Why does a child in a wagon seem to fall backward hb cfbj wwcrd 49t 7p; dlw-c/i,-28zewhen you give the wagon a sharp p-98wlf2p;rc w cwibdhj/ - 7b4tdce,z ull forward?

A box rests on the (frictionless) bed of a 1 6b i1 nrh 6kprinwe1ak(-,pytruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truckk616hrn ak(1yiep b-r 1pniw , and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on ita/mcv;d 0x1z/sk5jh h q9bi c.? Explain.

Only one force acts on an object. Can the ob6rwa;:b2 usdyjvc1l el1z/s0; fr *ix ject have zero acceleration? Can it have zero vel*ar2ilbxl :frv; y0us;z sce/ 16d1jwocity? Explain.

When a golf ball is dropped to the pavement, +shohbi9+5mn ; d saq8it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fors9dson hq+h5+m ba; i8ce?

If you walk along a log floating on a lake, why does the*xsi w:9vx6w) 3i235 tpu u hmve;kcea log move in the opposite directioewxuvi95* ku:we ;v)i a c36h2tps 3mxn?

Why might your foot hurt if you kick a heavy desk or a walqc)a:;a8 vr xhl?

  When you are running and want to stop qu,sw0 7zbd e/cb6xb-frickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) t7bxs -cb /,fwb rdze06he 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 t98x+15 rmem zn/t7f-x nwhw,x 8xpyifhe ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gi yntxe +/w1f -7xf8mniw5 rx8,hz p9xmves a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.cw xc1+nvf00i3 no k.v Why then doesn’t the heavier rock fall c+v 1nnox.kv0c3fw i0 faster?

Would a spring scale carriedsamiigw7 . t01 to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) mait7giw0.1 sin kilograms?

You pull a box with a constant force across a frictionless c1 ambms( :rk4table using an attached rope held horizonk: 41ms(cra bmtally. 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 gsgt w/s ;,4(n euxnxs.ravity there is a net force mg exerted on it by the Earth. Yet byu tsg(4ss , /exnwx.n; 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 when you are oseq qp99 u+b.ln the Moon 9b.lq+squ 9e pwith 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 Moon and on Earth.

According to Newton’s third law, e1 x 5 i)hv4mlok 4desh3t66lqv;k j(j5vmrf(jach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will 61jm4(6vdvt 5q45kl )(mje ;xhljhi kvr3sfo win?

A person exerts an upward force of 40 N u l4., cm9osiuto hold a bag of groceries. Describe the s um.c,iu4l9o“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 it is exerted.

When you stand still on the ground, how larq6pamtfc ))-mppy1 k; ge a force does the ground exert on you? Why doesn’t this force maa;fmp q-yc m)p6) t1pkke you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s ca,h0e9gwy8olua f 0r *w4tyow5(xh q4pr is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it r(w*,fpy8lwg940 x ya ewhhu450 ootrq eally?

A heavy crate rests onm1nw*o)i8guc j u9dg5v2 s8sc gsu 6m0 the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to v0suc8ui*1dmg9 n5 w2) 8ucso6jgs gmaccelerate?

A block is given a push so that it slides up a ramp. After the block reaches it8dvi4tx 20s ,s8v gufks highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?4 8s0 8ftxs,gvi2u kdv

What would your bathroom scale read if you weighed yourself on an inclined p2+ka cg5tlfx3 lane? Assume the mechanism functions3 c2 5tg+xfalk properly, even at an angle.

  What force is needed to accelerate a child on a ez,w46iho:o4oal k, isled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike afg2d xx (vx+75nbj2zqnd 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 withstandi q9yyv ,:hic6 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 )t,d:yx/qyhp :a m/cy $76-\mathrm{kg}$ 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 a3kd vqs odl3n+-z(h3fn 1100-kg car in 8.0 s if the car is traveling at 95km/fdk3q-s+lv noh3 (z3dh? -  

  What average force is needed to accelerate a 7.00-gram pellet6 8t8jx+fh+9 w2no2ae q exudh 9scx9d from rest to 125m/s over a distance of 0.800 m along the barrel ofx2w6 oj9 x+89e shxeud92f tn+qa dc8h a rifle?   

