Why does a child in a wagon seem to fals/ik44 0 hteo1xm 4meoox99gxl backward when you give the wagon a sharp pull fm 4 /9 e0s9emooxi44hot1g kxxorward?

A box rests on the (frictionless) bed of a truck. The truck driver starts thcv1e;+gy3h y be truck and accelerates forward. The box immedia1e g3vhbc+; yytely 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 truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? E-c f2yjf c;lkvsf*.vd 0gue42 xplain.

Only one force acts on an object. Can tqsr10 ze;wvu 0he object have zero acceleration? Can it have zero veloew010r quvs;z city? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forp f*wm0il c5,oce ni, 5* pofl0wmceeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floatidk, ympfr1xb - dx52w 7/uhtp7ng on a lake, why does the log move in the opposite directd72xp u5ym/wxh7,r-f d pktb1 ion?

Why might your foot hurt if you kick a h4zjpp z-(qucot7iz7+g 1-sj w eavy desk or a wall?

  When you are running and want 4xr+m- dwhf3yto stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to-h y3dx+f4mrw 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 jerkk( rz ykhz vu8pk66/ k -l/;2,vprthread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, whvp-,rkk6h/zv8pljr( y /zk r2ekk6; uere 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 gpyzy+ e 86kgrr hkp341reat as that on a 1-kg rock. Why then doesn’t the heavierpg +r p438kz1hy 6ryke rock fall faster?

Would a spring scale carried to the Moon gi2:koc ,dh(,p+tycbtqv, ( ysyve accurate results if the scale had been calibhy,ky sb(v,p yct:,tqo c(2 d+rated (a) in pounds, or (b) in kilograms?

You pull a box with a constant6zmki3g;c dr) dll ;9f force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or i9;3dg dcm)klr6z ;fl(c) decrease? Explain.

When an object falls freely under the influence of gravityyrfs+t r314 ,hqy4dw. aw aew/ there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal andr3 yh r,f tq+414/ydawwe asw. opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 17*xrmt6cux l6y-fgs nz6/mx3 0-kg object when you are on the Moon with the for xtz*ry7x 63mxfcm6gl s/un-6 ce 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, each team in a tug of war (Fig. 4–37) pulls wov*/krfnm;g3 )gtmga,+c:l4: rr tp jith equal force on the other trg+r) gtp; / nfkoml3 t:mjc4a*:vg ,ream. What, then, determines which team will win?

A person exerts an upward 3r xtsbgt)/p 3force 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 it is gs/ptxrb3 t3) exerted.

When you stand still on the ground, how large a force does the ground e 7ghae. qoe.hct7)w+rxert on you? Why doesn’t this force make you rise up into the a ro.)eaw.+q h7 7gcehtir?

Whiplash sometimes results from an automobile accident when the victim’s car is k)cdp4pc)c j2struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Isjcd cp4)2pkc) it really?

A heavy crate rests on the bed of a flatbed truck. Whyx .);6wbsyxhl /4 jenen the truck accelerates, the cratewy byj6xxh/lne4;) s. remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that w8g /6gz)r *tmb /d4vgqcu*uk it slides up a ramp. After the block reaches its highest point, it slides back down butug* )q utg/*d8/wc mrzg6v b4k the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed y--qx j jw;u.1nhx.e8l gl9m kqourself on an inclined plane? Assume the mechan8hu;xmwg-lqe.q jn .j 9kl-x1 ism functions properly, even at an angle.

  What force is needed to accelerate a chilu)c 3v zddq;wf;hnpf6x2i1 :od on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a b,moby3pb 98ou3:cs eaike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsta -rpk qwstri /xs)(s:7nd 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 lcjz oc 2m6x8ii0:)ira $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the car is tr1 1 emyc5-pjypjumfygicq3bd;*s .;m hg8*e.aveling at 95km j.je3 1;hfe 1u by*mpi gpdgq5*cy 8-mysm.c;/h? -  

