Why does a child in a wagon seem to fall backward when you give the wagon a shas ovx uu3 x0ih9c4dv;8/e7q 0:oywc mirp pull forwau x coe h0x:ivy3s;/d04wco8v uim79qrd?

A box rests on the (frictionless) bed oa)v kz3 p-,; ;edcsyxzf a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss thev s;3,); zpa dzce-kxy 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 sbs+ehb 6j29sfzk*xs2rlhf8 jt 1r5*zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero axvp:qmg 7)o d(*ay (qkcceleration? Can it have zero velocity? Explq7g(xopvam)q *y kd :(ain.

When a golf ball is dropped to d)3kbn*x x0o a7 imf9ythe pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the f of03)x n7byx9ki* damorce?

If you walk along a log floating on a lake, why does the log move in the oppos b5pa *66nmlyul6 ut,oitea6u66ulml ,5 p*nt yob direction?

Why might your foot hurt if you kicksk4 k+s6j(sav ed*r6mox-m3e a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceleratswm */l:opnial/kl 1 3e quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usin1m3s*lpikn la/w o: l/g 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 fromkxr. ebo4... 0h*ww.g nd*m m5jmcgvu the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers. .jo *nmg*vmgmw w0. dhu5.4xrckeb ..

The force of gravity on a 2-kq8,y 2g q.x;c5lwhv+ o nmn8eeg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasteryv+8x2qe,5. he8nw g qnomc ;l?

Would a spring scale carried to the Moon give accurate results if the scale had f f0bdo,8sk:) k/qeuqu0aa,v been calibrated (a) b,ud)va 0 fakquk /8o:,qesf0in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table 6nm5lpfjom z.j-.iu:dm 2/zx using an attached rope held horizontally. If you now pull the rope with the same force at a pmx l 5zjmiz6u.df m/j.2:-non angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net fiod0 5pml) 6jzorce mg exerted on it by the Eartp6j) miz 5dl0oh. 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 fn:l hclyjsg2tjd47 g25wkcb -s m++6borce) needed 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 a7chdt c-g+2ykmwj6l lsbn 45s2gbj:+ 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third la qu-i z h5tk)b6b2 g4i9jr5crww, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines wu2izcbk4t 96 5bj5 q-ihrrgw)hich team will win?

A person exerts an upward force of 40 N to hold a bag y:;svh 3 kak29zaky y1q 1qfc4of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitu y4y ckf2zahsqy1k;a9:3qkv1 de, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on) v2d7x;wuqmurl6o g) the ground, how large a force does the ground exert on you? Why d)mu)uvq wd6x;r 7gl2o oesn’t this force make you rise up into the air?

Whiplash sometimes resugh a)l5)wyh,cd- nhl hte.+- vlts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seeml+ e yc- tvh d)l.gh,)-wn5hhas to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of ,*7 n .kwny*w2nnky+8ycolzga flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the cratklwcgz.o* + n7 8y*n nyk,n2wye to accelerate?

A block is given a pu l cm44e 0txzaop7r+zbc;fh,9sh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration i +cl9 eha;7,cb p 4z0xrzf4mtos less on the descent than on the ascent. Why?

What would your bathroom scale 3t)+b 69slvioxva6 bu read if you weighed yourself on an inclined plane? Assume the mechanism funcb x69tbvis6la +ou)3vtions properly, even at an angle.

  What force is needed to accelerate a chiig2m(x op+ y6old on a sled at 1.25m/s$^2$?   

