Why does a child in a wagon seem to fall backward when you gcx) zvqzylb9+x 6sr06a9qrz +ive the wagon a sharp pull forward? rz l0qy+6zqz)x+vc9s 6xr9 ba

A box rests on the (friction:q9wumi cmr/ 9less) bed of a truck. 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)9cq:/9uimrw m 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 f/ 7schl7vvy 2uojfq*.orces acting on it? Explain.

Only one force acts on an objeckyg x8gj9sfa *5 3 okii./k-vpt. Can the object have zero acceleration? Can it have zero velocityfxokks- kp9y85g *i.jv/a ig3? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force 1 (zvslmc.mhvjhxg3i +t*w 1 .needed to make ith vxw*jh(tg..+iv mmzs31lc 1 bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log ls qeqhxw817x 3uaa22move in the opposite dire7ax1x eauwls2 3 h8q2qction?

Why might your foot hurt if you kick a heavy dv dj:8o)q8wbpvb52bl esk or a wall?

  When you are running and want to stop(f5t9py 3t k(ljsvd5j quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to ck(jt5p5ytf3dv j9(ls ome to rest.    m/s$^2$

A stone hangs by a fin+w :g 1t7 tkr;uow3fele thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above ur : +3tk1ewf7;gtowl it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg roct82b eiuzo+ ,q z)bncfwve r ji6.f72lwks/85k is twice as great as that on a 1-kg rock. Why then db5lwr6w82 8e7fq)vi+jfn t/coe. ,sukzbiz 2oesn’t the heavier rock fall faster?

Would a spring scale carried to the Moo-, ap+si+do72 d lskfj hpg*)sn give accurate results if the scale had been calibratedf)ijd-+oslh2 pgps ks * ,7a+d (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table u+/np; 2*lf 0drgta ssxsing an attached rope held horizontally. If you now pull the rope with the same force at an angle to t*pt r/ f+dsnsl2agx;0he 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 ;l:rh tm wjau 8nf89m1o9kck/under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equa tf8clkwn8ahk9m9m1j :; ro u/l and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg d:*5j x zv4pby2pk kh,object when you are on the Moon with the force needed to lift it on Earth. Compare th ky p5*jz2 x:k,bpd4hve 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 +dcj/kv/vk; p ,d7+e m(boini(Fig. 4–37) pulls with equal force on the other team. ,/njk; pikd7+o(ei m+ /vbcvdWhat, then, determines which team will win?

A person exerts an upw,l7u-1-q nei rn st5giard force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its -n ,i-lutq15ig7esnr 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 large a force .8j1k ntm/ r w6sfc dznn8lc8(does the ground exert on you? Why doesn’t this force make you rise up1wz sm/ crd nfjl 68n.(tk88cn into the air?

Whiplash sometimes res 7fb8lz su whv ,fv/2k.zc;/ooults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this.b7o vz8c;u2//swv f,kz ofhl situation. Is it really?

A heavy crate rests on the b:6 ;ji/zhpl uied of a flatbed truck. When the truck accelerates, theliu/:6zhp; i j crate 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 it slides up a ramp. After the bl;.cb sp0tsrvq wl* ue, (cj2b(ock reaches its highest point, it slides back down but the magnitude of its accelerpss*u2wc lv(b(t cr .;eb0q j,ation is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined uyc pg9 /ty8+be+ fux9plane? Assume the mechanism function+8+9 yetpgubxy9c uf/ s properly, even at an angle.

  What force is needed to accel + du)vfxl c5./xxwz;gerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider ati(vkybp350: kcsf v,y 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960bss:yquf93ufw d+4t- $-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ouf 3rpj8gv i-3f 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 11 h*ws (qcndi (io77jr0dpm,)a00-kg car in 8.0 s if the car is traveling at 95km/h7q dc)him *7(wdp(j si,anr 0o? -  

  What average force is needed to accelerate a 7.00-gram pellqgr /s.cr. f -xbom+-tet from rest to 125m/s over a distance of 0.800 m almb -fr-c.s/t.+rx ogqong the barrel of a rifle?   

