Why does a child in a wagon seem to fall backward wc 7h9)odaw)iihen you give the wagon a sharp pull fa)9h iwcd7)ioorward?

A box rests on the (frictionless) bed of a truc e(5d5:li1jiiou hdx gdj4v ;+k. The truck driver starts the truck and acceleral oid jjxi45hu1 (v;d+g:ie5d tes forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zevygj .+w( 2g5vbnr r*tro, are no forces acting on it? Explain.

Only one force acts on xef6yyi*rvep+ dwfu t ,kcis6p8*0-9an object. Can the object have zero acceleration? Can it have zes 8eyfrp6 -+,xv6 yi e9c*uftip*w0d kro velocity? Explain.

When a golf ball is dropped to the pavement, it bounces br.65 gn cr7fciack up. (a) Is a force needed to ma n.rifr57gc6c ke it bounce back up? (b) If so, what exerts the force?

If you walk along a log( cuv;*jsrs(f floating on a lake, why does the log move in the opposite direction s*c( srju(v;f?

Why might your foot hurt if you kick a heavy deskonieq:3o8 iz 8 or a wall?

  When you are running and want to stop quickly, you must deh*z76kcrvs0hczdk,kq8j j p40/nvk1 celerate 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 /zjk761kv 0jrhcqz cks0k * hp,4d nv8a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threadul. ou+(yooi+ 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 stoniuou+y+ .(lo oe 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 oa8 holz7y - ,hg5 :hs,rqevhh9n a 1-kg rock. Why then doesn’t the heavier rock fall fastvaqh9-7hlhy ,ez8r , oh5hs g:er?

Would a spring scale v su +:z/a7lw9njtx sujgy+m ((x0+m rcarried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogs+l+xjjvt 0s+ynuz9 m/(m(gua x 7rw :rams?

You pull a box with a constant force across a frictionless table using ano3 z):kkidl;do 3t;ph 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, oo : 3i;3dto; zklh)pdkr (c) decrease? Explain.

When an object falls freely0w5t r 2xsvm:(ho q0fg 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 equal and opposite force on the Earth. Why doesn’t the Earth mov2to:x 0rsm5f(gqw0vh e?

Compare the effort (or force) needed to lift a 10-kg object when you are on d7j n4cdcs.p0 the Moon with the force neededn .7d0j4scpd c 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 (Fk/e-1tizb1sf dj 97e, *bp njyl5j6vx ig. 4–37) pulls with equal force on the other team. What, then, deter1i7bfjbj6tzpj 9se* /1yevx ,d -l5knmines which team will win?

A person exerts an upward force of 40 N to t ,8qbn1;f-h ,elhmwvhold a bag of groceries. Describe the “rea,18 ;m-wfbn htehvl,q ction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does du817l7lm2(ei iq1 1oeagzd jthe ground exert on you? Why doesiouga1d7 1mdq12elizl 8 7( ejn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’socy2q nc 7p* (sg4vo)yu/kzum4: s(mh car is struck violently from the rear. Explain 2u( z 4c hvno(pu*m4cm)q/yky 7g :soswhy the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests o ws9mu; c vmxc+*)8d)aymfl ,mn the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the cratem 9m,)8)vfc+ xmcy* ;umwdlas to accelerate?

A block is given a push so that it slides up a ramp. After the block rek) qcu5cohkapi- 4m11 aches its highest point, it slides bao-p h1qk1acu 5cmk)i4 ck down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an ty kgj7bd,g2byp0f;2 inclined plane? Ass7j;gd gbt2kfb,y02pyume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/ *)( y,ihrqb7gsbl 9zds$^2$?   

