Why does a child in a wagon seem to fal na7ldq)553kdxmg 7bgl backward when you give the wagon a sharp pull forwardn5gkqxm57 blgad 3)7d ?

A box rests on the (frictionless) bed of a truck. -,acrv7lu6dql37 7 ,jkcm r krThe truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Disc7k v7,,-ar6rcl7rkmd lc3 ujquss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, arce4pw,( xdb0 y q.bs)te no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can its-(:njt0g4la md65 ;e o nxyrp.ymbw+ have m-sy .0 jt6;mpo5:b4gry(+ wnxeln dazero velocity? Explain.

When a golf ball is d xu f5 6kgdgh-siv0ux+-zla)0ropped to the pavement, it bounces back up. (a) Is a force needed to make it boasix5vlufgd 0 6-+h)0- xugkzunce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does they,it*b 7mb3 ht log move in the opposite directiobb*t3 hmti 7y,n?

Why might your foot hurt ci9 (0dcv-kka if you kick a heavy desk or a wall?

  When you are running and want to stop qui ht f.ns0w3k;sckly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the m wntf;0sh.3sk aximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a secti p8me1/q pvydjl0g+: bon 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 it? What if the person gives a slow and steady pull? Explain y qy8 /e:dp+vp1jbmg 0lour answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kgu;dxzcd 9c1o-3vaw5cubkj6 j5 i:-1n,v gxt l rock. Why then doevk1 x c- nxuo5z6ub v,19d5c;w-ij3ldtag: jcsn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate rj zcyhn* -)w,besults if the scale had been calibrated (a) in pounds, oz) jy w-b,c*hnr (b) in kilograms?

You pull a box with a constant force across a frictionle *h,hdlx9d*6jc fqz.w ss table using an attached rope held horizontally. xc9f d6h*ljw.qz,* dh If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely ss) j/xv+pqq* 44uy fsunder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the objecs ypsqsu44v*fj/)qx+t exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needeqk1s:f uz8)ljd to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally8zlsjk)f 1:u q 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–q5xpzjzu: ) t2ym uyxk 7)a;w937) pulls with equal force on theujtyu wm;9) xp x:ky7qa5z )2z other team. What, then, determines which team will win?

A person exerts an ur+nu/dv/0t1 m z /f 0qk(plgnkpward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by 0zk1 k+ t/nvgmlpfq/dur(/n0stating (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 the ground exua7 c4 gimnx;;ert on you? Why dxi;;g4 camu n7oesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car i lm31wpc,1cxd s struck violently from the rear. Explain why1l3,dxcm1 cwp 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 flatbed5,p k,o)6e)lnrlx cwh truck. When the truck accelerates, the crate remains where it is on the truck, sple ,6crxon5k)w l,) ho 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 block rer5lj 74a;h lasaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than ;s5hla4ja r 7lon the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inca.bwmiz*f fm :e79s8hlined plane? Assume the mechanism functions properly, even a z 7asi m8b.9fhmef*:wt an angle.

