Why does a child in a wagon seem tq24l2x sbdd-.vie t1nf;u4 qwo fall backward when you give the wagon a sharp pullflv -d;.s2x2e4uqntwqd b1 4 i forward?

A box rests on the (frictio0nhs( bgbur 4g 7/ah/-q,jy t h;qvf5pnless) bed of 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 the motion of the box, in terms of Newton’s laws, as seen (aay qhg;0s n,f4/7r/ghbvupbj5h -t(q) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces ao-9.pos 8otc+0vwazacting on it? Explain.

Only one force acts pxswww(q 6;kfq8+mw2py wqlxn9( 79 ion an object. Can the object have zero acceleration? Can it have zero vww(+wl swpf9 8qxyw7im2pqx 9k;(qn6elocity? Explain.

When a golf ball is dropped to the pavement, if ;)vo,qpwx l.t bounces back up. (a) Is a force needed to make it bounce back up? (b)o.px,lq w;f)v If so, what exerts the force?

If you walk along a llsng y5-mf1t; og floating on a lake, why does the log move in the opposite digt51nm; ys f-lrection?

Why might your foot hurt if you kick a heavy desk or :o:9)kptoyh4hsez m+ a wall?

  When you are running and want to stop quickly, you must decelerate quihlyto1 .; yilq(*, 9xv9emz /a f9eqjrckly. (a) What is the or*9, ax9f1 e ohlzyr jm(iyq;t9.e/vlqigin of the force that causes you to stop? (b) 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 ofgqlt 2, *ch8 xb7-igwzz2uj 7a,m/t il 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 togtuhlz7 , 2 8gxbw72 i*cj,i/ -tlmazq 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 1osaer zqq)x9te, w6 pa4v2)c+-kg rock. Why tx)zs6a24 aqtp,r)c9 ve+ e woqhen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon gg ;z0qffk 0c2jive accurate results if the scale had been calibrated (a) in poukzq;g j0f2f c0nds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table us ici0n i2qcm40ing an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (nqii02 c0 cm4ia) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls frpi sl ojtn .63ag-s+l5eely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposijnts-6gal+p3 l is.5 ote force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg1sz2 i 9zd1e1y4e *xe* bijfa9j 5bmeo 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 obj2zm1i * xy 1*b5sao9dzfjb91ejeei4 eect horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each te b zoaj;o o3n6dnb**7iam in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, de6bodz*annooi 3;7bj* termines which team will win?

A person exerts an upward force of 40 N to hold a bag of grbt6 8 fr igmza;:1b3rdoceries. Describe the “reaction” force (Newton’s third law) by stating (a) r zfi:a g6bdt3b 1r8m;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 groun-n3tsct cp x76k2x4b nd exert on you? Why doesn’t n72tc63stn4 pbxcxk- this force make you rise up into the air?

Whiplash sometimes results frmqdb l6c4*bo 1om an automobile accident when the victim’s car is struck violently from the rear. Explain why the head do* 1blb mcq46of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on th 1*rcumgt;u 7xe bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so;1c t7u*mgrxu it, too, accelerates. What force causes the crate to accelerate?

A block is given a push2uj5 r n c(g)1mxgw3hd so that it slides up a ramp. After the block reaches its highest point, it slides back down but the) gd5c3(nu2xw 1mjgrh magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined-c sr6ey kmyms9y +;w. plane? Assume the mechanism functions propecy 6 - sm9r+kyysw.m;erly, even at an angle.

