Why does a child in a wagon seemen8ro :ic g9g9t7- sthzwmc21 to fall backward when you give the wagon a sharp pu1h9w78sn 9 2 zirtccm-togg e:ll forward?

A box rests on the (frictionless) bed of a tdiw4hv2y-b)mx+j tio;a2 ar2eplb 06ruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is ridmbiabx0d lh-v;)262wipjrt oa y2 + 4eing on the truck

If the acceleration of an object is zero, are no forces acting on ita*rfh4ai8n (y8fj; wn ? Explain.

Only one force acts on an objecte4ay8 -uu ,*)aoiiex )gho mw+. Can the object have zero acceleration? Can it have zero veli*h)4 e u)egima ao8+,oyx u-wocity? Explain.

When a golf ball is droppeddi72(yp8u si/ eq9 zh u0zx29ehvyj+q to the pavement, it bounces back up. (a) Is a force needed to make it bou/dyxs+ 9eepuq zjvh0q z2 78(2ui9yhince back up? (b) If so, what exerts the force?

If you walk along a log floati y63p vn(3f4 m9/qx0 aya)mueiqab9fk1t, fkqng on a lake, why does the log move in the opposite directkmffy1/ px34(a 9ie f9atqqyvk qub3a6n,)0 mion?

Why might your foot hurt if you kickh9c/tzqo7 j04p gv/by a heavy desk or a wall?

  When you are running and want to stop quickly, you must der.q fz+mx ml8zl*5qx .;bydfj:y)a 4qcelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleydfl.mlf) y +8xx:* rz54abqq mq ;.zjration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread f*jzc6acr; ,(ds 2kv rlrom the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull onardks2rz(j;c l ,*6c v 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 roc (o66*wiiuupbk is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fallpu6uow ib6*i ( faster?

Would a spring scale carried to thj59ho -s8n:s neutk; t(bb 1c4w8pzlxe Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilog(ebxss4:1 l-t9c88bno up5z; whkn j trams?

You pull a box with a const 6zu,b s:i 5 pny:kt:imydfi k(77d-cnant 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 the5py-ybd:ifmni7tzi ,u :67(kd ks:nc same, (b) increase, or (c) decrease? Explain.

When an object falls i,q ogtm/n/ yk-z4ai:freely 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 ang-q:ziom,y/k ti/ 4 an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or q( w + hdfsn dluyn+fg:l;q)63force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the : dqlq36fh +;dwulgnn +) fys(Moon and on Earth.

According to Newton’s third law, each team in 7k 9g yz:kau:bnz4kdc517lkea tug of war (Fig. 4–37) pulls with ek4 gke5 n1 cyb79zklk7a ::zudqual 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 groceriesiq f,j22mubfes3jju9ma 5w ;r qfi+7 9. Describe the “reaction” force (Newton’s third law) by statina5ujwj2 ;79m9q b23 rsf i ff+qmi,ujeg (a) 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 t 8h( lgzjdaz;zo :.8ewhe ground exert on you? Wj(ge:h wl;8ad8 zzz .ohy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when txou (eiylh6 i;x*x4s6w d icd. h/f9b*he victim’s car is struck vb*dx6h/.(eys;foxdhi i6ix 4*9lcuw iolently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acaus sc+,hq2x w+2t9 lccelerates, the crate remains where it is on the truck, so it, too, accelerates. Whal ch+ css+,2 2q9wxtuat force causes the crate to accelerate?

A block is given a push so that it slides uprn nm.1al,y8ty6 :4vclyk: e xt-ph2p a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on tcnl1m:yp at8yt2vkn el:x- 46 yrh, .phe ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pt(x (f nc wliy; vy13lhb29p2llane? Assume the mechanism functions properly, even at aw22i((y3v; flbhptl y n9cl1x n angle.

  What force is needed to acceler:l ln+-e2 b qh htv53o76 npmvs19himmate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at mf/4l4 u4nerb 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 p 9.rb8b) dw+zuk7 prla 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of 8t3ek0(pgew ca $76-\mathrm{kg}$ 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 be )4ho gd91 s:/ndcfian 1100-kg car in 8.0 s if the car is traveling at 9n/e94s:i1gb fd)c d ho5km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rev68(zm t5a1st5tyr cw 2m *n j*vmb.h:gfup.zst to 125m/s over a distance of 0.800 m along the barrel of a:mvg *avy*.mhzj51 8t .6cs n2b(5mutw przft rifle?   

