Why does a child in a wagon seem to f iwn05vh4la3k(8n0resk6e tm all backward when you give the wagon a sharp v(sk4n6ltimr w00 e5hke n38apull forward?

A box rests on the (frictionless) bed of a truck. The truf72lo;3d2 lq l:zs h0kikv88i/ki epick 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 sta;8plsq7/o:ikd k 0ze3vl2 kifil82 hinding 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 acting on ybn5vb 9ug /:f;n+xrzit? Explain.

Only one force acts on an object. Can the object have zero acceleration?yl)+wq z5 kj3vlgf 0u4 Can it have 45y+j)uv lgk3 wlzf q0zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back:-;xmm 0l0x t32qpb smfzff2p ;sqzg. up. (a) Is a force needed to make it bounce back up? (b) If m2xbzf0zppf m 2l3:0 q tf ;m;x.s-gqsso, what exerts the force?

If you walk along a log floating on a lake, why does thexay; ufam ;ma42u79 c2effm:s log move in the opposite direct4x; fcm2myue2safm7;a a 9:ufion?

Why might your foot hurt if you kick a heavy desk or a wm*lft 6+sy9 ngall?

  When you are running and wad0n9f 1wdw s(lnt to stop quickly, you must decelerate quickly. (a) What is the oriw1s0n9(lfw d dgin 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 o d1geh4xbub- i: dmw7:f the same thread dangles from the bottom of the stone (Fie g 4x:7ui1w:hddmbb- g. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg( d u,y)x/dhnfhp:c f0y3-rr r rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fal0(nyd y/drhr 3)uc: x,hf rfp-l faster?

Would a spring scale carried to the Moon give ac,bbruac y :(4syer6-m x ndh+99hki0z curate results if the scale had been calibrated (a) in pounds,0ha+rd us -4n: yhkxbrimzcby,e99(6 or (b) in kilograms?

You pull a box with a constant force across a frictionless table using :-+zxh.n 9x ssmvvo9 xan attached rope held horizontalln. 9ovs - 9sxzxhvx+m:y. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influe pfzb:b k sp/a1.4/loynce 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 opposite force fob1 k:4p/ pzsa./ybl 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 nf8gzdl7 d ()g )apf8othe Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and onn( z7pl f g)gfdod8)a8 Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls w wjs6qj5roz a99b :4ouithar4 qz:9wsbj j5u9 o6o equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. De+6tm e76ebtaqscribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (bq6e7bmt t+6ea ) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the groun8 (nw +o9c ap2igc(dljd, how large a force does the ground exert on you? Why doesn’t this force makag lp(9o(+ cd2w i8jcne you rise up into the air?

Whiplash sometimes results from an automobile accident when gxvp9 gmp+*9rfx 2 e0wpf58 a6ubd0mnthe victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this mgupfbnw*f v9are90g0x2m 8x 5ppd 6+situation. Is it really?

A heavy crate rests on the b a4 e3ypmbub(9zkoo,j ky 4/)ued of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. b( 4u9uo koba,y43emy kz)p/jWhat force causes the crate to accelerate?

A block is given a push so th.di)o7 o w c-1+rua 29ozrnbjdat it slides up a ramp. After the block reaches its hido.wai-n1z o2u)7rjoc 9+ bd rghest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yl; gs09ekzq 6j w3conhv2nc82ourself on an inclined plane? Assume the mechanism functions properlyh sc86k0ol n9gn;qvc2ejzw23, even at an angle.

  What force is needed to accelerate a child on a sled at km.ok0dj 9mx 1 1.25m/s$^2$?   

  A net force of 265 N accelerates a bi 4;wk r;amxa,pba/ to:ke 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 accelerate a 96 7t(nm,vq;+y ww.mgds0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of acfcy- 1c1a za6 $76-\mathrm{kg}$ 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 ix07b 2e p0ok,g3 ze:3ncdt ojzp(,pj bn 8.0 s if the car is travelingz n, z pexpojj02( 3gdb7 pebcok0,3:t at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pev t5d1.43lgaypvx, * stkg3)1hocycl llet from rest to 125m/s over a distance of 0.800 m along the haclpyc ,t4vy33g51d.go)1 t lskxv* barrel of a rifle?   

