Why does a child in a wagon seem to fall backwarhvrng7 (5p 4ptb)6j(7n1ohy uvf- ctgd when you give the wagon a sharp pull45p obt 7pv(jhg)gtvrc (nfu7-h1 6yn forward?

A box rests on the (frictionless) bed of a truck. The tr 5;gsijjjt6w04c-7ig3 jbdh t uck 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, s4jh3it6t5 wjcd;0j gjb gi7-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.(gvlkh 1tn0 0 v1qiev no forces acting on it? Explain.

Only one force acts on an object. Can the object hav w- 7lxivuc1d +st-7hp,(( e k.w(wtwq 0tmqxde zero acceleration? Can it have zero velt+(kxp- vx 0 7 ,c(qw wwdlud-he(t.1iwsmt7qocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force sufi+wz yc 5h5z7en3isdt 0, ,needed to make it bounce back up? (b) If so, what exerts the foyc50zt i,wne 3+h z,isuf7sd5rce?

If you walk along a log floating on a lake, why doesuk k9e u.s0wm6 the log move in the opposite direction?emksuk 6u 90w.

Why might your foot hurt if you kick a heav99kj8. f.q6otkg0v -pj kthdfy desk or a wall?

  When you are running and want 2r3;tptu td*rp 5i1klto stop quickly, you must decelerate quickly. (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 d trrtpp 2tkl*i1;u53 a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread u0gatrd 5-/nz from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fi5nt dg-0ruaz /g. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-k +isca)bb5 fk l5rua;3g rock. Why then doesn’t the heavier rock fall faster?3b 5il bu+a)5ksc a;fr

Would a spring scale carried to the Moon give why*6x3r qa+8as j8x waccurate results if the scale had bewj6 *8 xy+q3waras hx8en calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an at 3e nk:hdgzmp)6sa / is;plw(bb2ns10tached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remain3ld1p sb/z ) enpnabswh0i( 62s;:mgking flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influb*jikx 8ky x,o:rrvv)7not-r) z2:s gence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on txjgr s,n7t x kz) -k:ov: ior*8)byr2vhe Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are m.n jln0wg3q/j62 v vdon the Moon with the force needjqj 6vgmwdnlv23.0 /ned 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 Earth.

According to Newton’s thirb+ li m/e0g1ktd law, each team in a tug of war (Fig. 4–37) pulls with equal force o1mk/bt g il+0en the other team. What, then, determines which team will win?

A person exerts an upwad6e b67ua07nvvej2u xrd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by vua 7vx 627dne6eb0justating (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 the ground exert oti 1 -nv-)rxtk-a8fb tn you? Why doesn’t this force make you risea8)t--f t rkbn -xvi1t up into the air?

Whiplash sometimes results from an automobile a tf/*4jot wy ru8bveh;im )1i0ccident 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 situationtv)4ei; w tf*o/1 hu0yjr8bmi. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the tra axb ;1zuf1/buck accelerates, the crate remains where it is on the /b;a ba1zuxf1truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push s:day l 0 bgnr 0 cs/et,fo5ym5c)-n8fpo that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of ita onrey nb8)cs-ypm0 t/ 5clfgdf,5 :0s acceleration is less on the descent than on the ascent. Why?

What would your bathroom sybz+zls7p hu-. wj jb2g r:.8vcale read if you weighed yourself on an inclined plane? Assume the mechanissz +g.lh:-jybzbv 28pu .7wjrm functions properly, even at an angle.

  What force is needed to accel0 :bbcxkk8ofx: a +s4ferate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik h5t(kz 9cv)uhe and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used tou dh,ij)/)bms)svuf 5 accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a *;-vqk-fh pky$76-\mathrm{kg}$ 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 +p.htyo:zy0ejsqvl 4* m0c ;wcar in 8.0 s if the car is travel phv:o0cq ;ly4z *.mt+j0yws eing at 95km/h? -  

