Why does a child in a wagon seem to fall backward when you gid5, q8)sdfob+ ugk/gn ve the wagon a sharkb)go,gns fd q +5ud8/p pull forward?

A box rests on the (frictionless) bed om + 2ssvb-j,vjf a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward ,b2s-sv jm jv+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, are5+p;nh/f4 wrg cn;d ;y c y8j3nc0zodf no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration?rolxuc,83p;de- l t*5.uvg ns Can it have zero velocity? Explainptd*g,.nlv - u 85o3c;els urx.

When a golf ball is dropped to the pavement, it bouncxxaz1gr m1a:; es back up. (a) Is a force needed to make it bounce back up? (bm:;gz r xxa11a) If so, what exerts the force?

If you walk along a log floating on a lake, why 26*:baaby ddodoes the log move in the opposite direcb6bd yadoa:2 *tion?

Why might your foot hurt if you kick42gbc ex)yu-ckh 7d;8scl)a q a heavy desk or a wall?

  When you are running and want to sj--+g(2 h xbjwi0zzv5+ otlyu top quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stopvj z(-ygu2hl+0w5+ijot zb - x? (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 thr;3jh1) pkb p,f 2vyrqhead 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 thrvj312)hrkb, q;hy ppfead, 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 twi+mer+su35op2 myde)l ce as great as that on a 1-kg rock. Why then doesn’to5u2s +elm +m3re )ydp the heavier rock fall faster?

Would a spring scale carried to+w.cs zqs.x 3w6vume4 the Moon give accurate results if the scale had been calibrated (a) in pounds,se3ws+..zc x4qum 6vw or (b) in kilograms?

You pull a box with a constas/ 0vochqncbm.2/))b lc 9 vgvnt force across a frictionless table using an attach vcv o.cl m/bv0) )qghns9/2cbed 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? Explain.

When an object falls freely under the influence of gravity th(5l/ eoo3 lcleere is a net force mg exerted on it by the Eaeo el(o3l/c5 lrth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object wite.;hx, / egm-j7/ ih afw5nnhen you are on the Moon with the force needed to lift it on Earth. Compare thete. g/5ifn,; a/h7e- hwijnmx force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in am);bnuf u h6o: tug of war (Fig. 4–37) pulls with equal form)6hu : bfn;ouce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bagm**df / 4ivwsi m-h*yo9xus2uq2l 0xf5-xnwi of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted,*20uhssiyu wx9 vwo-i 5ffq4m mind2*x*- /xl and (d) by what object it is exerted.

When you stand still on the ground, hory5h/8wh4 d7vce9.lv xmn;adw large a force does the ground exert on you? Why doesn’t this force make you rise upx c8he7v5y wr;m/ldn4ahvd . 9 into the air?

Whiplash sometimes results from an automobile accident when the victim’s s jn ,ol4j tjf0*1ho0mcar is struck violently from the rear. Explalj* o0 of0jhj,tn1ms4in why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whenz;9 nl62yymsw the truck accelerates, the crate remains where it is onzl69y sn;w2ym the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itsekfv07 t i+-cr highesti v7c0tek+ -fr point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incliksr/p; / w j:an,o mg;g-a0uysned plane? Assume the mechani;su;g /,ga: k-o njms0pwya/rsm functions properly, even at an angle.

  What force is needed toprlz q.m..c, o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N (l+6fikopl y5 )( k9vtdjr8xpe4i z)taccelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand 7kwsq;xz2bl -jp)19he/tq)lc2f ca fif 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 *0b(a+5gelno vl zdd2a $76-\mathrm{kg}$ 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 in 8.0 s if the car is t vw)ne.w gmr/eq3g3dmc1/vm)raveling at e mg. 3d/)q)mvwnr1 e3gwcm v/ 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelle wwlv-(h0hc8sxv - d) sbpqmhv,r3q .2t from rest to 125m/s over a distanc q3h.l-0dbwhx mv2vps,w)(src- qh8ve of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water w 6aamk5zxaehihr ev4-t7e;6e 1id*z,ith an acceleration of 2.5 aed*zxrtkae4- ae1hizv ;m6i57he 6, $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track x9p6 gu:hk ar2 -mna*f (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum accele+ b76htlpi+ap p(li9aration is 0.0680 gbplpahlt(i67 a ++i9p . What 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. When the ep8 +)fxo/*qp5av z;lf ydrfu- 3 hkb3vlevator 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 acceleration.hvl 5/ ) rayx*3k+p8f3 pvf dfobuq-;z     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,73 h ru-r6blv+3kkga r3 /j5bmy50 N. What maximum upward acceleration can it give the elevator witgbr k3vb35 khy-rmrl /6auj+3hout breaking?    ( two decimal places)

