Why does a child in a wagon seem to fall backward whex*:p k2ey9 pvlhfa 8z:n you give the wagon a sharp pulh y*92f:ap8e :pzvl xkl forward?

A box rests on the (frictionless) bed of a trucki7ppwt k+ g3 qtob f:603bt3xz. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Ntp+bif3 zxb p 33: w0tqgotk76ewton’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 obj scnx7arw1t8 (2ymp6x lr+h9ject is zero, are no forces acting on it? Explain.

Only one force acts on an objecz2avdwj i xbc(lab4*/ wr8 0/bt. Can the object have zero acceleration? Can it have zero velocity?ja cx0bd/r v8 iw4wba(*2b/zl Explain.

When a golf ball is dropped to the pavem;ephjahl a -* p0qrts2u -wzu6-b +*sdent, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so,*0d---l j*apaezh 2bspw 6;trhqus+u what exerts the force?

If you walk along a log floating on a lake, why dq3e;; rhb 2ylwoes the log move in the opposite di;;ywh bqre32lrection?

Why might your foot hurt if you kib.6b83:t;-vmoy qq amuwu 1-xkj n7v bck a heavy desk or a wall?

  When you are running and want to stop quickly, you must decele4lb m( 5s9; on:wdedmurate quickly. (a) What is the origin of the force that condd(:b e;m 45us9ml wauses 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, and a section of the same thrzu41 + ydmnr/0rrb td+k5nh0sead 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 person0t+sz/ny+umh4 01d brdnrrk5 gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock ti; cxiczt r08dhlg-; s*(ot+is twice as great as that on a 1-kg rock. Why then dcii;t- *(sgdz;lt0+8cxort hoesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon n16fmw-xw6/hr51 dtoi;t chagive accurate results if the scale had been calibrated (a) in pou oh -6ctxt;1w1a 56rfhdn/mwi nds, or (b) in kilograms?

You pull a box with a constant -;g x qe6r8plf q8p5dkforce across a frictionless table using an attached rope held horizontally. If6f e5gpl8qkx8- rqpd ; 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 ing9s s+b+rd qpgiu1/+a fluence 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 the1ai bd9qr s++ /s+gupg Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 1/u6w, q vp3qmi.5* gkkx2 03uypz hurx0-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 with a given speed on the Mok,g /w5*u 6vy.pu xkuqzmx3irp3q2h0on and on Earth.

According to Newton’s third law, each team iy ni;m:;u m;868nxk wdsuo wg5n a tug of war (Fig. 4–37) pulls with equal force on the otds6 ;x:8nwnu;y oi mgmuwk85; her team. What, then, determines which team will win?

A person exerts an upward force+w5 xv cltf3b. of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object itlb5v x.3f+tcw is exerted.

When you stand still on .7-/d xq qub3 /xe87 zxyvzau5phjmd0the ground, how large a force does the ground exert on you? Why doesn’t this force make you riseda 8u5.jqmq x/ 7b7/ x0xhz3p-yeuvdz up into the air?

Whiplash sometimes results from an automobile accident when the vpq (4p9 )77rkneu7r*w2rlrvr r be;lkictim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatipw4;7re9v rl l) rpqrbkrre(u7n72k*on. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the tre3,mx*cpp7- p ptxsuw b yam/8 yps442uck accelerates, the crate remains where it is on the truck, so it, too, accele s4t a2yp,7bm p/4 myx-xwpesp c8p*u3rates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftrpfy,) j n)1 )psh3acler the block reaches its highest point, it slides back down but the magnitude of its 13),p sjhpr) fc)lyna acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined: inalz/,pm zl x8)beoao5m*3 neix71 plane? Assume the mechanism fun*)lzo 7,embn1l oi5a : n/ emp3xzai8xctions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/8ua3q l- 6juxas$^2$?   