  A net force of 265 N acce qz -hchr* :/vlrl+oj8o d8fj5lerates 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 used to acceleraf6ln p- tm4t+goxly1vb 1 /q0ste a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 0txawyr3g n 7)$76-\mathrm{kg}$ 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 +0+ri ljj h.b.oj4oqaan 1100-kg car in 8.0 s if the car is traj ajhq+r04l.i + .oobjveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 1js3tv3;w)as cln o u95 xuz647jjll)e25m/s l)w9l3ta 7 34 ;6vnjuzs)ucjolsx5 ejover a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.iv+agw o/ z d+ 4yi+56j)phsbf5d s+w ho4viz6 5jip)f agb+y+/ $\mathrm{~m} / \mathrm{s}^{2}$ 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 track (402 g6a:3n*vzqhn $\mathrm{~m}$) 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 ) i0ctppnu j9xxtqd 9 3, y9z-pd;s to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cabc- ;0n3 j9t9duypp,9 dxxtpqzle? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless eleva5px59 mtb sdm;tor. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the am5 5bm;td9 psxcceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strenm(n xsgjb)6 0tl 5t9y jjxz7 0-e:dcdhgth of 21,750 N. What maximum upward acceleration can it give the elevatortl sxgmtz5) -h9eb:( 7xdc 6j0jndyj0 without breaking?    ( two decimal places)

  (a) What is the acceleration of two fa og; ik)y-d.ralling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal tok -gioy .r)da; 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 3.964hzhn.buku,t) y4mf nvb(t , -m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) 4v fznm(kt. nbh)thyu 6b,,u4is 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 vertically w+o s209cedz wupward over a pulley and a weight is hung from the ot+ w 9zcos2wde0her end (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 basketball player xh)wa,*-n5s ogzmi0mnck;g*
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dlops8*2 7 ae2nqbx*niiagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bata nbs*oqnx7 2 i28lp*e and is flying toward the outfield.

A 650-N force acts in a northweste4 9dia 5ljeyjf8 bkhl8h)w1( jrly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwar5f 98dyhb ke) j h4wa8ij(lj1ld? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" stlzn d-+5o;9/h oetktz rung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoin zlt5;t/dohez k- on9+t 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 anor6xhn6 -rs0kk ther 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 1 tuslge3t8n dwmg9g3,5- r. xk4.0$-\mathrm{kg}$ 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 apho 2js9vs :z4zo6fb gvu2e6 +t McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcesu2jh ge6vbf6:9vp zso2 z+so 4 $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 mg+2 -q/5pnafp cbwsem5q,( nip5 s0hd ass behind it, Fig. 4-47 . Determine t ,gbs5c5(s-npheai0/5+ 2mqpdfq np whe 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 the bucket-pulley apparatus 5v *pr+9sq cqlr6*qjmshown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowlv qcjr+ pr m9q*l5*s6qy 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 begaru 2 peky7 ;p6+m3tlld7g:kyx n, 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 bl8g4/ kis+r n1gpt hyt:ock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are k9,eb- uja6 zvm d4g ucfw1.m*87qxljin contact with each other, as shown in Fig. 4-5 .9kw1f8lxzqdm64 7-vgc,j e*m bjuua1. 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 above the ground9bbma5 ch* ye9, and the massless fricte 9* bbh9cma5yionless 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 moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of maszg ub.1qtq ,e9s 1.0 kg . Calculate the a.etg 1z9qbuq,cceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kine ;b 62a,kbs /yzaq)tjqh-sf1 ttic 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 sraiu39q(e5 nu1zrm +e k(yi7k tart a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What mi;ps/hw +bb i33tftvzc 4:roy(nimum coefficient of static friction must exist between yoc bfz:p3(r bh3 wst+;o vy4/tiur feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of star scv e +n6y5 fm3h)4zu6vvup:tic friction bet6vzy :nr3 )6ec+fs v54uhvm puween the tires and the ground is 0.80?   

  The coefficient of static friction 9s p ;s:0ppum ophgx*r( 6g/plbetween hard rubber and normal street pavement isl6ppxsh(; g9 p0gp : /ros*pum 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 at -8br j))9:lmnndbz*aj4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 h72 be ail.a.h1i- bvxrough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a h6hv28 n *ncn56l l aweoal1:fvery high coefficient of static fri25e86 nv1* nl a6fhwl c:ohanlction.