  (a) What is the accelera 9h4sk/, og4dfdww ;rhzmq / h6q3uz4ztion of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of thfzr9,hg/h qmd4wkzw3q oz4/us ; 64dheir weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.aq+mhx309 nmyr z;i yo.mj(dw:* 8ue5io pa8m9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates(8y +uhi.pn 8a;djyaomm me903z m5riq *o wx: 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 uy0*o kpz y/f;bpward 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;f0by/ ypk z*o 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 diagram fed1-vh;4d an wor 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 bw p6nq1r .qy6sevs +1naseball (a) at the moment it is hit by the bat, and again (b) after it has left the batnq6 pv61 w1yqs sne+r. and is flying toward the outfield.

A 650-N force acts in a no*k1dgv cng/o4 ;)dihnrthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces p4gc hnd og)id*/ k;1nvoints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildio81jw v1d;rnp:d4,wi. zt-yghwea ywh + 0zt, ngs 10.0 m apart. The sag in the rope when she is at the- +a h:ywdi,; 48zdo0h 1t,w.vrwgny etz1pjw 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 han9h ld ydz kn d/,/pkb,/uk+w7tging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0metozx p vw */1wm (1pajjtsj* u7b540$-\mathrm{kg}$ 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 housin10 l rg;au gmw96odh-l ul3gy*g unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sllugog1ha 09w -*m;lg3r6 yudum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind is*h7x 0ok z2yf:6ki3yn ns)d ft, Fig. 4-47 . Determine the ratio of the tension in the cox hokyfif2* k) nn d0yszs:736upling 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-pulley ap9 -pm/bvc(azl paratus shown in Fig. 4-48. (a) How hard must she pull d( -a pb9/mzlcvownward 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 began, nrdj ,;;wpor-+ hpoclk*zgs, :sqez- 3ep9+ ia 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 (masstd19:sy oi39f xuz aqjh0f 2-w $ 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 contact with each othe7b-7mws t 8rift r:qn)r, as shown in F7q8 -nrtb:fi7t)m srwig. 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 ;n wxs7cg gw*jm 3,f o,msgm)61.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is ren67x,jgofm;w *wmg )mss c,3gleased? [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 frqf0v4c x,i9 tm3)qeikictionless 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 cord, using the free-body diagrams shown in F3mi0xk )e 9tcvq f,4iqig. 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 kinet;o+wl:b* ,m ckx 0dvjmfv;)z fic 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 to sta7t hxpk.pj(2qrt 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 accelerating at 0v- 2nea.ae p(b:or3d h.20g. What minimum coefficient of stat-:h v.a2o e(drpabe n3ic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car canp(cocqx1y hsl5,q18lc./z -npq:fbk undergo if the coefficient of static friction between the tirk qnq, pcs.chqy/ol(:bl8p51z-x 1cfes and the ground is 0.80?   

  The coefficient of statiz16/il8c8 yd(5p bnhyc ;orr jc friction between hard rubber and normal street pavement is about 0.8l;zb 6(n8yd/c 85r jphcroy1 i. On 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.fo. 4vpvvf 5*v aygo/080 $\mathrm{~m} / \mathrm{s}^{2}$ 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 a8, vep7e0yxrr mea6i6 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 contacl yl4b)dr04zp t with an asphalt surface have a very high coefficient of static f0lrzdyb 4)pl4riction.