  A net force of 265 N accelerates a bike -+/ij*bb- ru heo*qyh*1s mlceh l6;qand 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 it9f k l 7l+k:i/ 0rpaxmhq,t*nnd(i1 rk is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a wtm.*bmas1* z /, yqmx $76-\mathrm{kg}$ 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 i2uj9qoier(+ey.ka x 5 n 8.0 s if the car is traveling at.u r29j5xqa y(ie+ oek 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelbkd 3 4dm *li*uobu*r4let from rest to 125m/s over a distanceu4b*udrd 3i o*lkm 4b* of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the wateeb5 mnf8xsi-u)mnt zs)va/(. r with an acceleration of 2.5 s8znmm-/ stxf()bav5) eu i.n$\mathrm{~m} / \mathrm{s}^{2}$ 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 tra;hs+amng ivv ty4ak1 t jp)*ice/0 2q*ck (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 o x+z/.cha1qz kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablcq+x.h/oz 1za e? 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.4og nf(xcqqd(hk fdwn *7 ag44h))xx scale in a motionless elevator. When the elevator begins to mov(nff hq*x 7)xk44xd4wgcn h. og(daq)e, 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 ldzp):ng5 us va)gm,9q*b, xchas a maximum strength of 21,750 N. What maximum upward acceleration can *s v), blx:g 59mga)zpnuqdc,it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling skyev 5;v4v0wkf y divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fou50wvkfvv; 4e yrth 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 tkyrcp9* h ogrxj0 rl68a+-n(che roof of a house 3.9-m high. When he strikes 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 l+(* gcr-0jclnpxa k6rh r9 8oyegs) 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 7cl zc(q)drxmj dpz2;/; gj6xvertically 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 hangjr;gcdql7m( zz 6d )2cj;/x pxing 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 8 wvt7 9eiis m97 xwl:lf5g*eia basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momentg+hv3sp0zr v3lu* sft7e) s i/ it is hit by the bat, and again3hgevp70 ls )ir *3s svut+/fz (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650ro6yrvc-nyx nn .xw9- n ow(h20z)-bg-N force must be exerted in what direction so that the resultant -w0xgn(nn rv9z -)woc.r -y o2 ny6bhxof the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontpm wy4/39h jo o8gd;uoszs .w 4f:ct(yally between two buildings 10.0 m apart csu(zp j8gh; wo3yoy9d:/owtm4.4 sf. 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 bucket0yt0a5 tl;mxt is hanging by a massless 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 14.0tgg5+z 0ta (0nc xchg.lii- o:$-\mathrm{kg}$ 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, A(qij s:.9g ybenj8, yg7j) qtwntarctica, as show9q,tgq 8 . yw)ibs(yjn7gj:ejn in 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( 15xg*rhps la same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fl5xsr( 1ahp*girst 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 apparatus shownwl, z 1:rp+f7sqioshmq5f 60c in Fig. 4-48. (a) How 7 +mh1pzf ic,:ros f0lqw6s5qhard 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 begane1 dn,xyv g*(i, 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 bl9bg7) at/pmec 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 frictionless horizontal surfaucwwg)syz,, vjfx)k / a:oj;* ce are in contact with each other, as shown in Fig. 4-yzkacg ) uxw /:jo,w f),jv;*s51. 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 ictlhuz. 0q-:y n Fig. 4-52 are each 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 object reach after the system is released? [Hint: First determine the accel:c-zlth uq0 .yeration 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 corn6b8txaj k 26f(ds*3ywoa t t7d of mass 1.0 kg . Calculate the acceleratiootatd kn86x(wfj 27a*s63 ty bn 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 kinetio wy2gzlk,q1 a7 d-+vfc friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.yl7k;bj/q )ngcw q(;w 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 minimum coe-t1vr.b ji1fe-q pwy6fficient of static friction must exist between your feet and the floor if you are no1v-e.pjt i 6q bwry1-ft to slide?   

  What is the maximum acceleration a car can undergo if the coefficis 6j bd6*gg1zun8 2tshent of static friction betwes htdb u*8ngz21 s6g6jen the tires and the ground is 0.80?   

