Why does a child in a wagon seem to fall backward3n pf5x87turyjl/e thz6 1hua o* .-kp when you give the wagon a sharp pull foz7t- nx3kjt6*of y 5huep8pl/ruha . 1rward?

A box rests on the (frictionless) bed of a truck. The truck driver sii06j p;/xnk)+ (sdywjv6rj ltarts 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 o r0jjiyl( s )6/x i6d;jwnpv+kf 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 zerogndew km6pd1ezg8l; 2 an9*n 8, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zef8nv sh,m9oz l a0r1/vro acceleration? Can it have z z flm vh19n/v8so,ar0ero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back ue:/hk x.esw85d4 k zjup. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fohs j. x5e:dkz8euk w/4rce?

If you walk along a log floati oklvyz6/yprh-it4k //p: s p9:vmf v-ng on a lake, why does the log move in the opposite directils6kor p pv vy:/-i9k:f/vpy zmh4/t-on?

Why might your foot hurt if you kick a heavy desk or a wa.. qwc ltwoy;ta7x,g8 ll?

  When you are running and want to stop quickly, you must decelerate quickly. m42(j v2:p iei7w4 lbr ekkkl:(a) What 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 (e 7kwv4ii2 prk lbm42klje ::speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a iux5-,pi puup-td 5 z2section of the same thread dangles from the bottom of the stone (Fig. 4–36)u-it5,d- i pp52zupu x. 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 that3b-5 oo n)uyut on a 1-kg rock. Why then doesn’t the heavier rocyu )3-u5 ootbnk fall faster?

Would a spring scale carried to the Moon give accuu. vb: 7c k7etw27lhbbrate results if the scale had been calibrateb: u wet.lh vkb72bc77d (a) in pounds, or (b) in kilograms?

You pull a box with a constant force w:aeu( n o:x (9mwj,95eudlk sacross 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 xnjee:l(sw9w9:5 u(u ak,d mothe box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net forcm, u6 )1u- omqrrpagcna9-*hme mg exerted on it by the Earth. Yet by Newtoum urn m9a-aqhpc r*m,)16-ogn’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force)0 wqpmz8 .wug ( w+xl;tp9cz6t 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 Moon and on Earqz wul m0 p98gw.t+;6wp tzxc(th.

According to Newton’ t jhibh2v(7+62lbrfh s third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the o2jrlh2tvh +7(ih b6fbther team. What, then, determines which team will win?

A person exerts an upward force9;y:l.hle gtwv)y+h0z2xhps nx97d+a *k e lz of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by wha720 yw9el kvgax+9e:z .)hz;+ hx*l hntspdylt object it is exerted.

When you stand still on the ground, how large a force doejs zck g6s1,z;s the ground exert on you? Why doesn’t this force make you rise up into th;,jc1gs zskz 6e air?

Whiplash sometimes results from an automobile accidenk (o5-z *x5q /oqy:t*parzcaimt- x.bt when the victim’s car is struck violently from the rat * -.abxx :oqz i*t/5o5m(yzkqcp-rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on t* jg) -ntyje9phe bed of a flatbed truck. When the truck accelerates, the crate remajyg *)9-ptnjeins where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesigq8 -xp0-ems ,+ich s its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the asse8hq0c+ igxp- si,m- cent. Why?

What would your bathroom scale read if you weighed yourself on an. f s(zk s08h 4 3pqzgdljy6zt-t)2 14hjinoki inclined plane? Assume the mechanism functions properly, even at an angle. k -4f6z djpi. 2zltg jos(4yis8z hh1k03n)tq

  What force is needed to acceli. w5smz tmt60:u,hkgerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceler 6j;/xwy2fs/x-qcgrbg3 n8rfates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wt p k 24/vu7byo5,fnbwithstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of aoo io0 slrur l/b0u/mk,/m5hd 7a2,an $76-\mathrm{kg}$ 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 sc yuno-5m(p.;v(xh frequired to stop an 1100-kg car in 8.0 s if the car is travelingcu n mvxy-s.o;(h(5fp at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellemxjso8/tro dq vu *;+:t from rest to 125m/s over a distance of 0.800 m along the barrel of a riflq8xsm j* vr;/du oot+:e?   

