Why does a child in a wagon seem to fal)o(2mzg(a7 ufy vw t;ym8g5gtl backward when you give the wagon a sharp pull;u57mz 2ggao)8ygfw(vyt m(t forward?

A box rests on the (frictionless) bed of a truck. The truck drv aw 6(t;gqlyzr00 ko3iver 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) blr(0 qz;60vyk3 woagt y Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration 9f*x .a/mjpw / v4he;3xdk( rjf9srivof an object is zero, are no forces acting on it? Explain.

Only one force acts ece axe0+h/z. on an object. Can the object have zero acceleration? Can it have zero velocity? Exp zch+0xee/.ae lain.

When a golf ball is dropped to the pavemensrqrb 1v2jun 3pp9:qe1 k1 :pnt, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what e 2 vukpnpq9rs:p:erj1 31n1bqxerts the force?

If you walk along a log floating on cdkih3 3uhq2- a lake, why does the log move in the opposite3- 2hckuhi3q d direction?

Why might your foot hugo ,tbns ya.1few34k5w/2oh lrt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceleraj nkg5e3bepo lpbk8-mds.*houjo+ 47z(: zg.te quickly. (a) What is the origin of the fogelobksgjj.n .o 7: m( zp ek5o*uh+z4-p8d3brce that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of j1 cpblz8m u03the same thread dangles from the bottom of th830m1cubljz p e stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twicmk *o g*d/ /km*cg;srbe as great as that on a 1-kg rock. Why then doesn’t the heavm;brg*s mk */*gckod/ier rock fall faster?

Would a spring scale carried to the Moon give accuraoph. b g8f)-w e ycsro8p0+m*ite results if the scale had been calibrated (a) in pounds, m*8 sr8ho)o 0cigeyf p+p b.w-or (b) in kilograms?

You pull a box with a constant force acrjuhv6) i: u.itoss 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 i) thu.:vu 6ijbox (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of9ku (3y wos+c t7wy2iv 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 forcek+2ctwu73v9w syyo (i on the Earth. Why doesn’t the Earth move?

Compare the effort (or fovd:pz*gj 51uj)l:yq zrce) needed to lift a 10-kg object when you are on the Moon with the force needed toj q)zljv5dy p:g z1*u: 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 third law9*qv0l(s5a e tkq.xuz, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whichlqztaq0kvs*e 5(u x.9 team will win?

A person exerts an upward force of 40 N to hold a bag of grocer1ivwlpd i- ;.rptx -)pies. Describe the “reaction” force (Newton’vx-pir ;itl .p1d-) pws third law) by stating (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 vgyihe ,*a0tx1 7na;z large a force does the ground exert on yg7zea ,v; ayh1i0n*xtou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an tmd5e(*f(fpg,*/+d jpd5df4 h oxxxcautomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it reallj d5pfc*,m5*xd g(fhx ( xdfope+/dt 4y?

A heavy crate rests on the bed of a flatbed truck. Wh+ a o: h+1nemw0pvod3uen the truck accelerates, the crate remains where it is on t dpwva oh1:+meo 0n+u3he 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 c62;vbmd*ac f. After the block reaches its*mcb 26 cvdaf; highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined p n1k1b3;fmw 8nrb . w+,vacaq,6rl kfg8fibz:lane? Assume the mechanism functions 8,8bfalf rq cvza11kn: b,i w ;g3b wrfn6mk.+properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25mn9 y +d9 mwxfis/s.wl3/s$^2$?   

  A net force of 265 N acczqenbgnw n *yqd e50686/y5la elerates 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 withstand if it is used to accelerasp j 2,3hb*:fv*xxukqte a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of+hm lf tjbx1cdgt ykpw95n+;/ g+8 g:llkm4p7 a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg cjs51qkm g)*d k6ix*haar in 8.0 s if the car is traveling at 95km/h* )j s5k adk1i*h6gxqm? -  

