Why does a child in a wagon seem to fall backward when you gi3gskm lo6t v -.sz)y*bn 9i3/gr+ xlrjve the wagon a sharp pull forward .lon3sy+g r/)i*gslt 396 m-kzr bxjv?

A box rests on the (frictionless) bed of a truck. The truck drivec0 mqu /q79 2 p erk6j 1as6xxmpq).,hyapq(wur starts the truck and accelerates forward. The box immediately starts to slide toward thermx6/pq 2ye(q09.u 7ah6q1mjw,x k) ua ppcsq rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are 1 jgi)yj46nkd4esunkbf .8c8 no forces acting on it? Explain.

Only one force acts on mu8 jz7e 6y;fqan object. Can the object have zero acceleration? Can it have zero velocity? Explain.m7y; 6uzejf8 q

When a golf ball is dropped to the pavement, it bouncx33ztgnv e)f6es back up. (a) Is a force needed to make it bounce btxg en63) 3zfvack up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opmsex;a v6s ;l*6 e16uz xphvprl *k* xt476ocuposite di;s**6zuxcxo lpv mx tks6e;66e7a4vlh 1u * rprection?

Why might your foot hurt if you kick a heavy desk or a gzha)p6 a*q bwv-aq84wall?

  When you are running and want to stop q ,bej /wvk3hs,+jmx wao/ vjo,7 yv1i9uickly, you must decelerate quickly. (a) What,, 1/ohbj9ix v w,ov+ vje3s/kawjym7 is the origin 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 of the same threv.u0-x 8w(+ a03(hngbtd)muecnnavfad dangles fro0. bwuh(8nt fa0 ()nve3c+udg nxa-m vm 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.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Wk b(j,q/ lwg2,tgc3 wzhy, cw/3 wjk ,glbq(2tgz then doesn’t the heavier rock fall faster?

Would a spring scale carried j5w;9u s j(ywnto the Moon give accurate results if the scale had beeyu5jw( 9; jnswn calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a msp4fh9t0b w0; 4f r5fky+clw constant force across a frictionless table using 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 (a) remain the same, (b) increase, or (c) decrease? Explainf5 ph4b40+rwkcfymsl f ;t90 w.

When an object falls freely undesj*h) 264(zqmpzx*qap1xekb gdn a2ce t3e( 9r 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 oppositee cdz3(a 1t*xsxpg4e jqab6(p qe)2kz92h*nm force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when yo2hs su7 ke-pz3u are on the Moon with the force needed to lift it on Earth. Compareu7k3eh- pssz2 the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulg-) fdum /drsl 2k6f3wls with equal force on thefld2m3skf wd) g6 /ur- other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hol0g:*vvsrc9irqnm: q 9j, 7bv cd a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (cmrrnq:vj ib ccv 0g97,v *s:9q) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on wu*;p a,vtgrf(g( la)you? Why do aaguv*f)(l,(tw;p rgesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accidnj3q,co . jus2mf)kb;ent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really;2nc,u.obqsj j) fm3k?

A heavy crate rests on the bed of a qr( m2pdp; 1vvflatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes th;1rqv 2p(mdv pe crate to accelerate?

A block is given a push so that it slideslk)a / uqw l(t)kle7q- up a ramp. After the block reaches its higk/-wkual )el7qt)( q lhest 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 yourself on an inclined tbyttl;8 *7bei t9vhnx r8h*tk3qa:wq al62 :plane? Assume the mechanism functionstt ebh*x8ql:8 i2aa:nv3 tyql96 b t; rkw7*ht properly, even at an angle.

