Why does a child in a wagon s3wp )la26uxob:u.k-h fyrg y/ eem to fall backward when you give the wagon a sharp pull forwary/hbr p-kuu.: x2ofa6 )wyl3gd?

A box rests on the (frictionless) bed of a tr)jajguw7 (lp, qw3o8kuck. 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 who is riding on t7w3( ,o)awug pl k8jqjhe truck

If the acceleration of an object is zero, are/xy)u( fp:td 5mdztf 5 no forces acting on it? Explain.

Only one force acts on an , 6m, u7otwymiobject. Can the object have zero acceleration? Can it have zero veloio,mwym 6 t7u,city? Explain.

When a golf ball is dropped to the pavtp 5/9vminuf.ement, it bounces back up. (a) Is a force needed to m/m. n9u5tpivfake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppo1u+efibm kx u hny4;+(site direcfbmn1iu ke4 x;(+ huy+tion?

Why might your foot hurt if you kick a heavy desk or oon:uqfms.ih76y(f6+o- nco a wall?

  When you are running and want to stop quickly, you must decele5-pp(a)f*)lj0 rzjhmx e6 fe3/dn ye qrate quickly. (a) What is the origin of the force that causes you to stop? (b)-*0d3elj 5ep)z6fn /y( ejrmpaq fh)x Estimate (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 of thh-s+990/rqlqcnbe( :vqoyejgg t5n 7 )wkc6 je 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 th-5)nqko gs+w(e lj en/ r6c y j9:b9v0gqcqt7he thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg r9+si mqb v z1+sqnh67qock. Why hnvq79sq+zbs +m16iqthen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon gi9v : )okh n ma):aq.j5-)0prcyidv cw (xzgub3ve accurate results if the scale had been calaxic)cqb9um:j 0rgn w-:.h dk)v z(5 o ayv)p3ibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attach2rg-; i5dgn oced 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) rogg5d cir2; n-emain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity te5o(0s -re-osn zd7- mg wfj:ghere is a net force mg exerted on it by the Earth. Yet by Newson-e-d 0 7fom esj-:gwz(gr5 ton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on the baj v85o :t;mh:ao m;vj b58htMoon 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 and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37)u7c 7t ipsf6g5 pulls with equal force on the other team. What, then, determines which team will5tc pfui 77sg6 win?

A person exerts an upward force of 40 N to hold a bag ,ij8 4ha zvl;oof groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what obj 8aoihz; lvj4,ect it is exerted.

When you stand still oq l:) d-ubrrpp; 1th d+pp)qy4n the ground, how large a force does the ground exert on you? Why doesn’thl ;dupdq-+byrp :t41p)r ) qp this force make you rise up into the air?

Whiplash sometimes results from/f- hjf 7rnbn7m h9bt3 an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situjf bhn7- f brh/nm973tation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Wheno dk3ke.lt k9 8lwo)7t the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. Whl97kw8.ettolko 3 dk)at force causes the crate to accelerate?

A block is given a push so that it slides up a ramp.h8tpuwt 2zjriiqf z 4tu3;9;* After the block reaches its highest point, it slides back down but the magnitude wi 93f; i;qhpj24* rttz8utuzof its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plan79 z5phwh4k jke?zjwhk97h45k p Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerykop6 cs+o n4ci;:)nv ate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acce,5rr/t)whu tj6kyy d1 lerates 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 rzj+bln/ d9wm-7 f r-clope withstand if 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 oo8nj( en ew1/jk8k4ihf a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg /:/ adcova),f1ezmqj car in 8.0 s if the car is traveling1d)/,aq fa vmczje:o/ at 95km/h? -  

  What average force is needed to acz 1 ki +7jqg7;s; j;(hrnhur. t3fouvpcelerate a 7.00-gram pellet from rest to 125m/s over a distaj 7pjkvnrt1oz hh;gq7. f (+ur3;;siunce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accele ge my/b(4p;qvgtou4* ration of 2.5 y4/bg( tqe;u*4gopmv $\mathrm{~m} / \mathrm{s}^{2}$ 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-mu)a9dn;mdx /r 2. jnjkile 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 th:wkz0v l*8 rm)w fvj4pat the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max = *mlj)v4w:z fw 0v8krp   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 mnrr scusf-5h(z,hktv( 2 7tt*i1reg(otionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelez2,th cnr (517(rte( kv ri-g sf*shutration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengd)p(uos 3q*h bth of 21,750 N. What maximum upward acceleration can it give the elevator without breasu)boh*dpq3( king?    ( two decimal places)