A fisherman yanks a fish vertically out of the water with an acc/xrwn7zxy0ws6o (dma- ;hmi 0 eleration of 2.i ;7nr6 sxm( /0z-odwyhma0w x5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 carymyzw xex( 8k mu3;);l can cover 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 kg ) is to be designed so that the maximumhzao0)b7d5al0v gim* acceleration is 0.0680 g . What are the maximum and minimum forces the motor should a g0dvozi *)bhlma705exert 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.y:(ubdjyb/* ,6bgj zj 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, and find the directioz jbbu6g:dj(/y,j* byn of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has ;f1wi:nqc 00h jj;eh6u bwg9 ja maximum strength of 21,750 N. What maximum upward accelerationqb0jgwuh6nf hw j ij;ec: 0;91 can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divellh3 ueu;ye*vwv)k (8m2ak1d x 6pzdff0ku; 4rs (mass 132 kg including parachute) when the upward forcekzupf;mv luu)e6fe8d 4k 2hyx(k * dvl3wa1;0 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. oyt)l-t rilhyjuumn* .0 :0 d:3xmk,kWhen he strikes the ground below, he bends his knees so that his toroyhrt, jtk0ll dym k niu):0u.:m-*x3 so 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 ry f1v k *l-:wdg11pqsnuns vertically upward over a pulley a1fp ylvng1*wq- s :dk1nd a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging 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 basketbal1 w5udz s54xy/ 7r;lmbjfo )ull player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the b* w bhvd7m :uts.4s+mvs-gp8inda2c5at, and again (b) after it has left the bat and is flying tovaugv*h4is7btmwp m2c:d+8 . 5s sdn-ward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force musti m3f -eoz)r.z be exerted in what direction so that the resultant of the two forces points westward? Illustrate y)ir3 mz-zf .oeour answer with a vector diagram.

  Arlene is to walk across a "high wire" stru7(n f,vh g7b2vq 1 aiqz:(ssubng horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is g2qv finza vs,(7 (sqbbu7:1h 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless corda7 3vh ,0itb hss *qjs/yze-8 t5hyo,b 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 14.0llq foiz8)2o)$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarcticarr, 7 *tzossr., as shown in rs t7*r.s,ozrFig. 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,vgh ) p :kl ;53yf4jtywer(9d w*;xzku Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first c y: jw;ye l3pr w5*d4vuzx)(fgkhk;t 9ar $\left(F_{\mathrm{T} 1}\right)$ , 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 appara *lpnp-,fnj0h7;z l entus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constal n;*,np zf -ljph0e7nnt 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 cvc4b,(nw7ug evxqjgcr-71e xxs82; began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a blocnr; gf9g-u p;gbdyb 0j/-gh h0k (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictiybu8b4sdtt) me wa .o *k.zj2et7,3dsonless horizontal surface are in contact with each other, as shown in Fig. 4-51. A forwb b4.d*k2a to dt38ms7utz),j y se.ece $\overrightarrow{\mathbf{F}}$ 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 ini f6o* t 6/zm5;p cjpcp)yio.njtially 1.80 m above the ground, and the masslc6opz*p.t /o6icjj5 y);fmnpess 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 fricth9la nb0/;2tt us lyx/z*b;jbionless table are connected by a heavy cord of mass 1.0 k0 ;9nxz h2;bstjlby b t*/ua/lg . Calculate 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 kinetic friction bei(p p:8lfcvg f:( eyrp/7 )qrytween 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 s) .kkk f0f8xjxtart 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 0wy xe/o *+85ebav8rjcuqx7z train accelerating at 0.20g. What minimum coefficient of static friction must exist betweex5ce+ao xw8zyb/qv0e j8*u 7rn your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo i8vam h9*em-3wk6 cbpz1,ni xrf the coefficient of static friction between the tires and the ground is khnz1 v9amrbe,wi6m3 c- xp8*0.80?   

  The coefficient of static friction between hard rubber and normal street pavemr*)d 1igqt5hjkn +ki,ent is about 0.8. On how steep a hill (maximum 1t,5dk * rgiqhi )k+jnangle) 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 -4.8kc he s )jplh2pa-(uop7l :,-x0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rou7x nvh*rkhy5-h1 4huc qhhr5/gh 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 very high coefficienn0iyw1k fnut:2z.(,qrge g :y t of static fneuqy.0, wt g:gnf :k1y2r( ziriction.

