Why does a child in a wagon seem to fall backward when yo73sw,iv b l0miwlhq67u give the wagon a sharp pullb7lwi, wshmq3 i70vl6 forward?

A box rests on the (frictionless) bed of a truck.4 -hmhh/z: ny.5tpnli The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris wl h5n t/.z:h-iypmh4n ho is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Esad am2a z5wxx2 9g-8vb)oo,gxplain.

Only one force acts on an object. Can .h al +tg7q.1fcsqwt) e*v mt+upf z:0the object have zero acceleration? Can it have zero uq fptg a 1.t+ z*0mw7t).v+fhsql c:evelocity? Explain.

When a golf ball is dpu f m53u9tabzpm7h57u9zvv8n q8 fd ;ropped to the pavement, it bounces back up. (a) Is a force nv59 z98q ptp 7ufm3v5mfud hu b7n;az8eeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the j+ lxkaz4u(rrci 36x3log move in the opposite dire3zciak+( jx436lrru xction?

Why might your foot hurt if you kick anoiz5wx a 0)0e heavy desk or a wall?

  When you are running and want to stop quickly, you mustekj/ mclglt-a3m 1ke2b v2 (n) decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimateam/vb t klgen )cjm-k(223le 1 (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section;5e r a4i61v d0gjon 2btxl-bg of the same thread dangles from the bottom b l 6tj-g4ra gi;bx 25o10evndof 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 your answers.

The force of gravity on a 2-kg rock is twice as/t b l ,1hflhzl/f x0litbf:39 great as that on a 1-kg rock. Why then doesn’/,39 zt/ hbliflhx0 bl1 t:flft the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scalt9(q9rgtq uz* co+8lle had been calibrated (a) in pounds, or (b) itl 9qu8+crt( olqg*z9n kilograms?

You pull a box with a constant force across a frictionlgn9jy- mia1b x// l9omess table using an attached rope held horizon axlj/9gmi-ybn9m o/1tally. 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 f 6bo 5mupr-pt-reely under the influence of gravity there is a net force mg exerted o turppmo- b-65n 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 move?

Compare the effort (or force) needed to lift a 10-jzl:r ie/(jk5a q:0 pkkg 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 horizontally with a given speed on the Moon andrj5l ei/p k0(q akzj:: on Earth.

According to Newton’s third law, each team in a tug of war (Fipbtrlvoy9b 6tnd 6;t5v5ov 77g. 4–37) pulls with equal force on the othr y9tvboovb7t6n vpt5; 75dl 6er team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hol5+)uhpk i1bde wh/ m4q8k/gjad a bag of groceries. Describe the “reaction” force (Ne w/4ghqkk)p5iu/ 1eh 8a+bjdmwton’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 the ground exert on42mlegra i.:q you? Why doesn’t this forqirlge2ma. :4ce make you rise up into the air?

Whiplash sometimes results from an automobile accident whenfipu9-m9p i 7g the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be ti9upg i pf9m7-hrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, t.r41we7k+ yug :e dzrcrxf/qhg 5 6pp8z06cy the crate remains where it is on the truck, so it, too, accelerates. What forc.6wk g z e5hfcpu0d/y4cq z:r 8r+rp 67y1gtexe causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itse87w:t ov7bg*,fny0c u5 rcdb(sy w.h- smdd( highest point, it slides back down but thcrdgd,bmts-7hycduew( o(w : by5*s8n .0 7vfe magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroomc1tb gt+8tnqm1x ns wh0d4yp:hd1e (- scale read if you weighed yourself on an inclined plane? Assume thetnsbdg8:4(ttp1c y0n+ wxhmd-1 q1h e mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled a b,7b ziz778s a;zxfrat 1.25m/s$^2$?   

  A net force of 265 N bk0dyud; l25k accelerates 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 ipe- 16z,)gzy hfg xet:f it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofn7t2hkhdd. 8qly9fq-/al3knq a)+rh 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 requj *vl5av/bsn 3ired to stop an 1100-kg car in 8.0 s if the car is travel/v3 v*n asbj5ling at 95km/h? -  

  What average force is needed to accelerate a bq11dj3 dbc7 vpe)wq0+yfc y/ 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of 1qjddy7cbc0 / yqfv)+bpe13 wa rifle?   