  What force is needed to accel471r-. mm4 yleh bfshherate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accey.z,- ydgplcc55mho4b ; .qqelerates 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 use7 qkgxhl/z0y kx s00:ed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oqohw;( i6/ s+rvq0nwa4 jq+ydf 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 requ+ficjvtpi33ova 7bwo; ;ar47 ired to stop an 1100-kg car in 8.0 s if the car is traveling at 7iavrpoi4f v7ta; 3j ocbw3+;95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from 9wnn e:;f z:8u lwy9j, uqu:yyrest to 125m/s ,w:uyu :n8w 9ynz ylq9f:jeu;over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accfgv *4tyj0ewe k wf/+0eleration of 2.*j y0ee+f 0wk wvtf/4g5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ca7-ye6 pesv z()ys gx um.fubr52cs2 4ur can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that tpey2ux:kqa 68 he maximum acceleration is 0.0680 g .akeq:p 82uy x6 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 5eb9r0qr5agt ,as bg3bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calcula5r gbt qasear3,9b g05te 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 strengthp;l 1s aw0bvi*:ef6u c of 21,750 N. What maximum upward acceleratios1 f *:puac6ibel;wv0 n can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falv+lj4eeif;cwwiz( b l ,:*:c uyup4t:ling sky divers (mass 132 kg including parachute) when the upward f::fe lit+e;zcp, w *:iy l4w b(cvjuu4orce 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 the gh/zesg5uqqt 08d4tkkcf1 4ef / mz-jash ;-3cround below, he bends his knees so that his torso a5k3;4h8fzh tm -1tzq -egufd4cqjkse0 /s/cdecelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vey(2hvmcj l(dr2cyo-, uz0z ,xrtically 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 hanu0vxdjc, m( 2yrlhyz( cz -o2,ging 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 baskew1ec-06 pmwzutball 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 voomw tp8yra96q91p* of a baseball (a) at the moment it is hit by the bat, and again (b) after it has pqv1m99a6orot8p* w yleft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forceeuj:+;srvk :2/joqin0g4 o c o must be exerted in what direction so that the resultant of the two forces points westward? Ille/njqs2r4 :kio; v0:+joocug ustrate your answer with a vector diagram.

  Arlene is to walk across a "high c bi; 2hn:)rehxkr)okc 1,lj3wire" strung horizontally between two buildings 10 cj), cx3r n1:)rl;h bkihk2oe.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 massless cord from another 3.2:u4:20e6ba:k hf j9ip s vbhxi$-\mathrm{kg}$ 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.yo5czq )w;nnp6i2 -ve0$-\mathrm{kg}$ 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 cqq u1w /n)9rza new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The w9)c/ nu1qr qzsum 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 mmfc s33 x 5yk(7nbcp x25dup)behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first carbfc 5( )mxp2nds3xyk7mu35p c $\left(F_{\mathrm{T} 1}\right)$ , 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 usibu 0ulvz :du .a/2;;/+esi c(hkmvw ksng the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to ra2e/hzbs :u i .u;duv (aml+kskc /0;wvise 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, ae g9d/ 5qmrw(2i5j8nctomfd mk +ee* : 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block k0ohav ,;hu* w(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 fricq+vpxdy e1mv/ s-iy72tionless horizontal surface are in contact with each other, as shown in Fig. 4-51. vdy/qpy21x7+ i esv-m A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abolftuf ,ol1j reayv21q 64x, f1ve the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum heigl11fq14xf,l,fvj2 r u ot6 eayht does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected i/6ui ov(3eh)l k t/hcby a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using titv/h( 6 lo cieu3/)hkhe 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 kineb;3w3qiea kh 5tic 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 50.d rz57f p0aj+ -(iiginwc/69 jv1ajv kbvcx .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 z7:rv w1r39 soxb6 syctrain accelerating at 0.20g. What minimum coefficient1cr v3x7yr:bs6ow s9z 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 coeffi5mpg ods/pn;. x2 p-nhcient of static fricti.5p;gs p hpd/xnno2m-on between the tires and the ground is 0.80?   

  The coefficient of static frictiollw-v682hc n nn between hard rubber and normal street pavement is about 0.8. On l6hc2n -w8lvnhow steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -: )z)vavtl +vh4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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;* q,irdg1m7hy t4pfch 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 asph487lc,pk)+z cb bqum ualt surface have a very high coefficient of static fpmkq)u+ 4 cbuz7,8cbl riction.

