Why does a child in a wagon seem to fall backw m6ntiau,+ q*fk xtjhxb-5 )t.ard when you give the wagon a sharp pull forwar u , natj.bx*hqtt+f5-)6xkimd?

A box rests on the (frictionless) bed of a truck. The truc atmwxaof /sl55454co9my:hck 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 besi5mo 4olc ywx fa9tm45a5h/c: sde the truck and (b) by Chris who is riding on the truck

If the acceleration of an object ifelcb wb x:w/vt3e.:2s zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerat1k6o-swf )5 hr7tk)e b,sdve*s j34cjk-ofdcion? Can it have zk)51s3) j c- bjhed6fc,o*- wvk4ktdefs s7ro ero velocity? Explain.

When a golf ball is dropped to thwno8s7vmgu7l ko., 6m e pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If smn8w7og u,mlsvk67 . oo, what exerts the force?

If you walk along a log floating on a lake, why does the log move ifaad; wr83y( mn the oppositwf( md; 38aryae direction?

Why might your foot hurt if you kick a heavy za .rz 5 ;tln6y)0ogqbdesk or a wall?

  When you are running and want to stop quickly, you must deck urb(neske(*n1,o: jelerate quickly. (a) What ien no(e1 ,r(k sbujk:*s the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling,6yvs: h;hm( )5oy7xvk lfmlz+ 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 your an+(vzoh)6 lvy5l:;7mm xy hkfsswers.

The force of gravity on a 2-kgtqg11 ggzn0 xmls 54 lexah7-qg-1 9*r qrmfg4 rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier roce7rg1 glg14g50*49 mrax1qxg m fqh-lts n-qzk fall faster?

Would a spring scale carried to the Moon give accurate results ifs4.dy95 xrd na su;8nx the scale had been calibrated (a) in pounds, or (busdax.5n n9dy ;r8 sx4) in kilograms?

You pull a box with a constant force across a frictionless table using awsssxl-o::ax -+ v9;y)wpbvufpqh8 2g *h-d cn attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaind- -)+xsguw 8q*-2fhvh9 v:pacs s;p:bw yl oxing 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 thukg qhdd1:4 2r.xv*td e influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the*.dd:h4dt xg2r 1qv uk Earth. Why doesn’t the Earth move?

Compare the effort (or5t(a8h xtfc,t force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally withftacx,t 5( th8 a given speed on the Moon and on Earth.

According to Newton’s thhbt2 i8cp2wxalh(u8gc k 75*lird law, each team in a tug of war (Fig. 4–37) pulls with equal xchu2kiw2bhc 8pal87g5t(*l force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N mosw,752.b nte 1tcva to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by statine5wsvb,ct7 o a2.m1 tng (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 on the : xymkm*+5i*axzk-bi ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the mkaykm- 5biixz+* :x*air?

Whiplash sometimes results from an automobile accident when the vi)oo5wcc4rl 3mbz; /e eq)u 5k7m h6hkictim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. m;iur q5e 5b6) 3hwk4chezmkcl /o) o7Is it really?

A heavy crate rests on the bed of a flatbed tru:sg0axng0z s9rl 9wu, ck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What:x09,9a0w lzgn s sgru force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After tpi h.; pdbma../b2c rlhe block reaches its highest p.pcmb .;a2b/ lrpih.doint, 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 inclae9h gg* 35os ;c/sn8vl4 kimlined plane? As3slka8oc5/miesl g 4h*vn; g9sume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a chil.-ynhn3v :s zez2v qe6d on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and*8gxr*kuvl (s 52 fp2gu zj2qj rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a r56c uc rkz2h54nqq wu2t;( dzrope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a grto 751(jt60aq *hcbn5ymqz $76-\mathrm{kg}$ 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 az vvsec kf 179lp4x:2sn 1100-kg car in 8.0 s if the car is traveling at 95km/pxv1s4:f9ke cz 2s7 lvh? -  

  What average force is needed to accelerate a 7.00-gram pellet frob a( * p+,zc+winlzx4ut 1m:bkm rest to 125m/s over a distance of 0.800 m alo* n,pz1wl4ibz u :xm(tc++ abkng the barrel of a rifle?   