A fisherman yanks a fish vertically out of the water with an acceler*d6a* 96d; vg:jr1ftltuniwlation of 2.dftrl :*t aj l6u;9nvwgi6*1d5 $\mathrm{~m} / \mathrm{s}^{2}$ 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,sxh1q20 v e*wfdyzxz 8oe3 6q 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 the maxdwqqg,lao9y oic.m*,1kqn1ul1 k 2h2 imum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =1co*i2dq2ql kkyh 1lw,19,oumn agq.    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. y-o y6 45qu4 chu7ifmwWhen the elevator begins to move, the scale briefly reads only 0.uh5 6yfq4uyoc w -74mi75 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 strengdin8t bk6rfka2 v b3+u28no;xzs+ ra4th of 21,750 N. What maximum upward acceleratidzan3 u8sft i 2kr 4av;62bk nr8b++oxon can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallin;j/ i y5*mow)*bphjdeg sky divers (mass 132 kg including parachute) when the upward force of air resistance is )ijpyeb /mwdho**j ;5 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 high9wt) rwr0th(q 1g2 s7t0x lsry. When he strikes the ground below, he bends his knees2wwxtqytr( s97 )00 1hlsrg tr so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N nj u/j;41mhk.mkz z6q rests on a table. A 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 other s16k;.qzm h/munjjk4z ide of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pla*q2jauk.zcr 2 yer
(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 moment it is hit by the30 +wdemwgkq , bat, and again (b) after it has left0e g+mwwqk3, d the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fo*j/:frrp;;k8v xoah lrce must be exerted hor r*:/jk;v8;lfax pin what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung r3oo( -k7iwdj horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10wi3 rjdo7-ok (.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 a9hcj:g j-d3 d3.2$-\mathrm{kg}$ 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 14.0 qh5g08.pbdun $-\mathrm{kg}$ 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 locprai0n944c4w4vxq*j m rc ,lr ation at McMurdo Base, Antarctica, as shown inc,0jr r 4m9pxr4q v4*4cl inaw 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 it5apv kr2e1n(m)sz opj 4o8 3mf, Fig. 4-47 . Determine the ratio of the t3zm sj ofpp2)8vn(ao m5 k14reension 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 he*:9 uv/iot:m,ooqv w erself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must shov: mu*e :,t9q/ooviw e 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 bnblvmub lpzr3o1 26 4 )b5x0pxegan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block n2ixl0*dc,lc ,aa zi 0 .5biwv(mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface p0uk7qcbe* e(* 8phqeo1a e)r are in contact with each other, as shown in Fig. 4-51. Akcpuq *oe he0*p(eq1)ebr78 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-zm)4oyfqdo a h* robg1 .98/mam8p1mq 9,dc gt52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. Wham*/oa)m8. , d4a1fy hroqpz8mc om99gtgq1 b dt maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on *:33blinrdgga681c 7kbtt;g ,hp jm sa frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diag3b18*a g6bsl gt7cktpid,r ;gmnj:3 h rams 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 frilvc5w.p /z gm6y 3(mdz-o.ut1id:qvn ction 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 rec9brbog8rc 6d 1dq1c b,vg8f 9quired 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 z(gm ums829zp standing on a train accelerating at 0.20g. What minimum coem 8(2pzg9uzms fficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta6 0oml72sldxa./x/bblhol+ qtic friction between the tires and the l xb. l +dql6mbhl o2xa0o//7sground is 0.80?   

  The coefficient of static friction between hard rubber and normal street paveme l3blhzkzx) 0.nub9z*pe ei4n,h6sk4 nlzs.4 b*he3e 9z,64bni lx0unkzh)pk t is about 0.8. On how 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 m,sno :.h l6tb o:/- /tjpsart0fq t9xat -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 3zimkb/h ph+h 5* aq,*y0$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very h -7 r0lf;xcgdiigh coefficient of static i 0fc; d7-gxlrfriction.

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 friihlu(:z - w x2 verc pa9)3y/:pvirl-zction 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 (36eiekgb;* hc 6* 5)sznqq-z 0 lqdeesExample 4-20) how large a mass would box A have to hk3*hi*edsls c-qzbe ;ee6nz5 g0q)q6ave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so tha7 e+jg5lky*r wy+udb n9r0br ; 5 9r(qyfhj;jwt it slides across the floor. How far will it go, given that the coefficient of kineticg 59qde(j f 9kw;rj; +nyyjr*rru b+7whb05ly friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass p ym/s/j*:n8 b-pb0 itdr;shu75 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-5:m-jbdbpu*//i ps r 0n; 8yhts4). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fkocen64vv8kllx8k9 s h 8u8a8riction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the tcxkehav4 snu kkl98 68 8v8l8oruck?   