A fisherman yanks a fish verticaof 7t(-hc-.vnhkjaz 2 lly out of the water with an acceleration of 2.5 -ho2c kjn hfa(7.vtz- $\mathrm{~m} / \mathrm{s}^{2}$ 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 carcro/oijl p3hn. j 7,s.jjf :gw2na03 b can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 ;xw rv u jbo4w76bt1m)kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and w ;1o 6bb47rm)uvtjwx 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 elevatorjq-g )f(,pvjq. When the elevator begins to move, the scal (-pjf,j q)qvge briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N.zk p(i8 *w. +d,d vhnpm9g)mgy What maxi8+v. g g,yz* hppkdmd9w(nm )imum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling s* as1+w-jj 6lj :n0ix sb,pt/pfyo a)wky divers (mass 132 kg including parachute) when the upward force of air resistance is equ6a-n/)s: j 0w*jy+ijlpx w1afop , btsal 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-mgjc p,*py*.s m high. When he strikes the ground below, he bends his knees so that his torsm *y*sc pjgp.,o 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 Ns y7hq: 8xr-x9 ohb/zk rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight han qxr8h /-kxzosyb97h: ging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskn+7npofl: k6,mdk 9a aetball 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 it r3 k6o82lbu5byf 0i+ rlcvd ;j/ o/kasis hit by the bat, and again (bkuv5kb crdj 6032/b;8o/oal+iy lfsr) after it has left the bat and is flying toward the outfield.

A 650-N force acts i4dt c)g3r 7sp(il nm.p.wwps64saq4a8vl 6esn a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer wit(q4s64sd)t3mp7wges.4c8 vsp.6rpl ani lw a h a vector diagram.

  Arlene is to walk across a "high wire"h:lyy .2is)cg strung horizontally between two buildings 10.0 m apart. The sag in the yliys.: g)2hc rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord fru z 8nw1908-ij ipslfzom another 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 1cmx 16gsh1 mvvlc k5zj1zal +v x426w64.0$-\mathrm{kg}$ 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 houk5jde a, xbkdye1 61k00 :dyqo9wyxi+sing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sue1y exox,+idk6dy09kd01j : qab 5kyw m of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 . pxr2u,iq gan.2/yc w(Determine the rat2/i uw(xg n2 ,rp.caqyio 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 bucketiy d:3pi0u4o54nv9afcte*l b-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downwardlai*fe :3ciy4o4td9nvbp u0 5 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 65uk-2lzfhxh (xi a11v 4d s *pz;i6uxu7$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (massbb *eqv; ;.zad $ 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 friywi/qy b9m9 k+p1g)ww ctionless horizontal surface are in contact with each other, a9p w b)iy/ w9w1k+qgyms shown in Fig. 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 in Fig. 4u7a)ws1-z nm t-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above s)n t-7w mu1zathe 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 byk;qrelf3d gd93jrnuo3 +8fka.) ( v rd 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-rkf.r98;ddf(ujero qd3) 3 +vg3 anlkbody 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 friction betweenz7gv8( yj6u i3erz2 d6 dmaga- 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 requ*uyg30piuqv7kh -m6 ylo33r7ivs2 e pired 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 standigcpa35 czn* i hg/9/thng on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and theh35gz9/ cah c i*ptng/ floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficienh:lwyi3(qz9s pnvf; )t of static friction between the til nqz(y )9vhs;w:f ip3res and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pa wn9obv6v./x jn*jf p:vement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?.von nx/*w9pv bjfj6:   $^{/circ}$

  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 atln5n7e1dg*dh, b bb 0d -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 rouh198 *xc xf xwa*dwdyka .hbyhi:8l99gh 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 as*dk* )sqjs/m v+ p,tao1g qy1fphalt surface have a very high coefficient of static friction. amj1 k)fsq/vp,to+ dyq s1*g *