  (a) What is the accelerationddy v+e37lqg 5 of two falling sky divers (mass 132 kg including parachq yddg+e37l5v ute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he48n f5j7nr jvf strikes the ground below, he bends his knees s758vnjrj n 4ffo that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests ony3eul7u) f- )szc qa3x a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end z3cqx)l f3au7u)ye -s(Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbakaq rbu2o7e/0ll 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 moment iaxv;n, wk,6llrq7v 9xt is hit by the bat, andk,qvv 7l6, 9xw a;lrxn again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly pukjagh* 3ma,tks4ub +)v*b* direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces pot,ua*hba*ug+spmk j k)3 v4b*ints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strxxw0n ; ftp enclk;d-w;7z1 3pung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mil;tz1cn x3ww;f0kd ep-x;7 npdpoint 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 hqw yy /+ ;7nla4xl,yb 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 1p(vb.j2et 5bf 4.0$-\mathrm{kg}$ 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, Antar jbgsgx y-9 / -d+rgre*tvg3fx2/+re jctica, as shown in Fig. 4-46. The sum of the xrgrv-tf eg+*2-/e 39j+ grbx y/dsjgforces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 pua m7bo0z; pon )gl; lbh/.(23w hvagmclling two cars of the same mass behind it, Fig. 4-47 . Detaag)mo(;b;vl0bhpg3cwl/7nzh m o .2ermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using t fpm j 9hedwq43mk.v1kqv0 syk2 6d6.phe bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowlph3d 6.9kw.k6dkm2q 0s mjq4vyf1ev py 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, e9 :nsoinh eg15q f)y );fxyw)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 block9jzcg11iv1 kh vaf d+od2,v a9 (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 surfacns;v ip/qu51flny8y) (sus9p e are in contact with each other, as shown in Fig. qvpfn )si9y l5; 1/u(nyp8sus 4-51. 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 .:sx l69m2qj7owiszo m /k7ad in 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 acceleration of the lighter mass and then its velocity at the momeji / o wslzo:x2aqm.9ds7k7 6mnt the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on 6y(zot; be (nkmz+gkccm.y3pj 18o4q a 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 diagrams shown in Fig. 4-53. Az og e( n.zp mo4mqy6y8 c+tb3(ck1kj;ssume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 b-3vq3k pal f6kinetic 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 ton6nhg)t*cw a7 start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating 8v7m bj,gy7)pfb +,mec-aer lat 0.20g. What minimum coefficient of static friction must exist between your feet a b,r8je bl+ fvg) p-,7ymamc7end the floor if you are not to slide?   

  What is the maximum accele7:8 yr 9kkqpinm1 kz0bjt -h)hration a car can undergo if the coefficient of static friction betweenkq1)jihbzt m:kk 7-98rpyh0 n the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal s () gqmd k gvy/*r:q9wlts*fq*treet pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car f ml/s:*q)vq9ygqd g(rwkt ** 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 decelerate5-cr./qz aq fu2zpvsq-j,r )o at -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 3.pp/rse ,g gy zng6qr6t4pag7k :iq1/0$^{\circ}$ 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 asphal)ty n g7cjpjv)v)q9n*t surface have a very high coefficient og) 9)pctv )yvq *jnjn7f static 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 frictqr-/*ow epe1:i o fnj)ion for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20)mtruf5a 043 8y,u+qij+n xgx h how large a mass would box A have to have to prevent any mox+ fu, ir h+58qam0 y4gutjn3xtion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floorx+hy9ph4 g))xn2xg v r. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impartshx g2xp9y v) rh+x)4gn an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest c6s,l,ldk20 msf3pb.qoi: s kon a horizontal surface (Fig. 4-54). A 62 bkkf 2:lq0s pdl,mcis.63o s,0$-\mathrm{N}$ 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. Tei+y9x--qdm pf 6ol6m he coefficient of static friction betweenmfyo dx66- +e-qpl im9 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 truck?   