  What average force is needed to azgja.;gy b)zv(5)hbh- ku o5 wccelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 h ;jzh)auok)wg5vbzb5g- .y( m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water w/gjj8y*o8 *z e5 hg b gssr:oz65,rvraith an acceleration of 2.5 g8sr,zjs:*ya*r rbgo556o/hvz j8g e$\mathrm{~m} / \mathrm{s}^{2}$ 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 sgnxdr(gi m3p)4;z g8 (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 ) t/1 bt.s3 typyis to be designed so that the maximum acceleration is ys/ py.t3ttb1 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevf ,7sgtqjc;2 6:z7 kkhtv8pppator. 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 acceleratiov,:p pzkpcgq6s2t 78kj7;fthn.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a h gcxz4b) 9+wemaximum strength of 21,750 N. What maximum upward acceleration can it giv 4c9zhge)wx+be the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (j0+ i11j mslqld,enc45ay p k +/bdma*mass 132 kg including parachute) when the upward force of al 1e,q 0smadb5n+* +iy1 a/jjkdclmp4ir 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 a house 3.9-mw7bt+c gb69phip,v) f 5 vm9mm high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (exclu mhbmg7+vmf9p ci6wp)t b59v, ding 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. vq569b3 r w k8zjl8,t eovaus0A rope tied to the box runs vertically upward over a pulley and a weight i8wzk ,j u9ltvrbsa38oq6v50es hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball play e-ltw:nwj+9kgh )mq e;w 5vg(n:cl(e er
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram ofd*jdv1ki: esis3 +7r b a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the ouke* 1:jsb+si73 d vridtfield.

A 650-N force acts in a northwesterly direction. A seru:agt1h+ yny.f/ moo0,cj7/ u 2lzxacond 650-N force must be exerted in what direction so tha c+u/ m/z71 l2gftyyoh rnujaxa.,o: 0t the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high k;ot+ k(,n tddwire" strung horizontally between two buildings 10.0 m apart. Tottn(d+ ;,kd khe 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 hang92zqe 7 *3hg y;btaraping 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 14.7u.;ojgsyi+y3kve mo 7u l*a1.7fm ye0$-\mathrm{kg}$ 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 McMurdo Base, Antarctifj+zu0 mxdurle*y8 ), ca, as shown in Fig. 4-46. The sum of the forces rulxjd0zeu,8f+)* ym $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 c, 3f0vcy 6tgyyh y:ec;ars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first cyftcye3 c gy:y6;,vh 0ar $\left(F_{\mathrm{T} 1}\right)$ , 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-pv tuio7v3s1cp)h by6* ulley apparatus shown in Fig. 4-48. (a) How hard must she pull phbs)u 1it6vo 7 3*yvcdownward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began,wruq4hvjmmb0h2 3z:j( , 5mfy 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 blsz2 f;mgn dy5x. ,zh0oock (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 contac(agc8m,f hkskn/g,ja2p 62wzt with each other, as shown in Fimks( 2hgp6wfz ac,g/j kn2a8 ,g. 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 Foialza/ r4s, tfb5e x h/ib11*ig. 4-52 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 hits the ground. This is its "launch"as,e4rlbiot1 /15iab*hf x/ z speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connec5 cuklc5 9su,bted by a heavy cord of mass 1.0 kg . Calculate the accele9lu5 , ukc5cbsration 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 kinetic friction between asdftdh2r90 *. gfre9;3gjf *i km hvjl3tqz0 8 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 ro0 2,c3ob aj tb2jp )m.b;hoinr(l.0rc jx j7yequired 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 accelerating at k)+jc bi-. nvqx* kk;t zk8*as0.20g. What minimum coefficient of static z*v *8 jcskkkq )-kiat.x;bn+friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleratila lb s axvfp7 x.76q1l07v5tfon a car can undergo if the coefficient of static friction between the tires and thevf6.lt7a0x f1ls xv7pa l5q7b ground is 0.80?   

  The coefficient of static friq:jgzh5c8yu lrpdqk.; 4o8 ,nction between hard rubber and normal street pavement is about 0.8. On how steep .r5p l,:;zo 48qyn k jcguqd8ha 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 atnkoh/kb(*u v( -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 lq/fjsz8g:o 99uw-r - c gij:ia 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 anfi3e0*0pqsn.n n 0k s very high coefficient of static ff sni n0*00nnsk 3q.epriction.