A fisherman yanks a fish vertically out of the water with an acceleration-lcw+ rlf2)oj;a1g qu of 2.cfl1+a;w o2jg) qru l-5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (402 q75;x3l4n nu5fw dyae$\mathrm{~m}$) 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 ,yroj w6z 6fa2be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should aor6y f, zw62jexert 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 elevator. When the elnyy vy 2 ht*/,o7udz.levator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the el,tuyn.y dlho7vz2 /*y evator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 2np9pfvd-9 dk9l q) awd):( zlh1,750 N. What maximum upward acceleration can it give anh)( :lldw99-9pq)ddfp zkv the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of te6x+zs-7* ht s9 zocdswo falling sky divers (mass 132 kg including parachute) when the upward forcese7z *o+ c69ssxd- hzt of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of 3:9 zx)iv.wbgbcqdm 0 a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. 0:93xwdgmb) zcvq b i.If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically d r36qx jn*b2lom58ofupward over a pulley and a weight is hung from the other3 d8o nl obq65f2x*mjr end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskekcke cxx1o (f,)k:)yktball 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 momeni e6a5lrz5( flt it is hit by the bat, and again (b) after it has left the batlifre l5z5 a(6 and is flying toward the outfield.

A 650-N force acts in a northwesterly dws c2;uemnsb7g75)qknap+ r3irection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate5w3 ke ps ar7nm+7b qu;)ngs2c your answer with a vector diagram.

  Arlene is to walk across a "h,c zgxhgnv2dirb5( 15igh wire" strung horizontally between two buildings 10.0 m apart. The sagn(c2v5rghxz 1 g bid,5 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 hangiez kp8*jbp a 6no.a(6hng by a massless 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 14.0jt wp pjwz eai,,3:*vh/8 df-+riv ou9s r*rv1$-\mathrm{kg}$ 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 McMurdokgu ,1gk82ine+ z6xv c)pf:lt Base, Antarctica, as shown in Fig. k,i6l pg2fxn t 1c)kvz+eu8 g: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 pulling two cars of the same t0av gc nh.x8hp zq(g5m;1y5nes8+yrmass behind it, Fig. 4-47 . Determine thhyy5egvqmn;8r (h s+5 za pc.1xng0t8e ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparat+ craa( gj39vzus shown in Fig. 4-48. (a) How hard must she pullga r 3a9+cjv(z downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race begmnw zd fa;k;6emgnf12(9awx lm xb/k3 o1pr94an, 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 blocmn.jju25 y r+0(euu bdk (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 coz -9,mtdtrk bnl8 +4dtntact with each other, as shown in Fig z dbk-nm48r+,tldt9 t. 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. 4-52 arebq u.vn-.ekw ei9lf -0 each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reacwvlqf0 ien ..--bku9e h 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 b+hek u8p j*36j6 nuqxfy a heavy cord of mass 1.0 kg .8 e h+6j3xpnj6f*quk u Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of k+g;;gk vylx78 dfwb8uinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a bhf; wlhv:;4j 5 9ddh:ievx m 0q0zs.j 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 accelereffcf1lh) tn s62wh 87ating at 0.20g. What minimum coefficient of static friction must exist between your f68 2lchtwhne f 71s)ffeet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta jfdier,qt10 ,lo59gftic friction bd ogjt51,0f9i ,lfreqetween the tires and the ground is 0.80?   

  The coefficient of static frictiaer / d uldd.fsc.xcpak l,e:l5o5)7.on between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a care75xlc)ockdfs.dd / ar:pl 5,l. e.au 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 decelerate6;n1rf: /i/yfyhr vx w at -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 roug 1f bya aipq0mo4,;fuvp3u) (ph 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 ac1h nieg-+l8zs*jh /eoq njvh6ms g7a +r)80x very high coefficient of sj qs 6+mhjhgr 0xa+1)-soe78nh*vlg/8cn i zetatic 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 kinetic fieg7 bj uyy5j;/zlbb+:p3b32x*sub v riction 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 wg,v7h lozo7e (og5kv4ould box A have to have to prevent any ,4v7 v keg(57ogohz lomotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will 9 c*- utptsr ;wuoej9d4bydpq3x* 8) uit go, given that tu9y-;rp u j3qudd* *9sp8wxto4tb e)c he coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg hrsh 0d* alc2+, are in contact and at rest on a horizontal sr*hc0 dh2asl+urface (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 c/du 0kwdxx,i+ 9ugtp0s9vev7 oefficient 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 decelerate and still avoid having the crate slide against k, 0/e+0 wvgsd9vdi9 xput7uxthe cab of the truck?   