On an icy day, you worry about parking your car in youv5(, bufccgrghrq /5 +r driveway, which has an inclinc 5rg+( ,b5q/frgvuhce 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 280w (hubv3 3kswcg(s x/$^{\circ}$ 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 a9 lj9cd;lfde5 m v/nm6(lhyshra+ y2- plane 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 speed of 3.0wd ww4ys;hwvu7s(y( 6 $\mathrm{~m} / \mathrm{s}$ 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 the7eb4m:a+as cq vg1wo( top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by sanie kjj :6-l9kcd):domeone pushing on it with a forcl) nd9jjkk- a::i6e dce 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 ck; z/n3g tsvd3/quewp m-o5z- an become dangerous projectiles as they melt. Cons ;g/m /w- evzpd zsuo-n5tqk33ider a chunk of snow at 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 mi rt.v(kj.ls1a nimum stopping distance for an automobile traveling at speed v is equal tos(1tva k..jlr $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 das a*zoy: i6lwtv vqb.x;(*w8c qh when the driver decelerates from;8v*b .c yvz:(t*i 6aqwqlxow 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 speed nt+tu9ep 7bj-$ 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 beoey /rvx qgr7zhm5 7r78a r2a3lt from where they are filled to the packing station 11.0 m away. The belt is initially sxrmzga7/eh25 r qo ar3r7y 8v7tationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficientd293w +m(zo,i4vz kwqycso7 d7g a 7af of kinetic 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) can coast down 22fogc q3p:ny d0v x16o0l ppaa 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 appro i*hc9jzcoh;i:p1y 0nq 76k nnximately 20 g of blood is ann* 10ji yzhk76;:o9hccipq nccelerated 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 c+-d80xlr+upzk,z fe ohance of surviving an automobile crash if the deceleration is no more than 30 " +epu z-k08,l+r xd ozf 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 prod 4u: 92. **esaj4evbafh feouiuced by an earthquake is a , and if an object is ff4u 4ahejb :eo*.a2vue9s* igoing to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident e6t,,gzw-5ksn3dp; tx/aun l involving two cars, measure 72-m-long skid marks of one of the cars, w/6nep,uw ttdksa z;,5n 3g x-lhich nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means th)(zqj;8*puax mu cy j+fl( 1gbat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore fri j*qpfxy)(lucm;+( zb ga1ju8 ction.   
(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 ,+lhm*r ql m;oand falls 55 m before reaching the ground with a speed of What was the average fo ll+mm;h,rqo *rce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stre e5e)a2wlif m4;*a 7l7g3l 0hjmsbao htch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having mjel mlh*of; el77s 03a4bg hia2)w5ato pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly porifut h6mwc/tu e+.h6-4;id qp tion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a leveltucqp wmi -f.d hh;e64ti +u/6 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 pi9 y0ayy ix 5dy w(g1 kcw/vj*-dj1yhs.ece of string while the s9 ik(j1yy 1jhy/*gx vc-5y.0yawddw 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 supermarket, there are to be sevgmliw69xm h 7:zspi2,xj2di 2 eral ramps connecting different parts of the stoiz iim69xghd,ml2s7: 2 jwp2x re.
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 (mapk*wg-qw 7h3ass M ) using the pulley apparatusg qp7*h3a k-ww 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 accele/f ,,pkxe d j(z:0c,qjictvd 0rating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an eni8;oh y+yat9ngineer considers the following set of 8ayi9o nh+;ty conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a 2)fhx 2wi,mv trg)vwj+zvk8+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 oo4zfahwp:78 sc)y b-sf 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 8zsfh-c74byw)aso p: 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat i ug6+1ioh+mjcs 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 m9c.5/tb01tglam:xltfkiy gsw o2 / o;aximum 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 fiel(zd /rjt :g:ied inclined r(dzjig: e:t/ at 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.