Why does a child in +nnl;o:jz hz hg:) wv2a wagon seem to fall backward when you give the wagon a sharp pullw og hnzl:v;:n)jz2+h forward?

A box rests on the (frictionless) bed of a truck. The truck driver szzcd-/5 /0l/si0/sdwk )u s p )drrdkatarts 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, azr kk /s)//)u sd 0lrwdsd5d cipaz/0-s 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 8k;h3 ,utmmem ;mws+cobject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the ob/d.a(c )kqlp5naqp)j8l,r el ject have zero acceleration? Can it have zero velocdq k, c)(rqllp/ajn.e8 ) a5plity? Explain.

When a golf ball is dropped to szvt) xu6 .y3qrfvrg.z2 a0d(the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) .)r6.dzqx 2vvfz3tgr s y0a( uIf so, what exerts the force?

If you walk along a log floating on a lake, why o- e v,aj6;rht1g1gi*yj 0ths does the log move in the opposite dgtrt h1j ,v-j60ae1h go ;yis*irection?

Why might your foot hurt if you kick a heavy desk or a wa k-mnc:cy3dh /ll?

  When you are running and want to stop quickly, you must decelerate quickly. (+/5n3 igjp4ubcx dc.xa) What is the origin of the force that causes you to stop? (b) Estimate (using your+x4. 5jgxpdib3u n/ cc 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 cns. b g0bahs9(+k h/;gqdo 3l et:x6xveiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sh9s:6doehv hx t/sng bl( b3xq0a.+gk;arp 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* pe 7ug;d-huv9oprb 3 on a 1-kg rock. Why then doesn’t uo9e ;rg-d3 bhv7pup*the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results ife)xjyu/9 hcy; d y3d:m the scale had been calibrated (a) imdyy dh;e/9 )j:cx uy3n pounds, or (b) in kilograms?

You pull a box with a constant force a/n,2 ktvn/ ygxa(k6sz cross a frictionless table using an attached rope held horizontally. If you now pull zk 6/kvgy /(stna,nx2 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 gravity there is a net force b-s hlgmx j:99mg exerted on it bym9 g9l jhbx:-s the Earth. Yet by 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 w )kfy1 z:n8mmdxld,4n hen you are on the Moon with the force needed to lift it on Earth. Cxy l8d4:, kmnnz 1mdf)ompare 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 we*/nezltn: + sh:g+jiith equal force on the other team. What, then+l+j * z/nhtges i::en, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of gr3fz4pb7ufo- xhm 10 16 gpthoyoceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magni 4h1mx-gobpyoh 7p10 3f6tf uztude, (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 does the ground/lq43(ytsz f/n 9q,rm mm3 fov d71-qdjye0pq exert on you? Why doesn’t this force make you rise up indv,m4( - 0qflt9p/qyqj73mndzyq1/fr o3esmto the air?

Whiplash sometimes res0g bya nfr7j68ults from an automobile accident when the victim’s car is 0g 76njyfb a8rstruck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whenpssvc033p. w mp cn+hq a0np54 the truck accelerates, the c cs4 v0hpm apq3pnnc5s w30.p+rate 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 2ht iv+c(r:a qthat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. +(:thr2q cva iWhy?

What would your bathroom scale read if you weighed yourself on anvuas u)p(;-:epz-fp :o )vpxk inclined plane? Assume the mechanism functions p:s;p:oxf)epk vu - )-pvapz(uroperly, even at an angle.

  What force is needed to accelerate rhf81 yy/t2m3ff6 rct a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N a9q*ybpw,z i3kccelerates a bike 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 withstand if it is use2lj) qme n (y6r4tgr;ud to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofc47qy5btiv 01wgv 4(erm a 2yc 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 rez,ej0mfn:h a eigw 28i+,v wp+quired to stop an 1100-kg car in 8.0 s if the car is traveling at 95kmia+z we:8f pm+w 0gih2,jvn e,/h? -  

  What average force is needed to accelerate a 7.g t:b w ) ,xig/xp.3lia4p7qqg00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a r4xi )37, wgq t gp.lqgxp/:ibaifle?   