  What average force is nee7l 6xui1czxz 2ded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.8ixxzc2l6 u7z 100 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of thev.wobo9:*tzk).yc j b water with an acceleration of 2.5 otj) ozb ybc:..*9kwv$\mathrm{~m} / \mathrm{s}^{2}$ 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 carz +uf 1r(rh *ubuwc+p( can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to byaa3/yq y1l nc g6v68oe designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppayy8oancylqg36 v 6 1/orting 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 scaay)ulaowuaj1dl+ gav. eqi,c: 9+n 23le in 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 thel2v)g i1+:3 la.eauu9,aj wody nqa+c elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum streng:mlga (pflel;0.bx t,th of 21,750 N. What maximum upward acceleration can it give thebtl(lapxl:g; 0,m e.f elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diver,tk9ci4iad ,ec1 rjqo ;ryqm)j9 f;5ls (mass 132 kg including parachute) when the upward force of air resistany ;tl;rea5ck4cofq i99q, 1,rjim)jdce is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9c7 z/ hjf0ly fkyl+u **gf+zvqs;mk8 h5hf04n-m high. When he strikes the ground below, hen0qf y fk +;svcf4yh+k8zu jhlg5f7* 0lm*z /h bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs4b yvh)4a -hnq vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the bvy 4hq- ha4)npulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pjui lybpc59 2yp gv;nh(hk9)*layer
(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) atvp3a/ hk7uzf n;z:4yg the moment it is hit by the bat, and agaa3uzn:/phkzyg;v7 4 fin (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force jrk7i0flul+. must be exerted in what direjkll rf7+u 0i.ction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high +2 2 n 4r*jqq;u-rwawvdaipr6wire" strung horizontally between two buildings 10.0 m aparuav 42djwr-2 q rwqni*p+ a6r;t. 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 cof ;o pupdv:k;hf-39lprd 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 1rq dr(9rw3y uf/9s (ka4.0$-\mathrm{kg}$ 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 McMuwom; )xdvp 0v)jgv)674 fsxnmrdo Base, Antarctica, as shown in Fig. 4-46. The sum of mdnops)v)w0;v g7)fv6x xmj4the 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 oct c9uqion eo0q4+2q;w bqe65f the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive a4biq9ute;2c0qq 5oqc +we6o n nd 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 upwarihznkn8 0q)8n-2kvs a d using the bucket-pulley apparatus shown in a)nvsqz0h i8knn2k -8Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race1ca+rhc:vct4 , xwd8u 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 bloxwsn , w-e0ynz*zb z .600jqggck (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 friction o+/)abnv y+qij q2*6,hp xtxmless horizontal surface are in contact with each other, as shown in Fig. 4-51. Ay+xxo q+j av2hq)tin ,mb6/p* 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. 4udz;+dqu af2f ;2 (kss-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one h s d+uz2f; qa;dkfs2u(its the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a ;** vvenmvxm :p 9;2zkd 4limhfrictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration ofp4vm kn:dvhzi2le m * ;*m9;xv 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 kinetic friction between a 3:ojvproz snkfhm, c (7- s*5hxble ;775$-\mathrm{kg}$ 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 sqh87v27c50bfhw(mk5n x v wqitart 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 accelerating a;c nc+ r56alhldbn5h7t 0.20g. What minimum coefficient of static f56n+ d7h cl5la cbrnh;riction must exist between your feet and the floor if you are not to slide?   

  What is the maximum ao+ js+p m0-mxrcceleration a car can undergo if the coefficient of static friction between the tires and the grpm+x ojsm +-0round is 0.80?   

