Why does a child in 1xd: eb5rph;p a wagon seem to fall backward when you give the wagon a sharp pull forwarde 5;:rh1bxpd p?

A box rests on the (fr;h a)c:g;fovo ictionless) bed of a truck. The truck driver starts the truck and accelerates forward. T; vhfac ;)g:oohe box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forcesb9*;:bc*a ggc rd: o9 bfrbchdz0m 0x( acting on it? Explain.

Only one force acts on an obh0z4 uljvac.1n zr z3)ject. Can the object have zero acceleration? Can it have zero velocity?4.3u n z0rhl1ajzc z)v Explain.

When a golf ball is dropped to the pavement, it bounces back up. c /: q8nuh q5ltsah 9wxp+5wy,(a) Is a force needed to make it bounce back up? (b) If so, what exerts the forcla :u9p+wtyxsc/58nqq , 5whh e?

If you walk along a log floating on a lake, why does the logf fbtwc5w)3 wjrc)ks7 m4m*cf71xhdpu my6 2: move in the opposite)uwk3fm4*)dmx75s 2wj6 rf cbpty:c w1m f7hc direction?

Why might your foot hurt if you kick a heavy desk o7g; ) ma8frxvxx gb9o2egd4e 0r a wall?

  When you are running and want to stop quickly, you must detx ca g9 nnj6mi je*tf;4j,lx,y2s3/ icelerate 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 a person runnix 6a jjmne,i f3 ty ,ctjn9/g;i*sx42lng at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceo/ld;exr5;mp6a rxo(d h00g) f r3 eupiling, and a section of the same thread dangles from the bottom of the 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 abopfo u(add plg;ro hm6e5xr3 )x0e0;/r ve 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 hyf zrkq:6v4(b3 iox; as that on a 1-kg rock. Why then doesn’t tfv3x4boq k(:r yzh6i; he heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scal *)dusbr5 kiyu:zq prv e9+x)4e had been calibrated (a) in po qvz4k: 9xr )rseu5pui*yb d)+unds, or (b) in kilograms?

You pull a box with a const+k1-yrfey9dm ant force across a frictionless table using an attached rope held horizontally. If you now pull the rop e9-m1ykrdfy+ e 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 gravity there is a net f7 3*;dur);b1x wjetunph xr 6uorce mg exerted on it by the Earth. Yet by Newton’s third law the object 7 pe1 bhr;3;u*x nu wu6)djxtrexerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or fc)8a :mbr r 9(o7nqz94w cbjpforce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given spee8mj9 p: (orzw 4cbaqnc97b)frd on the Moon and on Earth.

According to Newton’s third law, each team in a tug poa -twt 7yfy-q;+yy (of war (Fig. 4–37) pulls with equal force on the other tepty;fw+-yy y7q - t(oaam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of -bu; 4zu e fjl518xhv) ckh7mlgroceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it 8ujxl5c)b lh -h7k;mf1v u4ezis exerted.

When you stand still on the ground, how large a force does the grq7 ao8p6 z4hhtyb9+c6 uz ;gwuound exert on you? Why doesn’t this force opza47h 6t9 b6zyg8+wuu;q hcmake you rise up into the air?

Whiplash sometimes results from an automobile accident when the vi5hbipts9 r1 r-ctim’s car is struckrs19hitp5 b-r violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the z l4dmzqa2s y-.:)nqge7b5z-gb:ga b bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force 7qy 4zb:)b-l5ma:ge zd- s2nbgaz.q gcauses the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches i:x9 uu q qhjb7wl.(r0y6a3v fqts highest point, it slides back down but the magnitude of its acceleration is less on the desce 0fuwja37q ( rhbqyvx.9l6 :qunt than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on30,isioi9 i6f pjkf4u an inclined plane? Assu4 pu0fik9i,i6sf3 oi jme the mechanism functions properly, even at an angle.

  What force is needed to acc q*dc,i0g8l 0ulhpqz2wzsqw8v048c z elerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at a*)lwv.5) q zt0jn8p.xa gdeg 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 5 zbk*dtxd3a w6))mizn6e d/lto accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of aof:92 gw7lq;ld2b u jj $76-\mathrm{kg}$ 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 8.0 s if the car i d u.4hvjwe 1xxy:v:+ds tra4jxu1:ewx vv d: +d.hyveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest s*: t 4sdnhcg1to 125m/s over a distance of 0.800 m alongc4: nsthgs d*1 the barrel of a rifle?   