A fisherman yanks a fish vertically out of the wate c6y+2idwrg9*bhr4tyyp+i :pv h 6d3ar with an acceleration of 2.5iy3+yp iwbvh96*c: p+ addrg6y2 hr 4t $\mathrm{~m} / \mathrm{s}^{2}$ 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 coiy3i gdm0m,w3ver 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 t ze4b g ))9gcauyogg26akf +4zhe maximum acceleration is 0.az +yga9)42gg4bg o) uek6 czf0680 g . What 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 elevaqrt;-z.afj1/l xk )h *ujhd(u5td p3 ftor begins to mol3ff; -d)x5 az1j.pth*j(u /rkt hdquve, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21tn;bm0ubp r2vj8g7uzw) ld kk t5s+4*,750 N. What maximum upward acceleration can it give the elevatorru p8z)l kjg54b dt0 u2wbskn;m*t+v7 without breaking?    ( two decimal places)

  (a) What is the accelerations4cqv cg+ d0qlihpmea3 c;.;: of two falling sky divers (mass 132 kg including parachute)q:cvsph +la3 m04c;dg ieq;. c when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes .qt xm6ohd90v qle32o the ground below, 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, 2otxhqm3lve .q6o90d 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 7r,.p1lv7 k xghqaz b6w e(wb-rope tied 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 on the box if the weight hanging on the ot(ag.qve6, lwx7bzh 7w- 1bp krher side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagh6k-q;h 8nbc) j p.u0lzzdcv9ram for a 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 basebn;g a6agk53nbyzq)9aall (a) at the moment it is hit by the bat, and again (b) after it has left thygng36aaaz );kn 9q5b e bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forced yar)x:c/ yf93m pwmg78en5 m must be exerted in what direction so that the resultant of the two forces points westward? Illustrate x8y d7maecyg pr539wmfn )m/:your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung j) 3n ld9x0srx*hcmi apt-v,,horizontally between two buildings 10)mr9h* d, i psx 0cantj,xv3l-.0 m apart. The sag in the rope 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 m(1ad m .,e0iz jslo/ xypmgeu945v8bo assless 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 14.0y-t:n (ipf s e,g nt+u2j2k m4m.dn:pd$-\mathrm{kg}$ 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 Mq a2l.h.fnjysh(,a 2 vcMurdo Base, Antarctica, as shown in,.s(nhhyljf q2.2ava 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 pulling two cars of the same mass behind it, Fig. 27byadvqu af- nd67d* 4-47 . Determine the ratio of the tensidd af2ayv*n7b7u-q d6on 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 usil j0khnvf)zie*9qf4 *ng the bucket-pulley apparatus shown in Fig. 4-48. (a) Howhnf v9 qe4i0k)*lfj *z hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, ag.-t7yq o )vyi 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 blpxcqj: br:.ks)x q/ b/by5um.ock (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 frg/(2 v6y(ed bwk0hwx) yifo1fictionless horizontal surface are in contact with each other, as shown in Fig. 4-51. A w(6 xd2 iehyf(bv/o )0f1kwgy 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 ea *y)+ 9vagf mzylp0i4ich initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter *y y+miz0)94vg iap flobject reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy corgtshwb:yan 5 ;v -:x(ad of mass 1.0 kg . Calculate the acceleration of each bbnh:: wta5-v s; gy(axox 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 be2dxdm t wst;z1 z;,ey9tween 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 requir3r: tjc) l-fd skq-r6r06aim med 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 accelerating at 0.20g. What minimuo9 r-i bci -rf42v4wrpm coefficient of static friction must exist between youowr icvr-r 49 f-bp42ir feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient ss ir2h su0;g-of static friction between the tires and -u; rsgs20h sithe ground is 0.80?   

  The coefficient of static friction between :jp*ze spa-8z hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkeppz *-aezsj:8 d?   $^{/circ}$

  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 t ar :ikad0s)z (ic7c)iy-o3 c-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 rough 30ucw*6lv, 8 sj/hxccamb /yxg ps594ufv/x 7. p$^{\circ}$ 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 contac,. )eareiqcl( s 7a4obt with an asphalt surface have a very high coefficient of static frictio7qeorlab(a )c. es,4i n.