  A net force of 265 N accelerates a bike and ridery 3.w gkckc q.e- 5)pkfe7pohuyru- 27 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 92+kstxyik-nmsxbxi 9 g33,gif 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 ofv4vfhqf 7 .(s-s anfwzv )7xk. a $76-\mathrm{kg}$ 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 i ee+ na5 n(ftqxi*ll)9f the car is traveling 5flit+e lqn e)(an*9xat 95km/h? -  

  What average force is needed to accelerate a 7.00-gram t)ebn6qzt . t+pellet from rest to 125m/s over6tt. zb)qt en+ a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.)*t gnf2yh0qxns z t)nab*,, b45uykl5bxl **,2asq ng,h)5bun)fyty0n z4tk $\mathrm{~m} / \mathrm{s}^{2}$ 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 am0f /*3rczuann7 eau5e n*l,l 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 kg ) is to be desi2 uals0xsiotd.w d-;v(: coe+gned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the s.2;ou sddia0 txow+(svle-:cupporting 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 moz 0-a ;j8r3sr-njhjk*by o1ogtionless elevator. When the elevator begins to move;r3hgo8ka-bnr -oj 0ys*z jj1, 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.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wha :6-ey j43boiws(rbret maximum upward acceleration can it give the elevator without 34 syrw6-ej :reb(b oibreaking?    ( two decimal places)

  (a) What is the accele 2i nrn nj)t 8qscod8r35f./xcration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal tncrti 5 xo df8j/2c.8nr sn3q)o 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* -d2m6mcysgt5 w:g1 0cv pptb;pkf h) 3.9-m high. When he strikes the ground below, he bends m2tpgv6 -5pc)p; 0 s gb:kct m1w*yfdhhis 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 tigvanj25 l s1x(:nx/mfh ) rvw1ed to the box runs vertically upward over a pulley and a weight115 xav mvxrnf2h/lg:ws( n)j is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a eh gnwob1(o-thi 6/z* 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 momk 2gx6e8j )8+1pm6 k2mmssxfo7mr naq3-xe x cent it is hit by the bat, ans of3m6 m 2m pxx87 xq6xr2mjgaeek-+c1sk)8nd again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in k7t,r2rdabpv x1ejxs , -;x;p ex7m*ra northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward?mx ;sj, rxr*7re 2;t-xkbx1a ,pp ed7v Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between h fam*8-*lqu6y36pujrtv 7fjtwo buildings 10.0 m apart. The sag in the r j6y*f-jfu*qah7m 83u6lrpvtope 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 massle f29sw -oz*.qvtmk*blss 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 14.0)ppm824ewq fei r;;hn $-\mathrm{kg}$ 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 locatin+vu0j;vt-mnx-g t+c)fa k b-on at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum onu- tvm+b;j- tn acf0-xg)kv+f 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 brb (),)syel jk auic20ehind it, Fig. 4-47 . Determine the ratio of the tension)cika) 0u(brj 2ysl ,e 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-pulley a3yc78.jxhll; rktsws )+wg z/pparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant sgyhl+z wr;kx./8c7)s3sj tl w peed?   
(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/ar3zav vv, 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 (mass7+d5 oeqr dwtk h3 hbynt/l*-, $ 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 horl59keu2a6o v-8p lkj vq2g7orizontal surface are in contact with each other, as shown in Fig. 4-51. A f 2j6lu82r vlga- oko5 7pekvq9orce $\overrightarrow{\mathbf{F}}$ 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 Fp xj,q6e(;2 hn3qc bz*5nk pfhd3jp*tig. 4-52 are each initially 1.80 m above the ground, and thp jdeqb*q xnnzj2t3 h6c( p *f;3p5kh,e massless frictionless pulley 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 connected xlpikuwvf45 6p ,s7e-by a heavy cord of mass 1.0 kg . Calculi- u5,vppe6 k7lsw4f xate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kiu c6rpvye1/px,n9gb3 netic 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 starr6iwu1-v m7lpd n5s x6t 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 o; - xikq/tz6grw, w,vwn a train accelerating at 0.20g. What minimum coefficient of static friction must exist br6 twwig,;q-wx /v k,zetween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficj(2g1 sgb,m2z*qvrz+zb yl)t i ;xlm)ient of static fricti m1);lg(x2b g)iyq*+sz zm2,tbr jvzl on between the tires and the ground is 0.80?   

