Why does a child in a wagon seem to fall backward ;b i y 82oqto4zky(j/o9z9civwhen you give the wagon a sharp pull forwab( ok;oi4vy9 z9zjyt8c/2q iord?

A box rests on the (frm))f- lgx;z sr 4qw-oyictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear ofsf )-4ro ) ylx;qzm-gw the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no for/0-+cdmxqh m .zi en9vces acting on it? Explain.

Only one force acts on an object. Cbm o12mrq6ag7aq8w6ban the object have zero acceleration? Can it have zero am2bmw8q1 7 bo6 qg6arvelocity? Explain.

When a golf ball is dropped to the pavement, it bounces bactp/h tm771fe abv2pi 0k up. (a) Is a force needed to make it bounct 0btf1vpa7e2ih/m 7pe back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mo;pkvd)i i-9 hdve in the opposit)hki;vdd i-p9 e direction?

Why might your foot hurt if you kick a 8 3g0xtso eg98p) dzfq i1sh9zheavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicxh. bj8y,ci,a kly. (a) What is the origin of the force that causes yo8yb ,xijh. ac,u to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the i i30-:odm ow3ppjauh0rhr40 same thread dangles from the bottom of tiohur0i 3d p4r0 mjw :-a30ohphe stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock7 8nrlb:d(df z reth59. Why zt89r :ehnrl7dbf(5d then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if tfo 0mn.o qrf6uleej;7 xf6yqhu3wff6(0y :*g he scale had been cfguruy* oof:007m yfen f h6qq 6x ;j3(w.fl6ealibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frauq7wz 0d9 :+hxr 5nycu+ qzk8ictionless table using an attached rope held horizontally. If youyu9q+xc7q uhkwaz0 r8d: z+n5 now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of (p9gzw nyg. 2cgravity there is a net force mg exerted on it by the Earth. Yet by Newtonp2 . g(g9yzwcn’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) needed to lift wovx/q uql/* qqgo084a 10-kg object when you are on the Moon with t l8 4g*q//uvqw0qxqo ohe 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 Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pu4a6zhs(ir /ed lls with equal force on the other t(6/e 4arszhdi eam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describrvuvio6x:5e(t uk1uwc 3f*wg/h(fm: e the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its directio(t:xu mfv 5geru3o/6whu kf *1cwi(v:n, (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 -hrc gp/4h lj8does the ground exert on you? Why doesn’t this force8l/ h4crp-jg h make you rise up into the air?

Whiplash sometimes results from an automobile accidepqit mo+j/j;(tm+ ss4 nt when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward i+ (4si+tsj/qojmt pm;n this situation. Is it really?

A heavy crate rests on the bedhsm+7-k-9 )uojoep8 g )o oy/rkk3lgf of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes thooo3 )k mh8y k )7/gups+ge r-ofk-9jle crate to accelerate?

A block is given a push so that it slides 7ju* yvk(z m.l1i/tuzi0 usi- up a ramp. After the block reaches its highest point, it slides back dowi u.1slku-zv( zu/ 0im tyi*7jn but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom sc( 9k7yf cz 2-hd8 zxsy6to.drvale read if you weighed yourself on an inclined plane? Assume the mechanism functions v7zdsr-z 69c.xyd2oftk(h8 y properly, even at an angle.

  What force is needed to accelerate a c 8bb4-f-wruf c s*5 )6jliupjls+)ymrhild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerca7cju c3i55s. twua) ates 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 accelera93:*)yyaov :p vvos qtte a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of4ngw ly50q ldp5z:)s g a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8ogcn-bo1fr::g :as*c 8 gj.v - .qfrfz.0 s if the car is trav.gf8j:rsb :.rccf- fq: nz* ov1gaog- eling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fs89.o8g ij dzvq7xh 5c :es8ierom rest to 125m/s over a distance of 0.800 m along the barrel od8ij5.: iszc8ov h897gesxqef a rifle?   