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 fr ezvjau kc r2(o3i0w+9iction 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 kv ea t3103+(rok g81x/ /riblcwmzux have to prevent any motio0mk vk31 r/awz+3b/oxcxl81(ig r eutn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slide(1kq4woat-pq kg5 36.v:ex vf a l3qqcs across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the pu:vvotxaf k64 qp3 qwa35ceg.1ql k( -qsh imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg :mcbz4jh(q-h ;(ddgrlw ,3 hs, are in contact and at rest on a horizontal bjsr,cq;zwgl-hh(4d3dh : m ( surface (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 47 r8udvam(px6w6*r ; k9 rvxobq8y dma heavy crate. The 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 can deo8rk6am; bd8vyw rqup7x(m4* v d6xr9 celerate 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 drivhold5-+cvwh.ipu*y29 s ) n aieway, which has an i5l*siuhc)ypavo.w d2h-9n i +ncline 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 agn tl/)t; 4q gxd5umx/ slide 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 e77 sr+mz0 ,nme3f2bt fbil 6van 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.vl7kxt;ln*s(; nity 50 $\mathrm{~m} / \mathrm{s}$ 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 kpz5lw )k)eme(u4md4 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 in place against a rough wa+dl, bmi+u.b /fyuqp 3ll by someone pushing on it with a force directed upward.q/+ibyupm3+lf b d,u 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 rooe 0m4,qagy: l2p3l k :rmzavz j2+sii7fs can become dangerous projectiles as they melt. Consider a chunk of snow at 0 rlk+7s:giez mplzij a: ,a22y3v4mqthe 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 automom3ez7qsgk tn c5h4yae:b4d10-s -p lobile traveling at speed v is equal t k-dotc1hn-s e47 : mp4q0sebz3yg5lao $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,kxliqm2prx j) 2r11n a car slides forward on the dash when the driver decelerates from x j)r11nkq ,xlm2 i2rp 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 mas 34+ x)kigvxz)pks4i,q x 9v shofy10v+s+akg s 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 a conveyor belt froa: j.x1bxvu .)lvkyo7m where they are filled to the packing station 11.0 m away. The be jxv k lxay):.vbo1.7ult is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fri3a(bb mhmdgxfo)+*g 1 ction 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 efr4wn 6a4t(m65 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 mammalian heart, at each pulse approximat/sqdo a+hz2)m elhq dzo)+2s/ amy 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 cw ao.pzdr sk:z.ts,/qzx,h3e (ed 8v,rash if the deceleration is noa3(xz.dtz., q ee,:rzow /p v8,ssdhk more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a + ,+gnr(jvfzr, and if an object is go r+nv,rj+ g(fzing to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators,f-:ds; bnwpqab g6;g+ examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly bw:g;d;6s gapn- +fqbcame to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling nec9x ;v8hlpv:x7uc 1q4ag3d down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). Hou;cx3aq 1vc:l8egvd7p94h xnw 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 *awjop5h 6y:b top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistw hpyjabo6*5: ance?   

  A cyclist is coasting at )w;stg2z apy 1o) y g*uz,vcj0a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of )jpvya)yu;w201sgozg*c ,z t 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. An impo3rmem jgkbikt f,g s1v90e6-s:q1 3*pubds 9frtantggmuq- 90bkvs b33 k f ers:t6fjpdms*1,i91e 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 road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thinsx g7tcoop)m0vjz 8q-f d,1+h piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Sf t08qzomxvcj7og)+h- 1, dpshe notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to)4 rn7mupx/l imt -fb1 be several ramps connecting differet1 p lrxm)i-ufn4m/b 7nt parts of the 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 ) usinj uacw xlo7 jv)8z i*a:1p.g:fg the pulley apparatus shown ii cogx.wlzf8j:u7ja:)1 *v ap n

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

  A jet aircraft is accelerating at 3. u80j.senhnfpwhq+ f a.; .)g4orb8g r5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer considsd ljp *)80arz.9ig(b dbkp:bers the followi bl idkag89rs)bp d*(:.jp0 zbng 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 mass of 660 metric tons (660,000 w)g;hjn*;ap r$\mathrm{~kg}$) . 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 oz7dd-f oo2arjyx)/* vf similar length. Karen's rd*ryf2x d-/7ao )j zovope 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 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 usifl52yz/ w(g7ty 5l). xlvpem7cy v*dmng 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 mamp/ab-q9; uc 8an(t/:yoijzc ximum 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 hbse a;5ii/9iinclined at 21. ;i5h aseii9b/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.