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 fricti-qmui rxos6-mpj (. 8q 1bqo-zon 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 would box A h,v b6 --sfyh ;rmpzs-d1y3piuave to have to prevent any motion from occurring? Assumei-dvs-mfys1upbz ,6rhy-p; 3 $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrosget /p24jwdn*)wbvh5 s the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initewg4*jt 25phvb/d) n wial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest oio mq3mg8yqh5 ,2zpp ,t0;cmcn a horizontal surface (Fig. 4i5 hcyq 3gm8pom2tp,0z ,mq;c -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 he.p5uodoq zm+- avy crate. The coefficient 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 againu5mqo.p zo-d+st the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has areb zojfa+ 4:ep70 yr7n incl0rfob+74ze aejy:7pr ine of 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 28 0z+.8z t6aqds xu:2p l5rqzyt$^{\circ}$ 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 at an angle l 61jb0cdi, m*s(yeh z $\theta=22.0^{\circ}$ 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 in lnn7x5 qvnu(26z q;zugtw8 3w5pk f-kitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of :jz louxfz92+the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rh va:b)xo u80a5 t1aom8cit9qough wall by someone pushing on it with a force directed uptmvu 1 axoqab8a:)ci 95 t08howard at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dange3u6fj- wufr :qrous projectiles as they melt. Consider a chunk of snow at the ridq uj-3:6wfruf ge 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 anal19qdmqr7 5k1 ;cg4lcdxi w7 automobile traveling at speed vl dw gk741d9iq c5xl7 cqm;r1a 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 dash wh 22u3+yv b v-q witaoe2m)bo:hen the driver d)vqom b:wih2 2u-3+ 2vyeaob tecelerates 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 t78g.izrb 0+ k0-xu(ud rpbycxo 8 p/rspeed $ 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 frr,brmp.yr . zr )9zbbvsh;s )+9pi7o illed to the packing station 11.0 m away. The belt is initially+zhbz)yvbi .p rs r .,p99rs o7;rmbr) 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 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 friction betwee0d1 x9b)v-wy) oiapgtn $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast 4 j7anb di5py;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 mammcvyd8v ye (y,0alian heart, at each pulse approximately 20 g of blood is accelerated from ve,v0(d8y cy y0.25 $\mathrm{~m} / \mathrm{s}$ 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 suqcu.;-hhm0 idhspi8 *rviving an automobile crash if the deceleration is no more thsu;h qp80 .*h-cimid han 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 etb t ntttf5wl+*.l1i)arthquake is a , and if an object is going to "hold its place" on the ground, show tha 5b)lt tt*.fwtlit 1+nt 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;(74jx uzitza /f-eos cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop befxfot 4szj-aez(i7;u/ ore colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for ekv9, onfqkd p)wc ) wt7c:/(fjach 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore 7nd,ocf9 wtjkw:/)cf vpk() qfriction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and fo0kt 8gqup-:lalls 55 m before reaching the ground with a speed of What was the average force of air resista u-p: 0qkotg8lnce?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchhct12bv y (/qytj /nd6 where the effective coeff( 6 bhtt qcdv/2y1yn/jicient 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 upon emerging?   

  A city planner is workizz s*yxl -k9z1ng on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that eve sl9z*ykx -z1zn 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 thin piece 34w 9kysb9;hglz: q o6) imtoqof string while the jetliner she iwt3);z lgs 4omi9k bhqq9y:o 6s 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 supepqu+e+),:s)th gqsl 9(tjz gjrmarket, there are to be several ramps connecting different parts of the store.sgqt)s:)lp,++g (eq jhzut j9
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 (m8y kqh3ebrb5:ass M ) using the pulle rk8: 3bqhb5eyy 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 accelerating at df 2t4z:,ibmf3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 enp /mr *c;mt.ajgineer considers the followina j;mrm.*pt/ cg set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian tsn. 9:m fjbxfs)x;lnfs+3) /mosy *fyrain 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 ro4e p8bu j zj0xx7 lrf44oggsx5, jc,r:pes 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. Kjgp:xl0b, g4ujo5r7jfcsz4,8 ex 4xraren falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat 0xgl) 9n.se9x 6tkkbr 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 building is allowed to reach a maximum speed of 3.5e91g yz6h j;b pz-xqu4c jcq65 $\mathrm{~m} / \mathrm{s}$ 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 as,. frii yxat gt6 ;84pne)y+dn ice field inclin ) yt8 agxp,fei.stirnd6 y;+4ed at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.