A fisherman yanks a fish vertically out of the water wit9(o;ulmgvs */htv *zdh an acceleration of 2.g ztmdsvou9l*(*h ; v/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 colt*ml7w f;a fj:bh:;fver 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 be designed so that the maximum acceleration k ughs ,43h1eb*) co 7op/kebnis 0.0680 g . Whcu*hp7sk,k/ng o4h1o eb3e)bat 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 mot8jb,u.g )vprx ionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accelera8b.rvup) xg,jtion.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whabt0rhvj bxrsu -34c. 3tjrhu-c sb.3bt3vx4 0r maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accel7.w7viim5s x (xb by(beration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth ((wi7i7yb5 vbx .mxsbof 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 thhpzl+* * j9ufq;hgn /l3prxd(e roof of 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. If the masslf9 lg3r*zdxu /(*;+ pqnhphj 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 re f5aj/u ym- n790lq)4gaqwru vsts on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other si75awr qu4fjmyua-nl /) gv90qde of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram forvpd sp62yc;l ; a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the mome-u glm q-zvrxvdg4w2as0c ;- ,nt it is hit by the bat, and again (b) after it has left thlxdw -as4zq0r ugvv- 2c -,mg;e bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N for m:auw7i c61/:bkt5 )3;kv e vsxxgozygt;aj5ce must be exerted in what direction so that the resultant of the two forces points westward? Illu3 g 5 azckm :i/eko;5uxy)t7sa6txbvwg; j1:v strate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betyj9/n3rk omy f3hg) 8g c6hgs)ween two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is fy /r96jo3gh knhg3sc m)) g8y10.0$^{\circ}$ 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 hanezl o5s9,)fdlging 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 14.0 0cqj, u,6qufq$-\mathrm{kg}$ 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 McMus;p q2;hgwvkgd)9+ 6fm v3v mlrdo Base, Antarctica, as shown in Fig. 4-46. The summ dhvv)vg3g qlp;92 k6fw+sm; 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 mass behind itg 5xf30 kxy x9cn9yiq51jqb,t, Fig. 4-47 . Determyx9qj ,cxbi gk5qxtn91y50f3 ine the 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 usin ha2hpcn :ym0-g6e8q:c :ir 1rnssd r:g the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed? pc :y:rng1-amrh:2seic nhrd:q 80s6  
(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, :;ls lx;awtib j)(uuams:y / (m:g1n fa 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass(xpxnqju9 6 ml. uby4, $ 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 con;y1rxjg ca b69ahd(t y7rs- y0tact with each other, as 1h0jda-axyy ;ctr9 6 ybr7 (sgshown in Fig. 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 are each initial0/l,w qciakq sq8,*18psazd/akw6i qly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does th ack,/l 0aqpawwi zd8qs16i,qs/8qk* e lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connecte4i6nq7gxbv ,v d by a heavy cord of mass 1.0 kg . Calcul67v4xn,ib v gqate 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 ko33 m- ; he-piwwt*hyp;.z 5s *rbttltinetic 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 hj2z dro) k:c,required 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 accelerae *dsqtmq)o( 9iu9 s3zting at 0.20g. What minimum coefficient of static friction must exist between your feet tsq qe9d(3*zoum is)9and the floor if you are not to slide?   

  What is the maximum acceleration a car can unde6o;mnea- l1y )rb +gkirgo if the coefficient of static friction between the tires and the ground i;ok1gr e-iyab6)lmn +s 0.80?   

  The coefficient of stati:b8: tfnzlkt,6 qruk, c friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can youtub lqn:6zkk8tr, ,f: leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.846vzfkjo mi8te g09.g2j z* jk0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rougu60/n x1tkrnb 2xft b+h 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high h p8mn6bhk/vbe7:bszk7 c34 ncoefficient of static friction./78pkvch:em3 b6bz hb4n sk n7

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(*o4s+ f u( dkznqh(bc 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 4-20) how large a mass would box A havf -7o7mndnd: dy,7 gfde to have to prevent any motion from occurring? A d7 d nmnfyo-7,7dgd:fssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gih:b/ -a.th neeven that the coefficient of kinetic friction is 0.20 and the push impart enb-e.h /ath:s an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact a5p/ f,n,l4 /d(nu iinvmbt t4fnd at rest on a horizontal surface (Fig. 4-54 n4t blfv (tn/4ipm5/nifud, ,). 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 carryinr iwl- .mestl/0/wv6ag a heavy 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 th m6wia 0/w. lve-rt/sle crate slide against the cab of the truck?   