  The coefficient of static friction between hard rubber and normab,6i2sy*pswa5 9oh7yeu ptwc;,a3 lll street pavement is aby 9si;7 lba3ot2pew, hy*c wsua,6l 5pout 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 nza6,, , xopkovsmx(jp7d.+, vx-reh 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 re1klo-fvo o w2* ndj rk*h567hkst on a 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 ha)w 2,o4govt knve a very high coefficient of stwvokn2o, 4g) tatic 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 kiner+ a457jupgmx q7cw1 sy2:fg ktic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4;re vy oqugmg;*3+mejp(av33-20) how large a mass would box A have to have to prevent any moti y (*u+e3mgpjqa m3o ;v3ev;gron from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wilbsr/*yj 9;4/u p bqigll it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.*/b p9b ujsqiy4/grl;0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at r rm4o 2che+p(cest on a horizontal surface (Fig. 4-54).( oce2pm+c4 hr 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 q)nze4/ 6hyjhyterkf5 /a6 bn. cf6b.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 )q n.etrb c65/h6y 6hfb.nz/yj4a kfeand still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parkinggs(g*j/vx ipa+sh//g5pu t *d your car in your driveway, which has an incline /gs p/+h*vas(g*ugi5tx /pd jof 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 28if 9y2i(g h75-8squr qez2 voy$^{\circ}$ 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 tilted at4s e: p1 yl0ygqcp94gh 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 o+j;o u ujlt7n wg, c*e7pu4kq/f 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed mgc3ko;ii (qn ;)z-jlof 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 pushin 0d6j nz3:hzr*g l,dzeg on it with a force directed upd lzn:dhz6r3,*z0g jeward 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 csq4 7stff94h.x) 0i. seifn s n+lis1ran become dangerous projectiles as they melt. Consider a chunk of i. 1sr9 x4tlfn.)qii7h+fn 0ssessf 4snow 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 stoppin bisjb/ .r n:6hk3x 30tiboyt;+uu7veg distance for an automobile traveling at speed v isovi tx brkny0uj7;6b+es /i:u h3tb.3 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 dash when3ii t:ysq4jl)c s(y(hmat3b* the driver ms3qt:(c 4tijli yh) b*(as3 ydecelerates 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 mass0f bl3h dru(4le va1s aj8d2g1 m is 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 from where they are fille +ufj+i 8/yoccz9jk58spe r1gd to the packing station 11.0 m away. The belt is initially stationary angkefiu8cocy5 + zrjjps /9+ 18d must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the 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 frict6wq* c,aq u4lzn8e+ jdion 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 bicyclxl2a98b.y9ywc 0 tvr.) ku6gffmvgvj 7 l2v3ye) 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 -ki* )qtfqof o 5oq.xg-- 0qtepulse approximately 20 g of blood is accelio )qk5ofq 0-.* tqx-o eg-fqterated 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 automobileow-e. rsfa4h ,9gbjl6 crash if the deceleration is no more than 30 " g 's." Calculate thr6j,blha 9ef4-g os w.e 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 by3 l0u *vbp:rc3opb)w v an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with crv* o3:30vu wbpb )plthe 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-h ) biwhbi+h e+:em2a involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficienh+2w-ae+)imibheh b:t 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 t qpt;i5g.l4.nzl2-pfw/anv ym 7 jtv( d8ff;khat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottf;f;( l a yjnv-tnv.lp wg8qm z/d4 t7.i2fk5pom 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 top2u, iu* dpt(3v dksl4gduzb 7; of the Leaning Tower of Pisa and falls 55 m bvd,lg7*;idk pzuu ud4 2s3b(tefore 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/s but enters a muddy stretch wher(eik);2p+ uehcz5 ymy e 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? Iky2()h5+pycezm i; e uf so, what will be the speed upon emerging?   

  A city planner is working on the redesign )+d 61 t 4 lw9gade+l lr1ge+c:jcsgdfof 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 down. A particular small car, with a mass of 1100 kg , can accelerate on a level roadc g:gj w d1 las4cddl+frg+t1e+6l9e) 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 her0r8 )nwark. 8xce.x dl8s*a xs 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 string makes an axkwcxxn a)8la*rr d80s.s8. engle 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 supxy-f 6vz*56gb jr w.zaermarket, there are to be several ramps connecting different x-*6z ary.z56 gw bvfjparts 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 i;xkr4 a++ sa p/aulsr7s needed to lift the piano (mass M ) using the pulley appa7x;p+4k+srrs a/ul aaratus shown in

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

  A jet aircraft is accelerating at 3z b1xbo)0kjan+*wk4do4y d+c.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 f*n 7 h09tm(r2qutkpqbor a child-restraint chair, an engineer considers the following set of conditiom 9u7b nq2t*q(pkh 0rtns:
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 train5(q-s h82vh use9.8vw35y ww hhntvhe 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, kev5 m (c4p)iguse 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 stopp vgk)e4 mci(5s 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 boaey) pffrn/x1r.z d9*-r r dd,ht is using 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 buildingb o :/m:hd8vozjcmps1 b64(od 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 rw4xyk,1da rb1z/7 updo3og: goped together are ascending an ice field inclined at 1zr:7 xgu4kgd a,y1d/ 3oowb p 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.