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 kinaj4p+/nvo ydbc)n *dvy 4. sk8etic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a m.wy gptsaj s7a*t w//mnn9/7mass would box A have to have to pt*9 .m7/jman/a/y wgtsn wps7revent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slid:vdp/7x/a5jsvlds(3a b rdf g36/s nv( qtkr. es across the floor. How far will it go, given that the cof /s7(lvx r/n3dk: svgrs(v 5ab/tqj.dd pa63efficient 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 and at rest on a hr;fysns7oo1 ; .zcbd1:s)t psorizontal surface (Fig. 4-54)pb dt. ; o1sc;)syor1nfz s:7s. 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 coefficient of staz+hyc:twug62+j h;ln:w:7 y y(smu* mmja /bq tic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide w+ +(nm qu*:bwsm6::ahugyjlhjc zm2 /y;y7tagainst the cab of the truck?   

On an icy day, you worry about parking your car in your driveamluv 3/n 7qmwt9(ta:ud+p3 b way, which has an incli:9(v tbd3t3u7 /pqna+mauw mlne 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 wi 3mqjlo-wb)j dp+3f-kth 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 tiltedl-ehy.gx8l2 i 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-r s2c6.)/ey meliuwn initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hile6th0qmu/9v e69rig k l 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 s /1r-u g86.m lxlutrwat*m y+in place against a rough wall by someone pushing on it with a l/y1.wm xm*-+ulrt6star8g uforce 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 dangerous projeco7nsern-kp:09-ovu b tiles as they melt. Consider a no 0n vukp9oe-7:-brs 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 stou+13k+xr(pz) bz 2n izorjf3opping distance for an automobile traveling at speed vnzz2zr rj3 3)+oui+fbk1 (xpo 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 the dash 2780 3dvxrqsk4/r*pzqe ovti z 5r:fp when the driver v3r:zirp* qktd0fez/7sv 5 8pxo 2r4q 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 isva/u gdn:x3kt(as2/ o given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt fro9kt*jrqt kk*nw ),v8sm where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rap qw**r9kkk8)jvt tn,sid 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 coefficie.girt9:m jz k7maz p(,nt of kinetic 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 (in/30b 0gmth1f8g sr(xds :balkcluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified mod/xuvtlu 8 f:b n(c+vw,el of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fr:xl 8t nc,uv/w+f ub(vom 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 automobikb*nk m,sts;v4i8+ckifk d 7t 5:mh( qle crash if the deceleration is no more than 30 " g 's." Calculiq tifs(5,*k ;+dtm 7hv:8k c4kksbmnate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is ju 8x+czrqxu:+4 h qco g)p h6:d6+ggw a , and if an object is going to "hold its place" on tjgdx z+ 8 hugo6)rp+ug::xqhq4+wcc6he ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the .w ufn* s2l*4j-5 xmcjl/kzrfh/7 vwmscene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that c 5mj llzwvmk-ujc /nffh4*72 xs*w/r .ar assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveleaos z,74p6)l umk08u2h tybcpd along the 6,m k2s8cp z0h au 7ty)lop4ubroad, 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 pi; -w75 xxa3kmws*cxy,q/i cfrom the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the avepw yxa*x mqi37xci c;-/5w,ks rage force of air resistance?   

  A cyclist is coasting at a ste*+fp0f y 9r:lrlksy)mady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the ml:*k+ rpysl9mrff ) y0uddy 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 al )5hw+qfiia8xb 3qe4 5n5 htn city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level roafnii8w 5qx5a h 4h) 3bq+tel5nd 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 pie6jq iq. 9zwm6oce of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Sh6mo.6qqz jwi 9e 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 supermarket, there are to beh2 h0*tw h(d:xm3ip rn several ramps connecting different parts ofhxh*(npmi h:wr 20d3t 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 (mass7z:9(guurg*l -jqvl i M ) using the pulley apparatu9 gv(il 7gzu :rl-juq*s 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 at 3.zl8b:tn(c8jc jfd) 7 m5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 enginedswb dz+n:h;su. un /2y *dv,her considers the following set ,:2;*nsb.+n dyu dudhswzhv / 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 mass of 660 metr/l+:pm6 sb qhk-l5c rlic 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 ropes of simil4dy2y-:ta +l,a t khejv3dp+qar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recep -ta: tyvyj k 4,l+2d+adhq3ommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat bqd pwmy.z,64/jwi0kis 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 t x*bzvaso0i bx*,. ph(o 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 ab2b8yn )ye8a,)ws: yd afrzq5re ascending an ice field inclined atsbdy 8 wqf5ba2) y:a8ezy,) rn 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.