  What average force is needed to.n etz+rh(dmt: p ;2yy accelerate a 7.00-gram pellet from rest to 125m/s over a distance .e n+;tpm:hy dzr(yt2of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fishem,;m8 ltuxr. vertically out of the water with an acceleration of 2.em,tmrx ; 8.lu5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mil+23 3g hrvhto plry/(ce 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 z2l 3ncod4r)aeh63 wk +r l *(vapz+rsthe maximum acceleration is 0.0680 g . What arc +r 3dlewpz6r k4zahs)r2* (n ovl+3ae the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When the eleva8g0b ayif;)- rug5avt tor begins to move, the scale briefly reads;uya )8-bgg5t0f vria 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 haxz 8crm)o6xfwjav-b k) /k pb+e2(rp/s a maximum strength of 21,750 N. Whatp8e(jxrbf2 moka)/)+6xbwrvkpz /- c maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg9yl tvagmkj-i +0+e h; including parachute) when the upward force of air resistance i+talmg ek j0+; 9h-vyis 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.g 3k/m- wf(xez When he strikes the ground below, he bends his knees so thatm z xfwe/3(k-g his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically ut7l g(8;lnawa5 wo sd7pward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table 8 lo (wnds 7g5a7alw;texerts 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 playeca3hav7(og3 wr
(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 t8e (acz**que r.unehq3.cm f (9mpi4 qhe moment it is hit by the bat, and again (b) after it has left ci ah4 u fqre*c8equ9qme3 *(.(mznp.the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N for gol:ju 37uq)lce must be exerted in what direction so that the resultant of th7l:qu uj3)o gle two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontallyfade wn ha0kz)) *k/5b between two buildings 10.0 m apart. The sag in the ropen fa)z/e*k5d bka0wh) 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 massce2plz5rev x95l) y;q10/ erbdh p pdn3t/6ocless 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.suyv:k) p unu8t)4 6))eklmpj0$-\mathrm{kg}$ 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 housinn1xwozu;syq6jez 6y p i 2:7b;g unit to a new location at McMurdo Base, Antarctica, as shown iyqy6 w6:z1p;osuz2i 7xnebj ; n Fig. 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 pulli,wybc x ,7c/kcj2 q0ay 6devf*ng two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of * vwqjxb6yc 2fkc/a0,7 c,yed the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley appara sx 2jx.-wai1ltus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spee-. jwa2x1x sild?   
(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,l)5yxrr e s36w 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 block (massk/55gpz u;fhvjn5 0tp $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with hjx vn*w4lj66z ql2ct (on-.k9rw *ti each other, as shown in Fig. 4-5l*(ic.nvlz-qh tw4n2t*xr6 jj9 wo6 k1. 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 s9a;* jw ll3mhinitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then itwmjlslh 93; *as velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of m/oertfp 8 m)t:h+a)fv + wwyq1ass 1.0 kg . Calculate the accelerw+ )v w1f/qptt+r)a oem: y8fhation 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 betfsr1, )sozw)-ci6y 9biptq6q ween 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 requireuxsmu8llcw,6 ;g 4se 3d to 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 stan tom2tu.4sl;*qin : bading on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your fee;qbli2 su n.t:ta4om* t and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if 5s lxr-z2jw, kthe coefficient of static friction between the t52kw rjz ,lx-sires and the ground is 0.80?   

  The coefficient of static friction between hardt)m6p1i:jl wn ki 7ge6 rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car pargnmwti: 61 pejki6 l)7ked?   $^{/circ}$

  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 at6mwp (.xu (9nz g0ojfu -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 a rou3 r0dgs5ao4eipzn6xmfl.) :wgh 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 re swiz b.3swk/91li4 a very high coefficient of static frictiobwiil9e z wk.sr3/4s1n.

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 frictiocut)sgn ps :1k30 aky1-edt ,qn 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 Figgsg 2 .g2 ggg()vnzrr:6egb .z. 4-32 (Example 4-20) how large a mass would box A have to have to prevent anyz.z g gbgng2g2v)er:. s(rg6g motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wilno/l yf z(rh4/d wrt0:l it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiaz oy4tw:h/ /drr(lf 0nl speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and a)mrw 2ow l62jsp72r k /sutpu*t rest on a horizontal surface (Fig. 4-5urtp 2 wswso6*rp/2lj u 7k)m24). 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 co*zng n/ uktfpm i1/u o5*isj.,efficient of static 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 avoidt5/*sonm1/,*zji fi .puu nk g having the crate slide against the cab of the truck?   