  What force is needed to accelerate a child on a sle c1ru 7s)p xgk-3pk:xsd at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike ,ms4q/q e jyi,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 wit l:orxvt 9gol-u5c77 nhstand 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 of0k;r 8m gyp7lh 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 car in 8.0 w+.pn 23: pl,bk4 -pe(5clkwr vrdf* elf(yim s if the car is traveling at 95k-ffp l( ,br5plr2:*n(dw+wv3lpkyeckm . e4 im/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from reu 4e6-qy4+2oef7fi aw) udc ljst to 125m/s over ay4+j4i6qu7e)c-e d2oafuw fl distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of4+c ck( u0j0zy1ofcx f 2.1 +jc4x(ck0ofzu0f yc 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 covei47+ ufux:bda;et6g ld sn ,9sr a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the mae6d, yg/thp+paqm/m ;ximum acceleration is 0.0680 g . W/pampyh /m,gedqt ;+6 hat are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevatu: :qyuu z4- fd5tku7qor. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate theu tuky::u fq75duz- 4q acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength oft 61 t7iumtqd.mhyq 13 21,750 N. Whath1qu 1mq6.t73idyttm maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two gln c :epw4/1r33 lzoo7ohfw8 falling sky divers (mass 132 kg including parachute) when the upward force of le 43oon/r:pfw3ho1 7 zc8wglair resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the gv mgq8 iubk1w+4wr*t- round below, he bends his kneqibg 4+m-vuwt1 8*kwres 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 rests on a table. A rope tied to the box runs vertically i4i2r7 m6vch nupward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on thenc 2ih4im rv76 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 diagro5x3wx61+zy-gbdt1r w hdjb 8am for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram ofrn* (wzqmm69 p a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and ismq pznw*r (m96 flying toward the outfield.

A 650-N force acts in a northwesterly dfze v,c:fx bt,f*(k3 cirection. A second 650-N force must be exerted in what direction so that the resultant of the two forces pointvec3 :bck(,t* zfx f,fs westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally b-zm i 6s6stzjdjm:4-e etween two buildings 10.0 m apart. The sag in the rope when she is at the midpoint4je6z-d6 :mj mtissz- 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 anothey1( cfl3atyif,i7 -qt :sn 0dezrm.c4r 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 1s: e 5 yvthl;tep6b*h74.0$-\mathrm{kg}$ 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 McMugp-qp a5nq8 qk*i3+5bibjp fgr*y26p rdo Base, Antarctica, as shown in Fig. 4-46. The sum ofyi bi552 6grn ba8pqp p3+*q-f jp*qkg 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 p r( g2cipcdr.kdpku-6/p x1*rulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the cod(r/ *pr c dg2uip1-p rkc6kx.upling 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-pulle66g kr(nu1(f fetbxp /y apparatus shown in Fig. 4-48. (a) How hard mus/(g r( fpxfn6euk6bt1t she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 65 n7erugc()*n p$-\mathrm{kg}$ 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 bl hg:qlzfd/u ht new .7(0v(scqn(m77jock (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 surf,bmk3yb h 5cxj2 bfl.15f3aq6egx 4uv ace are in contact with each other, as shown in Fig. 4-51. A fob4 3fbbj5x xacy 6.lh q 5ukem,231gvfrce $\overrightarrow{\mathbf{F}}$ 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 iz mcx: ; +g5mb 1xq+k1mbn)x;ebkt z9yn 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 t:mgxmknmz1zb+9;bcte q;5+ b 1y xkx )he 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 thb-hbx05 uqaw i )t7x:pnx:2 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, usa: i2h7w : u)-5qnpxx txbbt0hing 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 kinetic frict7me1;*y bote( r -earqion 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 requi:nl cy3 hdonyp:7i qqqhc)44/ red 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 standinp3 7 n:b6d19wdd/abnaxqd* cfg on a train accelerating at 0.20g. What minimum coefficientnq p:dd/bd 3a a6b*wf1xc9nd7 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 thekjxkimw*( dt4jp qo; 7f a,n;1 coefficient of static friction between the tires anwq,j;f(xoj m i;kkdt* 1pa7n4 d the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pav44 0nwqeb/l sad:u+ x naj+w/uement0+dbxew4wa:u n s+/anj4 q/l u 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 at -4.80pvko a:se2y) 2/ yh8la 9gape4 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rouzgoq ww.+5e4 x v-iczy ;as.;ugh 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 wi4c gm((://.h d vz6dkpvnqset efo., xth an asphalt surface have a very high coefficient of static frictiond.qkt6:veo 4f np(d(gh.z/mxcs , /ve.