On an icy day, you worry about parking your caru y540c7e v1rgwba1d0b h na;r in your driveway, which has an incline ofg0ahe 7 a5rbwbdy cn4ru1v01 ; 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 sldxl ;r; l; f1hv :uuk6m3cf,dhide 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. 4-5 -*to/p/ +4m4tu,uy 0pk-cxrsgrh qxt5 lies 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 initial speed 86wbv /bh4r p+nga+fd 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 cd8dyj *xvd39hill 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 pushingwz.x1x-yxix) 5: o hoa on it with a force directed u-xzx5 h1xo: xyo.a wi)pward 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 roofsxv-2*7d(gc y 7mox.aih epxy 2 can become dangerous projectiles as they melt. Consider ac-x.mga2y2xd *vop7iyhe 7x ( chunk of 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 stopping distance for an au(fdk4je igdkw///k: utomobile traveling at speed v iefkjk (dkgu di/ 4w://s 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 drb)tg.qe+)yawlt52jw t0qg6 ash when the driver decelerates from 45bwt .6grt)g2)q5qyat 0jlw +e $\mathrm{~km} / \mathrm{h}$ 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 c0v wxuy*4h2gjv.s-k given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt frs81t6 kv 1)brhdc4sc d2p9i wkom where 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 the distance, then decelerates for the final half of the trip. If thespc94cr6 81v2h1 diwdk)tb ks 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 friction be(obud19xef ,bg( kgj. mdn, m7tween $m_{1}$ 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 65po f ;:fcbmgl5q4rj(2 kg (including 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 mamma 2v de,abxgmjm5m /r6ow)(bu9**v nzhlian heart, at each pulse approximately 20 g of blood is accelerated fromn mgwx/m j(*vomb295uh*avr e d),bz 6 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 chanclf+kmsqxrc(1 b,5 o/n e of surviving an automobile crash if the deceleration i5 ob1 fnm,(s+qkx lc/rs no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an objecnrr37f 41ywgtbz6g2 7wsr e0ft is going to "hold its place" on the ground, show that the coefficient of static friction with t2b4gfs71 07t nwrzr6gr3efy whe 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 acc s,sc *wz w3b)3lmvx jf,s+,mvzyu;+bident involving two cars, 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 pau ylvmwjb+ ss,z,;bv),*3szfw m+3c xvement 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 trlp+t8vdm;4c m;jt8(lf9wg / yr.q y /v8iuqewaveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveltlm84 .ct vv/ly qwg;9j ;e/8piurfyq+(mwd 8ing 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 t7 gppoz dya8nk2*: n7pop of the Leaning Tower of Pisa and falls 55 m before reaching the groun7zkp:7 any*2d pn po8gd with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a sk88 er+a6o 2twp7ngj p2 cvn/bteady speed of 12m/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 lasts for 11 m? If so, what will be the speed upt2wc+ 8b7n oprjpa 6/8en 2gkvon emerging?   

  A city planner is working on the redesign of a hilly portion ofp;h 7om efmqbg.v9jnr6u-.imhoa49;1 fkc5 r 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 acceleratemghno bh6mai9o9.. vk ;p q5r;mucejf741rf - 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 experimeed f 39j0s(s**;mrufc0sjicdqjc ; *wnts, dangles her watch from a thin piece of string whi*qr(*d;;i j3usd j0fe c0cscwsfm9* j le 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, there are to w1 am h +mrc:oti3z::mfl 1ab:be several ramps connecting different part a3:tb1o:mr: mwih al1 +mfcz:s 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 z ,av8.l o0hno+nwt vdx6j 1+e(mass M ) using the pulle6+n0 jvdvna wzeo 8h1ltx.o +,y apparatus 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 accekbb9 kf7aw8 3f:t, kj9ukvcn1lerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer conai)mc mx52ak /siders the following set of conditia)2imac k5 m/xons:
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-cas t8ohi7 i*cgy,7y f0vr Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety r6u*9oglh +6 zn gi)lobopes 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 fr ougn l9 oz+bil)6hg6*om 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 azn y u)q+6rj*o;y5 bpjqeix6(cnv8p , " 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 b 2*3 xb/: ad)(jno4vibpddrgluilding 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 toe tbsd)tr200 coa-3 kigether are ascending an ice field inclined at 20tcdb ao-ki32s0) e rt1.0$^{\circ}$ 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.