On an icy day, you worry about parki:( 8g2 eucyvziaw1h r9ng your car in your driveway, which has an incline ofw9(i1c 8a ehyz rgu2v: 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 sld5b xx 172*wa nvkopb2ide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at a( yp/i0 xdsx.vqc .m7an 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 of 3. 2pxml lgfdd51j*+i )m0 $\mathrm{~m} / \mathrm{s}$ 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 thl( nb .h*r7it3sn* r 0yj)qdeze top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held innu ,c al:6+6y+ymhfgi place against a rough wall by someone pushing on it with a force directed upwardfhy gc lm+, a6+6iuny: 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 1*ecm4 nh dicb:n8b ;g0pdkj,7.) l(e bwbqqacan become dangerous projectiles as they melt. Consider a chu 8w(4mqb7 g;1a:lkcb, npeicb. h)qjndd*e 0bnk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at spev1 r.mdf6ey k1edk1.fvmr16 d ey v 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 forwarp0: 6q1ziqpbj5klyc 5d on the dash when the driver decelerates from 45cjz5b q6lp 01yikq5: p $\mathrm{~km} / \mathrm{h}$ 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 g5tcvshquw*60h -u-j tvd;l*n x b*6kwiven 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 td cin 1 5 -m+y02uaya17njxbzzhey 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 ac5zn2n0 y1i m1z+cauayxj -d7bcomplished 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 kiuim/gcy (li(5tw 4n uij,wr7 q*p. vd6netic 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 (iwt),7i 8wuj2*n uqaa oncluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammaliar1;7 aa *d,t)tiftnok2/faae o/8w wun heart, at each pulse approximately )/ *,fdeo/tna1aw tt aukw87or 2aif;20 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if;umw6f (g gsh9 g3s -aa84oucm the deceler9h;s-c8om ggmf (a4uaw6gu3 sation 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 proxugy / a 6uxx5en;y*b+duced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static uyxb g e+;* x6axu5/ynfriction 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 involving two carss5lg-jh6 -8j vj jj+ne64 cowc, measure 72-m-long skid marks of one of the cars, which nearly came to a 6vh 4njjg-joce w8- jlj6+sc5stop 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 -wdx* a lah53gfor each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom aft-*5w daahlgx3 er 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;s9vm,iun dm9 of Pisa and falls 55 m before reaching theun9mi,;d9m s v ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a ste+rjdlzkuapg )4i 03c5 b:t5cr ady speed of 12m/s but enters a muddy stretch where t g5zbar 5dc irj)u:+ lc43k0pthe effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. Av p2h0 w;3ooo1 fu*noun important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down2pwo; 0f 1uovnh uoo*3. 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 ficy*jv+cf lz y(yp */)rom a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25cj*l+p/vy*(y)f yi cz$^{\circ}$ 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 se q2l(om1t c8 qtjdj1(+p3 xjtqveral ramps connecting different parts of the store. qd t3j(q21c8ttj1 mjl oxp+q(
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 needed4 zkue)+wgvli9d 5xjc: tg28y to lift the piano (mass M ) using the pulley apparatus :9ktjx8z+lw y g)e ui54 vd2cgshown 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 accelerat 4n crs368nk- nwjnh+fing 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-restraint chair, an engc m l(tbr9 a:4(wvs*snineer considers the followic v((nt*ablrws :49msng 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 asjgtkit3 /3:cvl+45x hmf .tu mass 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 ropes of similar length. ksngwgr/.9v/m3o 0 rywb23 f zKaren'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, asssvwnmryg/r0 3okw2 /gf.9b 3z uming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 w;ce neqpp.-tbd0i7 /$\mathrm{~b}$ 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 6t-uyl/(hvb7xh( zkmallowed 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 incluqf 1bnth , ndo+d9 c0+u+l8dcined d0dl nt h+++1b,o8fun9cd qucat 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.