A fisherman yanks a fish vertically out of the .f2l ( )pxco2kpz6 xdrwater with an acceleration of 2. rclf2xkozd(p6 2) p.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 car can cover a quarter-mile track (4(4b cwo +zwzm)37b9 npj p0; vul9okhh02 $\mathrm{~m}$) 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 6c.7tn757 s (xdlrfr5u meni rc5 v:lxthe maximum acceleration is 0.0680 g . W c5 umrrd ri lex(tv6s:5lnx57c.77nfhat are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the eleay* w).tz g.kfvator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate thz g)k.yf .atw*e acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strepac6d*7yfy0 uz9:,( kn*pr npzfy c/mngth of 21,750 N. What maximum upward acceleration can it give the elevator without breaking n yny0/*dpz:cf6 y,z(caufr*k 7p9 pm?    ( two decimal places)

  (a) What is the acceleration of two falling sky dt7s fpnd10b,: prtfa:ivers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth , :dntfsbfp10trpa :7of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he 1rhwawc)b.x,y p p i7;strikes the ground bw7wc bpap)h.; ,iyr x1elow, he bends his 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 tiedl+it 6ok 9jd1i. e4rik to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts ok1.r jked i 49il+i6otn 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:q+ dsah c,zu 5f8w7wer a+q/i 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 baseballt,yrd(esy49 eijvhy*b4 :f7rxc-k sil+f u( . (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying towar97i ss uk4(+crjxt: .e ifydl4-(b*hyf,vreyd the outfield.

A 650-N force acts in a northwesterly direction. A secrc 2g/b6sk 5w9smjt0 wjuv0b:ond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your ag:kjb msj9c s bu2 v5w0/wt60rnswer with a vector diagram.

  Arlene is to walk across a a dv,,jo h2vh;fg yr spz2,-7n"high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 1 vdry2,2;-v shpf7z ,gnojah,0.0$^{\circ}$ 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 cord from another 3.voabg s*u9bx hm3h1r nhf)e:-d3fz 602$-\mathrm{kg}$ 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-gzktm* *sl k 0 9mqwf8uv4q28uz8zht $-\mathrm{kg}$ 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, Antarct6 on+1nb x69xd4glim oica, as shown in Fig. 4-46. The sum of the force9o1n6gb n6ld +x4xo mis $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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, Fig. nxkiwloc - 196jk)n r2 4-47 . Determine the ratio of the tension in the coupling between the li1nlcn-k jo2w9r) 6 kxocomotive 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 uznw9nn 9 ))e-d hlbbmm)wq+8using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to -nww+m9)u e zn)bh9ln8 m)qdbraise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a juak1sd(/ f1-wu j q4r 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 -gu7im:d hx2h::ygu tblock (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 frictionless horizontal surface go8tsm3m .h gk.j 0r3h*xjmy9are in contact with each other, as shown in Fig. 4-51. A fotmg0h. y* jgsr83k. x mo9jm3hrce $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m l7 w vsqel5fc145n)(iw w -dpr7ncc+oabove 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 its velocity at the moment the heavier one hits the ground. Tio1)cw7 q+wnw r-cl5 s d5nl4e f7pv(chis 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 nn; :6dyjor4qca;al 8 mass 1.0 kg . Calcoal8j; n;n 6adqcy:r4 ulate 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 orrs5 h92x q i8ars.t gg*qzh50f kinetic 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 requixzr6aogr1nj2 ;+1gbk c+ss5z red 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 standing on a train accelera3ahual9xs)q 2 y;;ref ting at 0.20g. What minimum coefficaaqe;;yl9rus2x) h3 f ient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient on;mr8 mh8nxb(l8d 2u9xn sp6gf static friction between the tires and the ground is 0.80? du6l28n nbn8x 8mr(sm9;g p hx  

  The coefficient of static friction between hard rubber and no ejp 6o:8pght b9xl98crmal street pavement is about 0.8. On how steep a hill (maximum angle) can you leal9j8ppbo 68cg9t: xhe ve 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 -4m kx6jc6;xen4oo7 ;8ov ai s,q.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 roug( yer1 m* do4b:8ah hyjr*g(pvh 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. jr1jtbbd 204j4htqw a very high coefficient of static friction. 4 j.bbt2jtr14djq 0hw