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 ,.p7ry*oqvzzp4 j/w p friction 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 larger-jc(, hky y4v a mass would box A have to have to prevent any motion fr hkc(4yjyr- ,vom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across oc:ii++r/ c9h wnidy+vfo00e the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 an+vfiid ec+/:y 0cwrnio9+ho0 d the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact andgurc: *3p g6p3g1uisy;1 mhkt7p gf2 d at rest on a horizontal surface (F6ps *m:72t1pr3;uggy3ugf p1ghdk ic ig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a h;vu r xv2oqocnmx;b0-kn6:50rl t b,t eavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at cblr x6;5r: tb2vou n,kx0-mvq t;0no 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 yot 4y0/(:si)se sao el+j )xkgxzph+. wur driveway, which has an incli j4hy p)x/at:xeisz+0e(o+g .ss lwk)ne 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 a4bvm-acef,4xm4de+ 3q mgn 5a slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane dnbun7bd:idr ( ,;rt. 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 speph8rna.m 0d 1h1 r ds((/e5sjo5 qrdysed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of f/x3vjg ;jk5z6.0$ \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 againyxgbszmk; m6vd7p 7z;+ wv9l+2a ey3dst a rough wall by someone pushing on it with a forceam6yy3 xbv wgsd2p7dk ; 7;vlz+m+9ez 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 dc 4j q4ctnq-60w fcidd1iec;3angerous projectiles as they melt. Consider a chunk of snow at;cctqwdicn i1df3644 e- jqc0 the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at 6gbz wd + qcma9oz(g).speed v bgzq(+dozca )96.wgmis 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 ca+0 cf7pr ap l+f1 xbz+qbwn.4hr slides forward on the dash when the driver decelerates from b nh+faf+.x 4z7q0wppr+l1bc 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 cn.p 74g z:sok-l0t k9ku5 z1yxn 6wkrgiven an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to xfz8 lt6 l bsf:ac7q q)326kqithe 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 fx)3l l6i7qqt6skf b8a2zc :q 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 kineticg w13q*f6 zqje 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 (includame ta+b5 eb2,ing the bicycle) 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 bi(lwfy- h2v8( ),ts on+quh4/an aws heart, at each pulse approximately 20 g y)hwwsnnbs q(- (l f,oa 2 +itua/8vh4of 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 survivid3zt3nnhu5768 qce f/+k znwvng an automobile crash if the deceleration i3ndn8v573n uzt+ewfc h/ 6qz ks no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleratio zn(tf.x, :v*q1 l4wool mjpn.n produced by an earthquake is a , and if an object is going to "hold its place" on the ground, sho *qx,4j:l( fo1ntwovp nz m.l.w 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 z65qjlu qzi)o3r7 /wkaccident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to qz3) qjlkzo7/ uw5ri 6a 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 tmfq/s1 :jso2rhat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it f2/s rq:js1omreaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of thevw;q c4dhu ainhm mf:d:e-2gtv60 5b4 Leaning Tower of Pisa and falls 55 m before reaching the ground with a speb-n f46cqhmuegvt: a;24hdd0v 5w:imed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed ouv1ky. xl+ ot+6 wivr0f 12m/s but enters a muddy stretch where the effective coefficient l+v vixk+ryt6o1wu0 . of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An impor6hx*y r );t;4fnfscb dtant consideration is how steep the roads can be so that even low-powered cars can get up the hills withoucsdff46 xrhy )tb*n;; t slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin :; anwe-2pqoz piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that thea:qzn;e 2o wp- string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps conne 4p,ju f1wgm/ncting different parts of the stor w/1u ,4pjgnfme.
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 2-1 dvypye d+vto lift the piano (mass M ) using the pulley apparatus sh1v de-v+y yp2down 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 3.53jgr 4f51mlp,mzr.cziv b4 , -cibb5 p $\mathrm{~m} / \mathrm{s}^{2}$ 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 engineercrdg 5+w5f w/c considers the followi/ g5cr5fwc+ wdng 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 d2y kif(i9t *8it) dvnItalian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar le. l113 *z*js j,qnu pt djie3hhy(3auongth. 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 dao1u (jh s3 qlp3j*yhin 1e3u.*z,tjm (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 " 3b fq+khy2l :t10-1 $\mathrm{~b}$ 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 tallw .+np/ mdrg9y- 3tz*ypqd h8y building is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped toget9o1+ el a8 usy-rg7mhlher are ascending an ice field inclined at 21.lu-h 819ygrmo+sae 7l0$^{\circ}$ 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.