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 fri* ufya4c )j.hhction 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 g(mq:3xd+2 6izlam voy 2nan,would box A have to have to prevent any motion from occurring? Assume 2o+x:,m3qg6 aa(inv m nzd y2l$\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push vh6s e, os(:ji zxqde/m*ya *sze7,r- so that it slides across the floor. How far will it go, given that the coefficient of kinetic frii6e*d qho/,zxs y mree,a*-sz:s(v j7ction 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 , arek+xs 7ng*y8.aa fv x:k in contact and at rest on a horizontal surfaxnag*.s xy:+f8 vk7kace (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. Thrcqr//6;pl 6cbknm t+upfj 2k k e*/g5e coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum26+*eu 6nk/ gprp ljcmtk; r// kq5cfb rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whichpdo/ yg(so :p z77ef6a has an incline 6(fp 7:7ezsooya/gpdof 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*h/ke 2wwu8so4 hk 7ysth 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 tilgit*hq 6pu)u0 ted 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 spp c di73)h4ualeed 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 hill with a speed of sakf z dp8o:.nu iqudr):t3 134lb2jr 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 v,,mdnj sfb3.place against a rough wall by someone pushing on it with a force directed u fd j3mv,.,snbpward 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 sli9r( k9.z)c kt 9kywysuxw 3vw8ppery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at th uwtkr98x yzkyc.9sk( 9v 3)wwe 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 distance for an automobile traveling at tk yrwl wuh2044opf; 3speed vy4 3h ol4tw2kuf0w;p r 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 when the driv du27qucsw9dwtu *h*) er decelerates fromwcdwh)d u2*qusut7*9 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an indk n:-p .ker;ditial 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 staksl h s57npwq707 erewu:ns2 od. v.n3tion 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelera7 qk.7up.s:s 2 h rwwos nneel30dn7v5tes for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic qxr /u)5jn)rv 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 co)pk:4bca uaf5ast 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 simpliv :7x(v 6vjo3olhy lozxg2 32xfied model of a mammalian heart, at each pulse approximately 20 g of blood is acceleratedo v:ojh xyoxzvvl 7l62(23gx3 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 anz.vs4bbj f2;kt-0unde)j4e lc 0 i dn4 automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on.bine4jc-u ;sze0 bkvjdn20l d)f4 4 t 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 , and iwai7zlb 4/ry *, pn-dkf an object is going to "hold its place" on the ground, show that the coefficient ry,/*bkdna4wp7iz l -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 sq :teh1*z:)bisucx/p .f8cc 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 betweec/qfus:)sb8 h x*tczp:c ie 1.n 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(s bd ri3ju7 wpbu,i)w-ry2m0 hill (1-in-4 means that for each 4 m traveled along the road, the elevation chang 2j,m)i3wr7p0- (u uyrb iwbdse 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 from the top of the Leaning Tower of Pi9gumhzp pc0 2 exo;-98 fgytzgh/65 hrsa and falls 55 m before reaching the ground with x t;ho u0zhhrc2p fy56p98/e mgzgg-9a speed of What was the average force of air resistance?   

  A cyclist is coasting at a ste 8)ijwx :a(ugkady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if thewu ):8jk(xag i 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 a city. An u yan4gap421 q i/c5msimportant 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 rcqg 2an 1m4i/s4 p5uyaoad 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, danglesm g(/yzf)d ox)-: tgcj her watch from a thin piece of string while the jetliner she is in takes off from JFK Air))/c (fmjxzg:dtyg o-port (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, the bdqs-/mr1f;rre are to be several ramps connecting different parts of thdsrr;mf q1/ b-e store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the +e)xjs m m*1s:iv1qtrpulley apparatus ixesv:qmtmj *)1+ sr1shown 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 athnfsd z .u5:j2 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-resqsc* ( 5 yg56eru8 g:5:qsegoxfkqp+ ktraint chair, an engineer considers the follo 8ge*(sgfy:c k5uqq5g56epxq+ srk:owing set 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 mxt9 rt/6c jhvs8rk kp.5or) y9ass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropemnbgzn td;6x t+ /v.-fs of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the resultt n-fxvbtd g.+nm;6/z 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 8stuxf6v s k w69-pm* fd*) vnb2p5ppcis 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 buildt. u hyo6+zoyh;,+sop ing 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 together are ascending an ice field inctucv; .z7 au*clinec;*a .uu zt7cvd at 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.