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 kinn 8e8:l6of,9t lnvxth etic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A have to 8l caw w ,wbbge .weg9p+)(+ywhave to prevent any mot gewbbwp)c,ewy+ 8l 9+aw .wg(ion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidespf.1p9i xk ;ci across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0px ;p1i.9 icfk $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horpk r8)sld;s n)l nk74nizontal surface (Fig. 4-54). Asd 4;) l87klnkrsnp n) 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 ;beipqe)/sa.q;.d 4tms 3/vw rfm,zk0vtg (t coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver ; w ./vae sv3zqqfd4ttm,ib.0rkgs t(p/ e;)m 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 youri0hy 0g :p jgrp*bh)uc4sb9u7 driveway, which has an incub:0 pgs4 9 y hr0j)puigh*7bcline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with axyj.n.7cui:xe 0k ody1. con / 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 an angle 5 l yn6zx(odus(0;zej$\theta=22.0^{\circ}$ 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 i.y s9u:renklng8zh4:f+eg,3 w *v zjanitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest h)aezmledx6y6kzjw 5d wvs s/8 f*572vill 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.a kyp :6yr2dd rough wall by someone pushing on it with a force directed upward at :k.dr62pya yd 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangero(/6 ihelqh6t eli,j.tus projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch ,6lje./l eqh ti6iht(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 a3g;8pznv jm1traveling at speed v is e;z3mj81g npvaqual 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 k*,;utlhd9lc du8d9+ xmm d4bthe driver decelerax8hdd9+9t *, l;4cdkmmb udultes 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 p6og jz,kqh5 5 m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on aj8qh59og *z4fth 7ts mow(ya 8 conveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with ze h4syah978t z*jwtq 85 (goomfro 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 kinetz(i jjn0cu q2.cq/i8kic 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 zk.irw6,jljxo 96l s1 kg (including 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 ma:+ rofq3j3q+ur g.xlo mmalian heart, at each pulse approximately 20 g of blood is accelerated fromoq3+3x: foqgr+ ljr u. 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 dehj980mnzw 4 cw1yoi 3sceleration is no more than 30 " g 's." Cazs14 n3hwoc9 0iw8mjy lculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and.u3px9.r:rll m7pmv n if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at leas ulpvrm 7lnx:9p .3.mrt $\mu_{\mathrm{s}}=a / g$ . (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 involvinp qetz7z of,+dh in-2ce1l3r3)icyu3g 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 dcp f y+2c7e1q3 lh-tzr,eiz )3ion3upavement 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-iv 3,gjgk z)+dz3b1u.jq:nwxou/ :rmin-4 means that for each 4 m traveled along the road, the elevation : 3dxwrqok :b/j )u3.zi+gm1njzguv,change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the 5q3xpm2;i m (mg jep yf9b30vntop of the Leaning Tower of Pisa and falls 55 m beforiqbp9mf e mpxn33 m2;(v50jyge reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady spez)mq3of7/ kh hed 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 the mud lasts for 11 m? If so, what will be the speed upon em3/ 7fhqh )ozmkerging?   

  A city planner is working on the redesign of a hilly portion of a city+rcta mf;6xs39b6c2tf+d +xwo1zbhk . 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 ac z;x9m3ts ch k6f6xcobba++td1 2+frw celerate 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 0 c6t4v2jmtr5zen e6o watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string mak m0 6ce5e vo4tnzjrt26es 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 supermarkethud 8pgh: 3**rx:bihm, there are to be several ramps connecting different parts of the storxh hh :d gmp8:ur*ib3*e.
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 t- mfu7qw ia/:she piano (mass M ) using the pullimw - :a/fqu7sey apparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is acceleratiu2gdy8:z u6f ,tyjrwz1 fpc7* ng 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 x6cr45 0mtwtr a child-restraint chair, an engineer considers the following set of conditionsx 5tcmwr64 0tr:
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 660veb/gy zq y(;6 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. K2n)o5rh g1 -gi amr/ssaren's rope is more elastic, called a dynamic rope by clim21o n-ssai r)rhggm /5bers. 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 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 sq)f 5fl j)wnb/w 6 ui+/d/excis using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3.:r 5ni yn(wmfy3 .7rqn5 $\mathrm{~m} / \mathrm{s}$ 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 af w (fw0ai;;dkre roped together are ascending an ice field inclined at kwad0f; (fi;w 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.