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 fricv:cp mdg:( x vfo+:g2ujl.*wrtion 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 wvpllljkcipy8c :5 2r.- 1yz5rould box A have to have to prevent anc.j55lkcr ri8pz 1v l -y2l:pyy motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across tk.t:eqei gx81 he floor. How far will it go, given that the coeffi: egqe 8t1xki.cient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7 nh5o,q- ps.qb5 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4- .bh5so, qpnq-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 he0. ab:dtrt )uhavy crate. The coefficient of static friction between the crate and the bed :rhbtu 0adt.) 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 your drive5q*m/h +iv qgzfg:yxs6is+ m8way, which has an incline of 12hgis iz6qmm+ gf/+8s 5y: *vqx$^{\circ}$ . 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+w9a35wvsa9z y l+4zaq 5o yfe 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 lie sl i+ +vm)ynvhtb2w+oen66 r;s on a 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 iniux:s i7tmw 7-+mvw17r3aul cztial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the topd z lq7. 3xbzl2nwox3sqe6+( e 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 someone pushingf4+j dw-w; tkb: od2xzvgla oppoz:7/5d0i0t on it with a force directed upward v/t2f tzp :zoid+b ox0-7d 04: w;gpjdla5kwo at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as thn(q0xu,xol w6ey melt. Consider a chunk on o(uqx,xl0w6f 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 minimum stoppingz7zuv 0n/l:xofr68 hf9 kz;cc distance for an automobile traveling at speed9vzc/r67n0coxz l8;fuh : kzf v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward q,1ve+w: m7ea)dh1p h kdty4z on the dash when the driver)qe ,avh1d e71 k mzyd4+hwtp: decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given l1/qve x e7lo2an 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 the :veztd0usw+m8pl*- opacking station 11.0 m away. The belt is initially stationary and must fsdute- wm8+zo l*pv: 0inish 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 coefficient of kinetic frb 07 unn3fkv2viction 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 (iec2f )tc8n. t/x8fuvxncluding 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 mamm;wbngwy -y4 7wls +sw-alian heart, at each pulse approximately 20 g of blood is4-swbnwl 7syw+ ;g-yw 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 ch upxg.4)+a nihance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate thngu)hxa p .+i4e 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 accelerati 3pl cv+.mu2qion produced by an earthquake is a , and if an object is going to "hold its place" on the gc.q mui32 lpv+round, 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 involving two carswry 08 vv/6f*;ndj h-u8yqldpv3gt .g, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about -ptd8 30ryj wn8; vvy*fgqd uv.6/lgh 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-i+v)hb1w uk0u dkvh-v 4n-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Igh)4h0k +dbw- vuvuvk1 nore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of d9 ssla)uhn8)f (an7exip v/4Pisa and falls 55 m before reaching the ground with a speed of What was the a) xhd98/)ial ann e(f4susv7 pverage force of air resistance?   

  A cyclist is coasting at a stei7( b7q f r26u lies ldd36l(u4u1oxamady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Wimu2 bxu647(ae 7l urd si3odll1i(qf6 ll 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 porcyqw a-crs k*,4jth ;hv5b-: ation 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 level road fv,;4b: -rc cqayshhkj 5ta*w- rom 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 plk-*4dkb 4f b2lw 65i,b;4xqsutv uga +/inokhysics experiments, dangles her watch from a thin piece of stringu k4+oq ikn aiul;dw 4s54ftlk -6vb2bg,b/x * while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, therb/mp((tcpo)d 6/fnhhn znk+ +e are to be several ramps connecting different parts of the store.hfbmn ( (zoph//n+6c+ntp kd)
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 q,f(v*,b 3l vj/l9y*kf+mzyzw fbe k )to lift the piano (mass M ) using the pulley appafwv), (l/*f,f3v+9j zzy*el kbmqybkratus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3*d,wg;j kepsbo )tf7 1.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 chcdzv0 g* ofela;3y:(vild-restraint chair, an engineer considers the followinefacv3gl*d( 0 o;:z vyg 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 6ed8otk34 * f1xt7hqvk 60 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, B+f3hobtww* ;u ill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on hfhw bow;* u+3tim? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1 yj*oyj9cv ,q*; cb9qq0-1 $\mathrm{~b}$ 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 tz)zunye * l1e+ a4d9fmaximum 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 ic.xa15 vmii,ep e(c p(y.kb.n ae field inclined(yib .apenmc5.,v p.e(a1i xk 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.