A fisherman yanks a fish vertically out of the a nsqpc n.73 8hel:tesu.(g2jwater with an acceleration of 2.u ae. e 7 jln(gqt:3chs2sp.n85 $\mathrm{~m} / \mathrm{s}^{2}$ 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 co*::ziox 3sqnyver a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kko9 )n c5sq-k(dyiag74 vq3z2cx(azk g ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces tqik5zcs4g k(k yxq-9oa )vanc 723dz(he 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;ut(t5d lmec/ a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, anlu5e t dc;(/mtd find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 217iwlz6qa3 be j2f:ue 0,750 N. What maximum upward acceleration can it give the elevator without brea ezw6lqf:uea230ij b7king?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includil e(htr(8yw8 dng parachute) when l8ytweh r(d(8the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he sth2wm i7gs om 31yf8ej2rikes the ground below, he bends his1h fo i2 2m7emj3s8gwy 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 run7 q7q.t m):7n vwalidd(hly.ts vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tabq(wal n hidv d:tq)y.7l7 7.tmle exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball ple 0q (lf-1ztc5l/umuaayer
(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 the8-wd4qgx2 nm q bat, and again (b) after it has left the bat and is flyingq4 2wn-8mx gdq toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forjmacb1zfz(vv ;;gt/,d -8jnkmmj:o: ce must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your ansgcjz,tva8jz jmf b o: v-m;k1 /n:(;dmwer with a vector diagram.

  Arlene is to walk across a "high wire" )ufhqy:8zt c+osa ,n7o e ol,5strung horizontally between two buildings 10.0 m apart. The sag in the ropefs:oaz,l ,youqct 8 5 +noe7)h 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 h056fhb fhc z.vanging 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 1zc;m6 cvz7 o /ih;ue2rc*rar3uqn. j/ 4.0$-\mathrm{kg}$ 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 loi p+9iu r:wswauf q8r0fw.**bcation at McMurdo Base, Antarctica, as shown in Fi.ww +u8b0 uaf*rsf9r:p*qi w ig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it,9* j0n l/.ndr d 9qo)zufx)rui Fig. 4-47 . Determine the ratio of the tension in the coup z)djn)quf9uinrxo r0/ l*9d.ling 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 rxdu +rg3i9(txsf;m1h0 tp w5apparatus shown in Fig. 4-48. (a) How hard must she pull downward trr wxsmit(xh9fpg0 d 1+ u3;5to 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, a w ncq3(9 2p*thijc mx*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 (map6kol;gjsp q .lw4nt-c x/n8sn: :at4ss $ 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 aresg ; c:z,ipb1j in contact with each other, as shown in Fig.bpzsi:1g j,c; 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 abofvm21+i s znw 5d40tp:tfput m/d-u/eve the ground, and the massless frictionless puli2fv+4mu /ws:ndpf01u /pd 5t tm ezt-ley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connecd ax9)(us2 c/s y)lxzx1,ncl cted 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 sx2clxy(n ca,s)1/ cz)sl u9dxhown 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 kine2z3krtt 8 i(i8diet1je2q2/y6rd8 hs,o wo nntic 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 toc+lzsa h, j(4k start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20/ i+)w2ruq xrxjs9q(b g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to sl)ux jr (bir+q2x9wqs /ide?   

  What is the maximum acceleration a car can undergo if the coeff5ns swu 9p1tov o5y3-tm*2ifd icient of static friction betwostmv 5 f51o3-*d t2 w9upnsiyeen the tires and the ground is 0.80?   

  The coefficient of static friction bet o(6hj*p4y azupi r*klt 23t5uween hard rubber and normal street pavement is about 0.8.6l4tp(jort 5au*y3 2 h*ipkuz 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 lxxn.b68dc9:j xcv h5.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough 30c c3a omr;*i/vic)rg7 strsd;opc+ 9 6$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an as+x 8eex(kx-( ex7 jevqphalt surface have a very high coefficient of static fri8ex7ekq(x (x ev ej-+xction.