A fisherman yanks a fish vertepte5pwj9+,jfrf9q5z-p qk *kz y;6 f ically out of the water with an acceleration of 2.5 65jff;9zwz9f p 5re-kppey *j,qk+qt$\mathrm{~m} / \mathrm{s}^{2}$ 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 at sv7mye6rb 4fzc78b7 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 maxim/ ml;oy,d2bq0qp j1 kxum acceleration is 0.0680 g . What are the maximum and mimly jxbdq1q, 2k0/po; nimum 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 ixzqwdc t5j1 .avrpcr52ju ;:*.pm3r09jp b fin a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceler r;dtijfqc* za0v.pwu551 bm.jr:9prxjc 32 pation.     ----待选择----downupward 

  The cable supporting aix5wlwrr . eg4i, pi8; 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the e erglwi5ipx 4i8 ;w,r.levator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 13+ icl)( yqu;as2 kg including parachute) when the upward force of air resistance is equaysq+ l()iu c;al 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 o t6l+*ib:teiwzwpq(9e9x i+ bf a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approtei weq b+9iwzx+l iptb96* (:ximate 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 tablep(;67oums oa t. 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;m t(op76o uas 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 di 8s8pt iuvsyivv+n(3 /e*p. dnagram 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 of a baseball (a) at the momen9* (iibwq/ 6wiyrz5ug t it is hit by the bat, and again (b) after it has left t i6i5(/guwiq9 *rywzbhe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65 s*gb(qg.g0 wr0-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer r*gbg.(0g wqs with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontdh 8: qc: zi9ksjd w/255cjhgeb ()hudally between two buildings 10.0 m apart. The sag in the rope when she is a5dku iw)h c g9/eqj ds2z:h h8cj5bd:(t 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 cjgv 0 322thvify d 7hmxsgh87w(d 9*wmassless cord from 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 14enbe../(p ld;ro3v nq .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/mby/9l3ao (rop fbe9 to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the f93rlbmof9 byo/p e/a(orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 . 3bgzp)-j k/;+8lxxgx7 a ifub Determine the ratio of the tension in the coupling between tha8xf3 kb7bg lui/)- +zpx gjx;e 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 tcrlvn7a xsap c + w*;.gs,ub /1ai4ze //y0vzhhe bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cons7/h+;wp/cvaaig r.l exc v0,yn/1b *azz4ssu tant 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 raceit.0c nin:c25 f +rnax 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 block (mp5 4vcypgp95r,bm-uk0h- glxass $ 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 horizowk.ji s u7e1)ontal surface are in contact with each other, as shown in Fig. 4-5)jo.kiu1w7e s 1. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initialwf ,,w2ncer3jqpn.* x ly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground rw 3njw,n2f,e x.q*pc. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of ma) zdg/vp -1*ws.ri lz+p04n8kjg lcokss 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fik8z*/cd. s1wj g lpop4gz in-+ kr)0lvg. 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 betz/ 4v4nqdrfb ficp/9vv 9k +i,ween 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+ddk(ikv -iuyi 9)i )uired 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 train accelera+,qifz.2gn ) y:ihi evting at 0.20g. What minimum coefficient of static friction must exist between your feet az2i fi .:ehnig+,qyv)nd the floor if you are not to slide?   