  The coefficient of static f5+f ;m- iu:xcflwe* m:fq5b chriction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a c* -hwq5mc:l5fx+ecfb: fi ;umar 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 x9smsz )b+*u50vzs s vat -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 restyluhl.4q2az) inr, bj(ua d9yr7lm74 on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surfac 8pffgn3a;me8o)t1 wzsous,ikm3d6l/ **qh e e have a very high coefficient of statied lspg ;q o1)3mhnf ktoiw8,af/zu 83e** m6sc friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic frict0mb 3 eta8i9avion 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 (ghj8 4yut8) a6fhd e*-e tqm2nExample 4-20) how large a mass would box A have to have to pre8d8) huge2*q n-6 fhatymtje 4vent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the:l0c*heyg* gg floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speg h0*yc *e:ggled of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110w , ;6doxfjs uqm(: drx7w80ra kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 8o(7u w0q6sfa dd;,rr: m xjwx 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 coefficifvblp:b uan6hg5b5;9ent of static friction between the crate and the bed of the truck invu h96: lpfb5b5;bgas 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about prw5 h/ -djo(tscz w4x8arking your car in your driveway, which has an incline ojs /4w85hdz cwot-r x(f 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide wi-mdo mypiz+,rd8 r3 9yth 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 0lia16lfk11ika 2 qgoplane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speedgn5xvm- jrw *+ of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill witkedr m4t : w6er g3wk8zc6+z;yh 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 ro;-p 5vrax8y9qurx;b* 2dizxs ugh wall by someone pushing on it with a zsa 9vxry5bx* p-xuq8d;r i2;force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles a*zxsn 0wvp s*+*b /zcws they melt. Consider a chunk of snow x*b *wvw*p+c0 zzss/ nat 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 aut8azkwrd(:gl0 c qscz; v:s3, c:rr:pkomobile traveling at speed v is equal ga z0lr:kc q :rz::;rs(3 vc8dcw ,skpto $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 th- xyu-qxv: vv1e dash when the driver decelq :uy-vv 1x-vxerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is givaeun- ckg4 ;y.en 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 c;ga0/ ipjghdv 6 (:j 3:c6qmw.l-llkb9 de euconveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speedpbw 6v ;l: iglujhe6 a -k9mecc/q.dl:03d gj(. 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 ful6qp ..eiuv)riction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coavp u i68yp1 ,yvz(j4hgrh8mh4st 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 moe +wwnfrdvt2-5f pk;tow */ k)del of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0*fekwdf5ptwow tvnr;+k) -2/ .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 anif4ggiq u5j:;f w gk+: automobile crash if the deceleration is no morewg5i:+ ;if4k :ugfjgq 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 , and if an okr,l7wsz /n1uajf (o2bject is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mustzsk ao21lru(f j,n7w / 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, 3:ou +e+y7 1;gjfrh il (du sn-r)ullzexamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction betwrd ul+ o; y1-j7gzh+ef)(ns:lr3lu uieen rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down9jqbj(gi g 4z: a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom afj: q9jb(ggz 4iter 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 Leani nt:6yw ;o6e.nz63 qubjg fz2ong Tower of Pisa and falls 55 m beforze6o:fno;yj2 t.66u qb3 nwg ze reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretcdg. s/r s8; d:uwfkr7rh where the effective coefficient o.7swf8/k;usgrrdd r: f 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 /c)- n mj:4hfg.p8yfjfo *pzka hilly portion of a city. An important consideration is hopzyfcgn)jk* /.o:h mj-f pf84w 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 thin piece3 lfwb9t wm2l5 of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices thaflm 5wb9l3w 2tt the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connectin6 zq (l)9jg/f+ uxvfyxg different parts of the svj)9lg( yf/6q xu +fxztore.
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 forcayf4n 1u 31 23nf,wwewlx0e bte F is needed to lift the piano (mass M ) using the pulley apparatus shown i bl3f0t23newwux11an,ew4 f y 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 vf8z.f3hq1z*svu.n8 d u tk s0 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 eng0;gc0g1j2ynvzv obp jtpo/ a a.xp-1 )ineer considers the following set of condip/vg-1an0pc zbo 1.jvat)g; 2y0joxptions:
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 Ita y *eo(dnnp)q *iz0,xqlian train has a 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. Karen's r+fof xrj uu +h0so fpwj37sy+y 9as(2(ope 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 hyyps+ 3 (ow7ua+ rs+fjj09xf(2su ofrope. (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 i l3khh-- jjrl;74pysn s 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 a)0dc e:2dqlwnllowed 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 i nh91jokyus q73( -iymnclined at 21.nsk 39u1y-q y moi7jh(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.