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 frictionu xaw+nj ):bojzt;8/n 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 (Extqm;u1c*kz:)* mcp rm,7o fpoample 4-20) how large a mass would box A have to have to prevent any motion from occup uk *qco;*ro:1mt7f p,czm)mrring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it gi4t9mns or*hh ;.)z ato, given that the coefficient of kinetic fr)r;h4ztn hot9 mai. s*iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 rylez5k ,2lx- kg , are in contact and at rest on a horizontal5zrx, 2klyel- 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 a heavy cra*njq,q6ro:ih6 4g ejkte. 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 dei g46: jqhn6*orkjq,ecelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry ab l6i7nb paux):out parking your car in your driveway, which has an ilp:u76) bnx aincline 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 a a b:s,./aw z2ueftvb(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 ang)cit2i w7gg2yvu, w2fle $\theta=22.0^{\circ}$ 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 inio1y)x c0x r/-seiadtx2 o:l1n tial 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 kipvz7z 56.atz:uoy .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 pdo80+j)t emg dlace against a rough wall by someone pushing on it with a force directed upward at 28o e 08g+djdmt)$^{\circ}$ 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 as they r- 6lzm vu-a+hmelt. Consider a chunk of snow at -lu6-rz mhav+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 automobilj+*3sr4 vckyi e traveling at speed v is equal to ri* 3+j cks4yv $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 -;x-lm snnj0 twhen the driver decel;lnjn0 -mt-sxerates 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 given an ia ruty- q04 9io4grf;*xop t.hnitial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where tpz 8snbs1zuy3r z h*g04rz5z. hey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is 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 min 8uyz. 4zz1*zshs0rnpgrb z35imum 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 kiosso- juz0pm4+xg*8kss)6 wv netic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle)e9yaou 9; lk,lyksj b7 i)8.6cyq/q fnwb)ym2 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 appro4g4 f*j 9j7e sv3esojm*8wxuuximately 20 g of blsux3geu8jj4*j ef4owmv 7s *9 ood 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,:pexm)v , ca dg,5thhwz q-7r chance of surviving an automobile crash if the deceleration is no more tha:c,w5d he rzt,)xv-ma,hqp g7n 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 accelexiqg2-e 5wwuzs21tllh.8 *oa ration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the .85wu*xgot lq -azhwl212i escoefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the sceneywlv pe* y9*ks waz36* 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 between rubber and the pavement is about 0.80. Estimate the ini6wzs* **kvypyl9a3 ewtial speed of that car assuming a level road.   

  A car starts rolling down a 3 k/dh:v et-f:ms*qg q1-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 wdvh kgf:qm/s 3:* qt-ehen it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa anju9m0rdb fn .88oj n2;)utxysa*r,a ud falls 55 m before reaching the ground with a speed of What w8yjf0uubam .rnotj x)9san *8 rd,;u2as the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mudd1zh wkiya *z7c )7j6rzy stretch where the effect hrck)w7zz 1ia6yzj*7ive coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redes2y.6cx uv2twly7 /beuign of a hilly portion of a city. An important consideration is how steep the roads can be so that vulb7.6wcy2yt x/u e2 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 physo4uhe ;3l6ysfn sv.+tics experiments, dangles her 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 strinhn4.6eul+fo3sy;vs t g 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 bedb0k *omx e+:jkqj+h 6t:gf d* several ramps connecting different parts of t+mdjtd ofq6kk+0b* xh : j*:eghe 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 ) usi dg bd ,ya9.6ari0qfr-4gm9vfng the pulleygr dr6 .aiyaqd, vfg9-b49 mf0 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 accelerating at 3.) ,mgj2swv:f3uxbg j3 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 engineer considers the ovc(s ,zlzxd vzs6l7++b, xo:following set of conditio,zzlos++,6xs dlz vc( :7b xvons:
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 trai2jfz uk56w8 ehn 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 saf.p, 4nneuv 4ij91n/v)y vpl q 9sywvw56n-icyety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.)lw/n j9 9e.isvy4 vunq)n1-4ncvvwpip 6,y5 y (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " sd*kwxsq8(3i *p5 k k.j,g/u r7cdgox 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 bm- dbrgp8 f*p-uilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending ae1zj7m dmi by46o9 zg1d ,jb;xn ice field inclined at be1,z;jgoy 7d1dbi 9zm4jx6 m 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.