On an icy day, you worry about parking your car in your d* /pwn fm5 h;bdexq/ktfu ,+g;riveway, which has an ig h5tknfd*xe pwu;+/ ,fbq;/m 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 a slide with t(11s *nuec sc )u1/tagrvtra3c;u9ma 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 anks.vk0 pl8i42. w bjmwbyv-d 8 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 3.0 h6q dkcm65tqh t(ie55$\mathrm{~m} / \mathrm{s}$ 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 steqvc:td,w92t wb 1 z1meepest 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 wall by someone pushinm9l+p0w:k fcq g on it with :kq +w9pclm0 fa 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)pbx fy hk9 p.bb.yw o:6*marwfx )d36 projectiles as they melt. Consider a chunk of snow at the ridge of a r6 yb fk)a6rpm.f)3hx oxw p. 9yd:bbw*oof 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 mini 2z .1uumb8/r c-uqb8k9uhvzcmum stopping distance for an automobile traveling at speed v im.z 2/ zhc bk8891cu-uqbuuv rs equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides fo xv0qu1as 0:ehrward on the dash when the driver deceleratess1 auhq0v0ex : 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 initial speedc-1o s.ab)o b: g/wavk $ 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 conl95fuko : pqx+5 ctw4sotpx+6veyor belt from where they 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 fo+soopu96xf k wq:5 c 4l+5pxttr 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 friction betp+g a*,vnd 2.+)n ofjuwa+i vwween $m_{1}$ 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 bicyclehpgo1)pgk3:)b zkp )u) 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 w)l7ploe47ak0cag x*f z8 7dwapproximately o)pc7ax87 4 ga0wld7klze w* f20 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 survas9l * y+lm/i()2xtzlkb ,6s9ae w evfiving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force w/9(k,+ i9 sa vt)lys bazf6*lx2eelmon 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 : khy6b.+i:7s gngzy cphp .p0an object is going to "hold its place" on the ground, show that the coefficient of static friction with the grou sbnky+ .gp0p pzg.:ih :67yhcnd 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 s)c ae*w4p79g eu 7kek0-ww hb1c*wfb, examining 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 between rubber and the pavement is about 0.80. Estimate the initial speed1pe* wfb ea 7ckwcwk7s49 g)he0*uwb- of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fgv jdjs750h4 a.btnqg4z :wa;or each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveln7g4t sz jqja 0b5:vwh da;4g.ing 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 and *fpygxatmjdu hy (mf6d8 (80*falls 55 m before reaching the ground with a speed of What was the average force of air residdm*th( f8*y0p(um 8yf x6gjastance?   

  A cyclist is coasting af61 5bexfbi/wt a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the sx b be1f6i5f/wpeed upon emerging?   

  A city planner is working on the redesign of a hilly port8 2ne l+g:etdqion of a city. An important consi qg8l n+:et2edderation 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 exp:l +bn0yvhg i9j0v2eg eriments, dangles her watch from a thin piece of+ly9hi02v 0g: ve gnbj string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She 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 supermarkaapa;o ywv-5;- nm6s, x*rthlet, there are to be several ramps connecting different partpny tax5 ,*;sao -lhw6;r-mvas 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 .:g qa7 vbs6q tu9kxsk ac60r0 is needed to lift the piano (mass M ) using the pulley apparatus sa0a0:curk gqvbq 79sxtks .66 hown 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.a lruim 3o xi9z)5i1su/wde+85 $\mathrm{~m} / \mathrm{s}^{2}$ 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 e3m+nj /pz1*tff i 5scvngineer considers the following set of conds1 /m3 cvfpf5*n+ijtzitions:
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 d :k4jvzlxuq54xj4i(mb:()7tx0wzkhnq ,m r 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 anzl1ai7iips1( i 2iinrz83b/z d Karen, use safety 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.) (b) In a similar fall, Bill's rope stre13i(8r lnii/1pz i7za sbi2zitches 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 rh*3 1psp 0nk+t9pjn fis using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum- :mb3rv9c r8*i jupbt 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 whoe.egc )q69dxsm58m w l are roped together are ascending an ice field inclined at 5d8.6eqmwms9gce x l) 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.