  What force is needed to accelerate a i.p n:dm4s* ;;rgccz uchild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider xu szpya 7a6r q3+a8i(rvf6b-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 acmb5// s2sft qjcelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ojvi3mca4y0n;m cg: c +f 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 s if the car ism o,jq,wjli )(8 dooi: traveling d,(joiw mo :8olq )i,jat 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellekcjl:s1 :b s+st from rest to 125m/s over a distance of 0.800 m along the bar+jk: 1sc :bslsrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acce+grgcl prve,el3 ok0h. n,-e (leration of 2.5,egk. ve(l-+0g lrcoer3n, h p $\mathrm{~m} / \mathrm{s}^{2}$ 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 (lxs9oc9(m c6i gg kyr*t0:j pt)) b(um402 $\mathrm{~m}$) 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 t(;g,6y*6mfbupcyi t fo be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert 6(*upfigmf6 cby ; y,ton 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 motionlehhsnrv :6ns *;cp a2e8ss elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s re:v8 rncnp*h;2asehs 6 gular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg ej hn*6l.k2cx plevator has a maximum strength of 21,750 N. What maximum upward acceleration can ij. k6c x2hnpl*t give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including,e6ijlfge+aq d.j *i 8 parachute) when the upward force of air resistance is e6ai e+l.g, 8 j*jfeqdiqual 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 8u wb-:3ehni sd 8aiqj tvg(0;ground below, he bends his knees so that his torso decelerates over an approximate distance of 0bgq8v:t i a3h en-8 sju(;i0dw.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 ve 9i-g qpv(7j,44webyou xbv2r rtically upward over a pulley and abpyq 9wovx4v4r2 7b,ej-( ugi weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram form4ez naadx4/dh f17 j0 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 of a baseball (a) at th chfxsw;x 3w12e moment it is hit by the bat, and again (b) after it has left the 1cf2;x xw3 wshbat and is flying toward the outfield.

A 650-N force acts in a northwesterly dire0tsxd/sw-,ay(1y8djwt xz ( b ction. A second 650-N force must be ex-8wdy,x b sjyz w/d(0 (tt1xaserted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betweentt (koc6spz ;p2yq-2;jznc o2 two buildings 102 pz(zq62 ;k 2tj;conycs-pto.0 m apart. The sag in the 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 from anotheroig 4a27-zjb2nr)fte 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 1uyu s*qz11gjj oo8+q7 9hfv n/quq6m( d e15qh4.0$-\mathrm{kg}$ 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 x-k5wsp 7srx4McMurdo Base, Antarctica, as shown inkp7 -4xx5 wsrs Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulz (mfj5r1wpge5 9c*-vci rz r6ling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling br rrivepg69j( c1zf mz*-cw5 5etween 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-pull;k bsk;3in +ksey apparatus shown in Fig. 4-48. (a) How hard must she pull ;3kns; kki+sb 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 racenw1s+kb48nj3p- cye; jl -rws began, 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 bfcdyf 6,i(ju4lock (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 in contawbnfy4 i fw:kvmeb ;,1i m941rct with each other, as shown in Fig. 4-51. A forcfw4:1mmk; r yb4wbe i,in19 vfe $\overrightarrow{\mathbf{F}}$ 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 abovejybftx f3,j r( o7y1q6 the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pu1(fjb7oy3 , rqty6 xfjlley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of mas isx3tisvs 1pfxd1;7jl2,ag.q+ kbc*s 1.0 kg . Calculate the acceleration of each21assb7.qxxvpc3 +jti sk;lgf id *,1 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 kinetic frdz5(+r dxd14a27wymrv 6ndfliction 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 requis9l(*:01oh.xd ) tpse uhv mucred 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 standing on a t 3 v7qvi,vifn7rain accelerating at 0.20g. What minimum coefficient of static friction must exist betweenv7 v 7i3,qnivf your feet and the floor if you are not to slide?   

  What is the maximum axdc0jpbk)i3+)4 rkz is,bt+ob sus1*zy :7 tm cceleration a car can undergo if the coefficient of static friction between the+0k:,)c+kto zip1s uy xr 3sz*td7ibmbs j4b ) tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal streelb)z:apl 1 (u qxo ah,q.(f,kxt pavement is about 0.8. On how steep a hill qfl)(lb u:op1q,a. k, (xx ahz(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 -kp m9- ,0ftrno4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rougx0o6i6mdqrxajaskp5 /.7q :nh 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 sw k (kz77la-8:e hk8v qnra an3*t:roeurface have a very high coefficient of static ez 8rhao*q:nn a7 t7 3-8k(w akrvk:elfriction.