  What is the maximum accl2b w38b.theb56mjb veleration a car can undergo if the coefficient of static fv6hbe tbmwb 32lb 5j.8riction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber anb r/q vg;f/pb+d normal street pavement is vb/rqfgb/p;+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 -4.80ttfv n5qe0cff*+ zb jcr8 6,drsk+;1v $\mathrm{~m} / \mathrm{s}^{2}$ 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 :b5rx,- avsvh rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffi s3j r-0dbs+z:auyluc 8vd/7rcient of statvu3:jd7b/cya zr+08sr lds u-ic friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kineve*/yj.jj 60 cpqm3:7buk qj stic 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 (Examhzc lwenqrap4.* v t7,fpb(2;ple 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assume fez vbw plq p*7tnh2, .4;ca(r$\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slik3ohn- ( ekk7ieox3id2t ;jl2des across the floor. How far will it go, given that the coefficient oftx(i3ned o 2k;ejk-32l io 7kh kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at re-b ;6buw0x;byu x8:l* yeuwlpst on a horizontal surface (Fig. -* e;byl wyu;8l: u6xwb ub0xp4-54). 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 coefficien:r8 o ,yze e*o4upt asro85c-wt of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can dtw8 oc,4pso8:azee 5uo-*r yr ecelerate 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, whichfi7/xb:xya;4 s9txg.d hzz(g has an incline of 12xdg z (ygbi7hx4s/fa.xz :9t ;$^{\circ}$ . 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 wih7qqt, +3lb:jv y 1p:vjo qq-nth 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 tilbjklf v/nc :g v.jy1a0o1k m4.ted 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 sio +i7t 1up2 ip u)-56gvnwgjfpeed 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 166; i7bsrv3xgr2tibc3gv tp 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 t hbp 7;mjzf0+ 99tigwa rough wall by someone pushing on it with a force diriz9w pg0m; 9f+h ttbj7ected 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 ca7 pekv9oo2n .ah7pv3un become dangerous projectiles as they melt. Consider a chunk of snow at 9nao vh.7 o kp3pue27vthe 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 autom:f8s irn *ks)vobile traveling at speed rn ):8if*kvs sv 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 on the 5yt 8sl1 on7kve9;f ow4juewilr h:48dash when the driver decelerateswo7f84o4vye:k1 l8 9 n;tr5iwlehusj 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 an initial sp:vlgpkr .-ar1g - r)qoeed $ 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 whesp eozlaynk09ea (g -u0zn4.-re they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half tagonl zee40u (0a.n p-y s9zk-he 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 k64xsug -) el8fz1.4fivws l(y t fi5ihinetic 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 bicyclu )+twk: iyb9ss-.z0h2oq rrt e) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pupb(5xhnu 1ipn9vz 9 h0(fo;u llse approximately 20 g of blood is acceleratev (ubno f0hu9ph(pxl 9in1z;5d from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crasjn 3 mx8j7g mm3oq7oy7h if the deceleration is no more than 30 " g 's." Calculate the force on a 7j nm37o8 j mqmgo7yx3 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 acceletl2 s*11kl+4 jvqcj94wbsby0nty, r xration produced by an earthquake is a , and if an object is going to "hold its place" on the gro,sky tl+xs1r b2c l4 ny *v9qjt1jb40wund, 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 carj7 qrm6)im f uh/;ut2ys, 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 pavehtu m)u/26 ri;mf7qyjment 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 each 4 m tr bq ne4 6gigjgh;7(dc(aveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55jgg q( ;gnhbd46ci7 (e 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 ocs 3j4(u-cjwwu*s+a i p4bop0 f the Leaning Tower of Pisa and falls 55 m befos so 4uwucpi0a4(-+j*wpcb3 jre reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s0 +2xk wwc ebzb;1 yv:/y 37xn-wnlfob but enters a muddy stretch where the effective coefficient of friction cx3nwz0 n +: w xk2eo1;wv7-bfbl/yybis 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 worka:/ihor y0*qli bj)9wing on the redesign of a hilly portion of a city. An importa9bjqyw*a io 0/)r:l hint 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 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 w fo8uwn91lr,thin piece of string while the jetliner she iw 8, w1rlu9nofs 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 super hzx-5ma60u qzvj4 )lvmarket, there are to be several ramps connecting different parts of th 5zvmuvl) xq06zh4-j ae 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 for:gv x tmriyv4k;b;k07i z ev09ce F is needed to lift the piano (mass M ) using the pulley apparatusx;v kb :z47ygr9v v t00iiek;m 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 atzivr3dibev y h.wf b6.ou+/ta:qhm;0-tm9f 6 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restr,fdzkde2+lg1 k- arr4jf by4r9 0cfj8aint chair, an engineer considers the following sfdeg98r k j+b2r4krz , jlf01ya4cfd -et of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,0cf6+t mrdm 24evc;q.ip1gzg ( 00 $\mathrm{~kg}$) . 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 z 2,.xinlxae* 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) Est, inx2a* lx.zeimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1 ez;ws,nna7y og*(lchtc-0b 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maxrivk6e z8+rt08p kvz4peyt9,imum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field incu5fkl d;ojydl /f*q(5 e- ah2clined at 21.0;2u q/5*d(c5lfk- lae jhyo fd$^{\circ}$ 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.