vl ,wjoo41+4 lfa force 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 can become dangerou rjp2w8ooyp 2yly/,7rs projectiles as they melt. Consider a chunk of snow at the ridge of a ro7py2ywyj,lr r o 28p/oof 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 stopping dis )8pflcf.(xyatance for an automobile traveling at speed v is eq.xfcpa )y8lf( ual 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 forumw5h 0un(f1k-6el3 qs5d bhd ward on the dash when the driverm1nd uueh sb0 6d(k5hlfqw35- decelerates 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 initi; 2k- 9mk1cw3tnseak ial 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 fr.atm)0b km7k hom where they are filled to the packing station 11.) ktm0a7.m khb0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for 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 kineticf39co,8s f6oqgv 1fya 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 tol;vc:d ce1u cl -3ew+he 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 puls 9hnuz:tp n13le approximatelnn z93 1uplth:y 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 chance of surviving an automobile cr .jody7 )bs*y1 ujqw*d5tg0rho2:h zmash if the decelerationhu2 bj *15.h dwq:)rmzo*o0s dyyt7jg is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal accelerationg 3x1gk fi1lvkz3u zn,02na .d produced by an earthquake is a , and if an object is going to "hold its pla z3g1 1nlg n a.3xukvd02i,zfkce" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, ebdswosp+l.( 0 xamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came too+ l(s.bsdwp0 a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-iwq+vv6albk )7 yk: *apn-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast 7w:yakbkqv +v)a*6 plis 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 Towe4ff qg;h+9gl zr of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistalhfz+4 ;gq gf9nce?   

  A cyclist is coasting at a steady speed of 12m/s but enters ze -+q l8ll9eda muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speel9d-ele+8 qlz d upon emerging?   

  A city planner is workinby th9bufjsoh:(315m g on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills w9j:uob1bh 5(t 3yfhmsithout slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles h.joqyqinf 249yw xjt;;mj 2 d4er watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that thejxn twij; ym 4q9y2 2dq;4fj.o 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 connectingx z4r+ t5si k04eoefu;b8pwy- w00lyp different parlrxe e y4ubpwwtkoz054p8if s00;- +yts 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 k3cav;pn7yz 1 xzk0 a5 ) using the pulley apparatus shown iv7a 3zy;1 nzk5a cpkx0n

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 at :dsy,zq- 7 vmx3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-restraimzf xnl),tp 9dj/5: dknt chair, an engineer considers the following set of dx k m :)jtp/ndfl,5z9conditions:
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 7p;aw;lo 9 epf ku 0v9im4s;hw(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 andhq br*oj 6*sc1 s.nar5 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 distanc*nrscrsj 15 .h6o*q abe of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "4xag jbps -6dt u s6,fehj:4*enn ,)ma 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/44na3eo5 (p e zx,uqairo3e i 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 ascendih8ri 1vm af*;wng an ice field inclined at ia mhfr*;v1 w8 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.