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 freheoxn37r(f;-0qg +u vcp tnb33s*75rgj xy ciction 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 iakc bjk(ui(+oqn 6 +74-20) how large a mass would box A have to have to prev niqjk6+bi7k+ a(o u(cent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gtp6 zz .d,iax5 l 3zql,2fvnp;iven that the coefficient of kinetic friction is 0.20 and.fi5 a, 2zpqlztp3nxd z6l v,; 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 anddi.y6:rer).gsrbuirl ) ay;) at rest on a horizontal surface) udylisrrya rbi;re.) g6):. (Fig. 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 heavy crate. The coefficient of stsm2am z(tt 4+fk7ol ke9oz6,x atic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which thelskx z69fem a,o7 2m(ztk t+o4 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 driveway, wso8lolv4 +j (hhich has an incline of8vjohll o4s( + 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a )ik:hpy4or ,)z49jdlnu zu0x 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 t0)oxisl02 5iqkol +ctilted 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 ( *ob0b5v tg*cgaiu (kj ddd;*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 spn0wp0a9mj f pgt *8n0qeed 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 som4pdy 1h/n89bdfty9h s3bp5 .t (eigha eone pushing on it with a force directedh3bybde4ty9 at1ps.h9i/ pfd8g h( 5 n upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous prc,xy d (-zqrv0*yev:ler,rg1 ojectiles as they melt. Consider a chunk of snow at the ridge of a roo,r-e vgl yqdzvyx0(*c :1rr,ef 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 trjldd )um 50lm- ytvsq;)vo h1k9c)6hfaveling at speed v is equal to k9v0d;) thfs j) oyml5 d1uvhqm c6)-l$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 sli z3kx0 b/77ao)kh7vwdmnhds9des forward on the dash when the driver decelerates from 45 m/xbh7 hvdo9s7k37wzda0 k n) $\mathrm{~km} / \mathrm{h}$ 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 ini0p (rrn imz.z9kt3 5brtial 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,l+vp+8r7b p8uo jyq;3jbit e 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 decpo+ e 7qjtbi 8jb+l;p38uyv,relerates 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 coefficiz h5d skxntn4 q*fei c:cx6(qjk( :0;eent of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6.0,k v-tke:x5 knc(o -wg$^{\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(6etzrx4xe ,g ylp:+e alian heart, at each pulse approximately 20 g of blood is accelet+6(ze:y glp r ,exex4rated 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 cos1m,g m94saohance of surviving an automobile crash if the deceleration is no more than 30g,4mamo1 sso9 " 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 acce (bxuzs6srwwy 7vkq j)2r): v:leration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, showz2 6srw7rqvsu)(j: ) kw:byvx 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 at2mzcz ac((+f3*w -7 riakqrtn accident involving two cars, measure 72-m-long skid marks ofm(a(r-f+zzkcta237 iqw*c rt one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for eaci6 u(k0 nv r6u/w,stgmh 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the n 6vs u/imu k,06rtg(wbottom 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 thexowws-,dg.p,y- qs) wo5( vqw Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average fowd,--wowxq(go5s, s w q.) vpyrce of air resistance?   

  A cyclist is coasting at a steady speed of 12.c90r+ad uhof2k nb 6ccb:q0xm/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lah 0 6rn+q.ko2 :c fb09abccduxsts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the ljl/7a. /9k dm +jm3k4 xcxjoc/y num1redesign 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 do9 3/d amnkxc/j ymjuc7j .k/xl+4mo1lwn. 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, dgv7 0nv iw;vokgr,b-9sk4fzve3t p 16angles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the stringskvgw p,67rv4kif39 bg0v nz1o ;te- v 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 connecting differegek cbu:(t :9+jsuov+(eyam( nt pacm(be (u:(v+a skjt9u+ey:g orts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the, cpajf6*6 cnt pulley apparatus shown injncc *66 atf,p

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 3y .;lny5ne)o(d /pdrn.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 engineer considers the f.arvo l(08 5qb)fz9oslmqm) d ollowing set of coql.sz(d)o0fv)958 brolmqa m nditions:
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 masmeu81v( gpy8ou a;4uiz h5rt,s 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 Kds:j fp4s;+8j oico .lvu.9siaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill haofsi j jcui9dv.;:sp4.ls+8o s 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 him? Which climber is more likely to be hurt?

A fisherman in a boat is ujy(g ( 1dtw62fp*kzoua c5n1d sing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building khse r0rq(cx 221h o hqea83d-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 together are asce6 /2reva.lpr4bto a3gnding an ice field inclined at 21.04tr. beraav2pg6/l 3 o$^{\circ}$ 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.