  The coefficient of static friction betwz 7; flp-ybn.r)v pt7,9jwko0-zwsz h een hard rubber and normal street pavement is about 0.8. On how steep a hill (max fz7.tn;-j0-plhp 9b7sk v zwyw)zo, rimum 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 decelerate4a 1n ii+h4d7 o im- xwd7o6x)k6eby6nx*edn h at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on ax1r)5 f 0ormlvor3c f15e wt(w rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a veb12qfbb-3 wd,vobg/ sry high coefficient of b2sb g3,qvb /fdowb1 -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 eww c)n:n tv/,i/j.aaq u3no7$ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would boxy 7c1c1 j1cgvl ztzk)1 A have to have to prevent acj y zz gc11)1cv1l7tkny motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far4+b2my2 i2fq)n e iocx will it go, given that the coefficient of kinif 2o2n)2em+qy4 ixcbetic 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 ho9r jmepmmn6fd:j). l5f9 -h rdrizontal surface )jh6-em :d.9fpnr5mml rj df9(Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of s fatn45mqm6 pc,4;f2lp eh) whtatic 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 against the cab of the truck2 hplc,;5fehq t6f4mn4)mwpa?   

On an icy day, you worry about parking your car yng+ (nzee7 +c*wnq y)in your driveway, which has an incli c+ey(+ngqy7wnn* e z)ne 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 slb.4mzj 7j1eg yide 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. 4-5vw 6bvl+3/1phaz llr*5 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed ofw p/p ub*a)7cv 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 steepesttq yl6t ft5acz3 +:.euc4np+t 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 jh- ++e)4,rq wexsji 1go8lar by someone pushing on it with a forceh,jej4ar- lo+x r8+eqsw ig)1 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 becomorv4 7lw+ :socmx)l sa,bu75j(a- nvy e dangerous projectiles as they melt. Consider a chunk of7x 5( rj :w-vuaovnml,lc4 +bss7) ayo 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 sge :ky,xg*4s0bqu2 cut/f r +jtopping distance for an automobile traveling at speed v is , *ggru2sbt4e/fxy qu:jck 0+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 when xt,zp-h:hyxk-fy x0w /,k+ k rthe driver decelerateskx-: zyxtrxyh-k/ ,,0hp +wfk 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 givenh ;d3-axzt u9u 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 they are filled to the packing s))aoi )qouu)ru6 kz 7qtat)7q))6) ouuuqk roaiz ion 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the 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 kxxgs 1wu+ynghv nj 1 3*i:l4n8,e0bfq inetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a l)5ek:w o0f lnh a.dr* 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 an ugx2x55o+ ve mammalian heart, at each pulse approximately 20 g of+5og xve5n2ux 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 crash if the dec y4a5px2 7alfi7l,gzy eleration is no more tl xyf,42gyal7za57 pihan 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 acto. tztccuv g ;;6xm/+celeration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mu/ oct .6;zvtx+g;tmc ust 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 sc5w8ot 2g6: .;/wzh;mjz 0*b q hswfgxjh bc7toene 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 car assuming a leq 6oh cws/bxtmg.z7hzw;fj2 w 5:;80hgj*to b vel road.   

  A car starts rolling down a 1-in-/ v 4vqj+d,an.* pchau4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). v j. 4nd/+ u*hpcaqav,How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from trz q(l8so /xce6-bpd-qu+, qjhe top of the Leaning Tower of Pisa and falls 55 m befr xe+szqu q 8cd--,( qljp/b6oore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch4(/ aor w*pp2w)rk clq 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, q2l)arc(4o *pp /r kwwwhat will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly pol,dcr;yhrylzf3 6 bx4 9e2cc1 rtion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelzx ;brr49l c l,1cycyfedh362 erate 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 t a +4 wgf f6e2;*fvwczwrij9s 1tw*q++4pxeta thin piece of string while *s+w9eqgj2+r *zatpfw;f +tc 4fiv6 e 1ww x4tthe 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 connectinwj:c wf-u 66wpg different parts of the wfp6jwu c 6:w-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 8np li,sdu 2f(needed to lift the piano (mass M ) using the pulley apparatus shown (fsldi, p un82in

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 accelerati0 x ze3,nn:eu8r zrc3ing at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restrainhfyrjz6ms:3 oy)jo-9:j yxz6 t chair, an engineer considers the following set of condition9:szyoyy6:oj)z 6 jfx3j rmh-s:
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 toh-,r5 nzov;) hyoz2 elns (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 an4uw v4bm*3zropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large v4wa bz*34nmu 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 zwv 6hso-n4 r62o1f;duvpmrg f1ct;7" 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 b*)qgorgy :nq)x:pb:7h fh;vs uilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped togvj;5zk9/m p jcether are ascending an ice field inclined at 2km/j9zjc5; pv1.0$^{\circ}$ 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.