On an icy day, you worry about parkd:n8i pk 9ze 4/+sz-i xjdc*reing your car in your driveway, which has an ix9zj8/diz eek psri c-:n+4*dncline 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 sli*ykh3/-vesz( m: psrbde 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.aui8eh pz7,+1 .ufg n2npft)d 4-55 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 initi bh9 *c obzdt o6-3ni2a rd(2pusrt17val 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 the steepeshuxd- 5o-y wp/t 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 rough ms;l8j(y+dwxxen;k13n ey xzk-*o .s wall by someone pushing on it with a force lkwsx ;*d e.x xmsnoe3jy- y;( z+k8n1directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become d1gvi) xodpvf p (;t*ku9 d5ux-angerous projectiles as they melt. Consider a ctp;)g5oxk u9u vpi 1v-d(*d fxhunk 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 az9x t-8z+gkr.9l qe. m5rany automobile traveling at speed v is 5zlyt. 9n.qr+rk9 eam- z ga8xequal 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 faa1 y- yzw;6csorward on the dash when the driver decelerates fr;1-ac6 zyy wsaom 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 is98iwvc1ncwb l7x a ,(m 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 fromwb6kjdge0y4 +:8 t glh*fe.ms 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 os w0ejkdb.* :mgt4g 6y8eh+flf 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 coefficien5i:/aurvtf5 hh )5w nc:o6c bft of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including ,e/9emubudrs4:sg 47xe t 7gm 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 mammalian heart, at each pulse appsjb40v db+qn*f-gcgd7s nj:) roximately 20 g of blood is accelerated from :+b v*cds qdnbg4nj0f7j- gs)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 alew(h mxtg42-d)v a i 2em 4jck18-hajutomobile crash if the deceleratm(4kahc2jhij w4)-- tm2g8e 1xeldv aion is 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 z+j:2 7 obqcqpk hvf)zw13 6wmproduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficiecb+3w2zkhf6)jmw1q: p v zq7 ont 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 th a w48m8rerik1e scene of an accident 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 ewmak48r18ri 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-6) w1n ) bkdce.u8ashx4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after tsde ab) x )hw.8k1c6unraveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top se/b4pqi,ypw)g r8sq:r ; qf.of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistanwfr,4.qsbiepqg:)q8p yr s /;ce?   

  A cyclist is coasting at a steady speed of 12m/s bu7n0isz/ mpc- u+rrjm/t 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 upon emergin0/ jr7szm/cu i-rp +mng?   

  A city planner is working on the redesign of a hilq/py4,.hx1fk g. favply 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 withoutgk,h./f.1 4avpxyqfp 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 pi;(fq)s ac f7al7 vxo1+6r ofuiece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-5x f a c+vs7(l)1oi7of6au q;rf8). 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 be several ramps c3l xbl t6:9rrk -dawd1aca07yonnecting differeb 9lwl r-aa :a7tcdd63y1 krx0nt parts 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 ti0* xeo ai;e g;32ykqqhe piano (mass M ) using the pulley apparatus shown;e2qy*i0q g ;oeia3x k 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 accel o)ycty*tw1, serating 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 pqivw+h- 6wv 4for a child-restraint chair, an engineer considers the following set of conditionv -pww4 i+6hvqs:
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- zvpsvz56xmb *3+g: clcar 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 zlhp* gbu;0)o f o0q9xropes 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 0 g flo0bhx* );uqpzo9m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-)rkzmn0 j r:y01 $\mathrm{~b}$ 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,vi alt6cyr giy8(:znha eq4 m:w8j2/ 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fiey55fis wnf5a 6ld inclined at n w6sf 5y5i5af21.0$^{\circ}$ 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.