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 frictiu khdevmre.0,4h 5- i8 kv-vtzon for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass wj))a016g ,hc amellozould box A have to have to pr)j ,omall )0 zea16hgcevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it ykh :d4l vf9teg7qp.9 slides across the floor. How far will it go, give7py49eq:d lh.kftg 9vn that the coefficient of kinetic friction 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 kg , are in cowv- nw0 j3(vis;p4mx1jxpx1 rntact and at rest on a horizontal surface (Fig. 4-54).0(sxjip1v;x v 3x4w r-wn1 pjm 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 friction ;l7w(bjae l 7ibetween the crate and the bed of the truck is 0.75. What is the maximum rate at whi;jl7 i7wea(b lch the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about park-qhj*zzba .9;:d q6x4 zrjpdjing your car in your driveway, which has an inclin6 :;4qh9ard-dp jjzz qb*.jzxe 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 witupd;mq r-,zu7 :8hm p2 lfmn4nh a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on dip i0vc;i a*vr:8 9osa 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 m2(o2u2nx eu yof 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wq i.zr 3 i+/ :8ua)apsul4lsyuith 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 pushin xjd:qq8jw, 39u -grm;l u-xbsg on it with a force dw-8jqj9,bqx-xdr; g um:3lsu irected 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 dangerousu.ezda-9wr -v.ufww + projectiles as they melt. Consider a chunk of snow at the ridge of 9fzwuw+wa- rdv.u e-.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 distfs4thk0/j ih4ance for an automobile traveling at speed v is equal toi4k/h hj0ts4f $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 when the dr zn 4/zddz8*+ec hi7qm4) lqgkiver decelerates frz4+ 4k l)zd*ic8ghm7/qdz neqom 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 initi48 kgfxau)uh uc9db-, al 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 they are f o dand(vfh4 06pqi;e+illed 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 tp;fdo6edh+i0( qv a4 nhe 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 betweens ,74heaam*jqq( g2tm $m_{1}$ 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)gw:ml8 sjw9)ti/q o dfn23cj )t i-d3h 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 approxy 3szo)8oiq ki.3pko:imately 20 g of blood).qpoisk38 zoiyk:3o is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash o-)v e7 x2ng s/bqnhl /i/ugi;if the deceleration is no more thab)s// in x/g7i q2vhugoln-e ;n 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 accel,da q/sc1b6(a.jvj 3ifqd/ hheration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction whc dhj (6d,aqav// sfjb.qi31ith 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 4eiy .s:xzgk8o;6ff0vskca * the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came tof4eo 6 kiac sz8k:s*vyfg.x;0 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 m)7 o9kz nneh63(jxi9;uunww d-m5 fgyeans that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) ; u7 9 k6iy()on jzunhn9f5dme3g wwx-Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is drop jjk rczsya )scc0c;p,wmt ;6- 3w;gw4ped from the top of the Leaning Tower of Pisa and falls 55 )g3w y6smjz,0c wts-p 4aj wr;k;c c;cm before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s 1plgh 8 swz.05fxl tm/but enters a muddy stretch where the effective coefficient of friction is 0.60. Will t/flz 5wlg8s 0.p1mxh 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 redejx3jf )r,a0ct jjd,*nsign of a hilly portion 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, j,jrcj30t , n)df*ajx 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 experimentob-a*7/t xtsf1teta. s, dangles her watch from a thin piece of string while the jetliner she is in takesbo/*. 7-tfx et atats1 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 severt2e-zc h w h,x6mtk6+ney/r;ual ramps connecting different parts of the store.txnch6+2 mh-w ku;re6 e,zty /
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 ) us1ywkzdbe q/x/.+ t1dting the pulley 1bkqwy/+/tx .dtez1 dapparatus 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 acceleratinc 9yq)qy9h uixuz91h 1g 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 engine/;a 4dvow 58g 7dsqcojxhwz;4 er considers the followic7 hxodwsdj5 ;g zvo;4q/48aw ng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metricb09 p cyjr2gu1(mh jd: 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 sbiz:r6eowfc) my8 0)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 :f y6 )cob0zs)8wme irand then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1 klc gr:3kozjer y.,.xuky;7 50-1 $\mathrm{~b}$ 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 buk97z 0 ml7ufgrilding 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 rodn )2v ,x-.auzt:n wxlped together are ascending an ice field inclined at 21.0:u2vlw. za,-dtn)nx x $^{\circ}$ 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.