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 kii9jr/slh744 wn l 9pqma ibx(c(ww:f/netic 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 mass wof qo3/g + x)r4jwjl8hssuouyv0c wo *j :h+5d/uld box A have to have /)+ :j wc0sld oh/*yhfo ju8rg ojuvw4 x35q+sto prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across u3cznw 7a.ea1the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of e3zwa. c7nu1a 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and atmgk-n8l iqcie+2cl1 zor, 6*x rest on a horizontal surface (Fig. 4-54). A 620,8*q1r-enziclmc i 2lx +k o6g$-\mathrm{N}$ 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 stati kera -e(vx)+tc friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver + xa e)-v(ktercan decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your tvw+tplm bu)ht/5;y6 driveway, which has an incline pht);+lv6t m yw t5/buof 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 with a 2.0 flawy( xnz18$^{\circ}$ 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 a(pxg49 l6zxd ongle $\theta=22.0^{\circ}$ 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 3.0xr l1p, plz(ap 21qdn0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a .o n(oc(l -itekm6 )+(hjvlz yspeed 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 pushing on it w- deykfox *dutu1cf) ewd.* +;ith a force directed ex. ky**f)+1fewd t;ud uod-cupward 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 slippern sqm )it /ubq0z64z.ky roofs can become dangerous projectiles as they melt. Consider a chunk of snow at tq0smitu .nk/6)z qbz4he 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 stopping distlajan -p 09x3pkd1 32bnswfx 3ance for an automobile traveling at speed v is2wfbx dp1 a3k-nlxj39a3ns0p 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 slm6exk8ol1+b ;;cnyle ides forward on the dash when the driver decelerates;8x ; ylk+ec1ml n6oeb 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 c2 6vzf(w9hazw jv .rj,cw5 p;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 from where thmx1f *8sngj1w4ivmrzg6d ()g ey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the tm8g)1n jv dg4( f*r 1gsi6wxzmrip. 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 coefficiex vf)4ka 38cjbchy: w9nt 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 (including the bi -3 0bqczzixb 7lfm5h(cycle) 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 oy:st1wf8f w *r,hrb0 pulse approximatelyo w 8y 1f0swr:fbh,t*r 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 chnbyk/4 d7hwa/ wr/6 gv*: dkdeance of surviving an automobile crash if the deceleraavne/dhw7d/6d:wbr 4 kyk/ g* tion 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 acceleration produced by an earthquake is a , avxvjrax 1w0 7.nd if an object is going to "holdax1v7jr.xw0 v its place" 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, examining the scene of an accident ip zz4k sfj12nr4 s,2symg,t r)nvolving two cars, measure 72-m-long skid marks of one of the cars, 4 r ns2zsy,) pgmrj21sft,kz4 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 car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for e;*qu(xu*9kn+t pgalt) hqwy , ach 4 m traveled along the road, the elevation change is 1,yk+hwgtxl au; 9ntu*p(qq*) 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 frorq r, disy/8x:m the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground witdr,q xs:y r8/ih a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stdwt. en wz 7/vor5ezxrs(+f(*eady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the5f +r( xtonw(v/z es7.zdwr* e muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesig-icgn ulad ;0padr 594n of a hilly portion of a city. An important co9 a4ualin -p0g;5ddcrnsideration 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 road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin pb(--pewc0w(t3rto rzux2l6 o x :+wfu iece ofzwo cfr20tx3( rpu(:-bwelxwo 6u+ t- string while the jetliner she is in takes 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 supermarket, there are to be several ramps connecting differel5yquwxa32z+ pgb*dupr( :* ent parts of the stx* +lz3g r pb :a*pduu(ye5w2qore.
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 nuj 9q/mm: f-u ; *0acwzi3eakzeeded to lift the piano (mass M ) using the pulley apparatus shoeqaw * u 9f0;-jkcmm /:azziu3wn 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 qt z, hsw27 )ixp,*lup3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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,uz:a+:qi w4y z zw8+oh an engineer considers the following set of conditions:o:zwh8 yiq+:+uz 4 zwa
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 fnch xo.7,mxh 48nexe+v r frz*q)-4a 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 similar length. Karen'lj))t0:njbhln:. nghg 8uad( 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 (Fal ::(dnt jgbhljg0n). nu)h8 ig. 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 uglin 6vq)u *iz -f-lk+cj -jq5rkv)q3q3dv*osing 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 ;zo xo7mu a2i9to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ic**f cry2ig*ziewg*fh q/h 3 l4e field inclined at 2q fc4gyg*/zi*hh*3 i2lw*fe r1.0$^{\circ}$ 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.