A fisherman yanks a fish veo;sm-j ,w:a q+hw+n ovri,. wertically out of the water with an acceleration of 2.5 n,ew;.ro + v+hw:jo -as, qmwi$\mathrm{~m} / \mathrm{s}^{2}$ 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 canf*; t.l 8m3-t6hmobq8sdbwbx 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 be demr r jcv14l+x/signed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supp/j x+rr clm4v1orting 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 bat jvf0 yo6jchq gc4p9-.hroom scale 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 the elevator, and find gf.vchjj 9qo46-y 0cpthe direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2 (hdpd2y2wew( /up c6t125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it(p6wy uw h2ct /dp2d(e give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling s2 fbqz ;j7yvyw;p8s+vgno m4 )ky divers (mass 132 kg including parachute) when ybsn782v4g owf) qy;+;mj pvz the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a hlon8e4xfs40a64dgud g fu b* b o52yh;por- 5fouse 3.9-m high. When he strikes the ground below, he be5gd6oo lr u4aunxys5b 24fg ;-ffhd*4p08eob nds 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 runs verticx, t: )z8 ewbql/uhf dah)y5a+s8z5paally 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 sideu,/alw5a8ht z5zqy fd) :ab ph+e8x) s of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbapi y6 6yknx*f)ll 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 baseba )m89mc) 6ksxf0b jk .xf.qsp3iihkl -ll (a) at the moment it is hit by the bat, and again (b) after it has left thqfx 6sxk)- )8s.f9pkmi mkb.icjhl03 e bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A seco2cb*8shiu 0 iwnd 650-N force must be exerted in what direction so that the resultant of the two forces points we02i*usi8 bc hwstward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strungi, yut:q7ph *g horizontally between two buildings 10.0 m apart. The sag in the rope when she tqhi:p,gu7y* 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 masejiq8 136 svtj;t9y n4amt 8etsless 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 14.01k hy2o rf0l1zarbhp4/ck 6c0$-\mathrm{kg}$ 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 *ak e(gcigej5 l0qt62 unit to a new location at McMurdo Base, Antarctica, as shown in Figeqij(*g 5ae0lt6c2 gk. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pe41 mwcps7kodr.+v 3 hulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of d op.k134sh cmv7ew+rthe tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus sho a /vvk7ofoey/4dbo,:kmw w84; d rac;y4k/bpwn in Fig. 4-48. (a) How hard must shev;84k pm :ewfdow/4rab; 4d,ockobay/kv 7y/ 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 race began,y; ku+d* ri.eq a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block qttdor*jy ,a*bv i ;cv1k)0ajk0; 3lz(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 contact wtoifad d --y:sf7)71m f/dqhws qf;fvt*xv44ith each other, as shown q7-vifafwdm4: s1/ o v*y dxt;) 74fqd-fhftsin 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 initially 1.80 m above the ground6 vp yau8n0(c5iig2od, 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" speed. 6u5agid2pyco(80 v in Assume it doesn't hit the pulley.]   

Suppose two boxes on a fricticd h; +bkoe-v:onless table are connected by a heavy cord of mass 1.d-hk:+ob; ecv0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient o 9+/sm-tssb a0jirddvy+9 )zdf kinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start )ti;m, mxo w(wa 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 qh 1s:tn;ibp6standing on a train accelerating at 0.20g. What minimum coefficient qh1bp i; n:6stof static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coe2f72schd sr(t fficient of static fr2d( tss2cf7 hriction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rub0d1n /8w9 dt4;w 3* xxehen gevxbrw9pber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? xtg14n nwwd0; x*w3ex 8e9/pbed9h rv   $^{/circ}$

  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 oypf0jut9 91/ /m(,en rtdl4hi/hs bl -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 azo*1p -mxxap( 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 asphav exdyw -5mgp9d o0vk5i8 )lr0lt surface have a very high coefficient of static frict0-0od 9v l rdv)k85ypwe5mxi gion.

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 fro*sh0sg 5k lp*iction 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 ei 2r.-emqu5 0sf )noslarge a mass would box A have to have to prevent any motion from occurring?5)meune -2sqi0 fsor. Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, g bfr68n se1z1wiven tn1b w1e8fzrs 6hat the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and zp:franf)3,y 110 kg , are in contact and at rest on a horizontal surface (Fig.f:n3,rz )pf ay 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static 9p3ztr/a+z ,ow0fh ge friction between the crate and the bed of the truck is 0.75. What is the m+petz /zo,3wf0r ah g9aximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cyd4asn cw/)u+fx w3:laz( 8*;denw jl ar in your driveway, which has an inclid8 jwfa /n; la*3wcz +s:(xy4dnwu)elne 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 i8i8 28lxwpgva slide 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. 4h2nt+hp(eb5r 3)k bbx-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 initial 4 d(0nfy-r2lp20(lx izsvfh 8qg vw:fspeed 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 stu ;dv,,amn:dg9ttd 4 feepest 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 againf *vl* nwdy./4ui8 cwsst a rough wall by someone pushing on it with a force directed up 8v4 .si/wd*wf *nyuclward 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 dangerous projectiles*u ;yqi 7stzs )/sqs 2smiir1( as they melt. Consider a chunk of snow at the ridge of a roof with a pizq2iys)iqitm *s;s71 ( rus/s tch 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 automobile traveling at sp6zr hq 0ms3w+r; p )ucnjfnxal2bpl4,bb /,t /eed / lz0al4)jqr x;,m/62t+bnppr 3b cn, sfhbwu v 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 dasht4 8uuz3;hs seboard of a car slides forward on the dash when the driver deceluhse u4s8z3;terates 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 *j o98rwgti1n+ m6sn qspeed $ 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 filled tokqbxz+qg.bnx s 95 o3: the packing station 11.0 m away. The belt 5 3bxk.nxb qsz+g9:q ois initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If 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 ki0b qjd u9-hy7bb:+8x,jivk l lnetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicy2j bveo4 hvz :91dzq(zw-wze*u6ej *xcle) 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 simplifie)*j9xq p m3oevd model of a mammalian heart, at each pulse approximately 20 g of blood is accel m*pvx)jeo9q3 erated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if t -w(a;lvzyz2d he decelerat-(vzl; ywad2 zion 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 produced by an earthq3 (y ly6j0yfrruake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mustj6rf3yy (l0yr 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 th69wwvtg xb a-5e 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 between rubber and the pave-5xwa wtv6 bg9ment 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 mea vivwlm0;8kgu.,m89fl o: qz ans that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whomvi98: l,g;.8alk vzq u0fmwen it reaches the bottom 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 fromjb8z426 ia4r+-ctaqxngqu e3, ;0oeoqx yf(b the top of the Leaning Tower of Pisa and falls 55 m before xzq x -bb qo(ay ,fr+2cu eqg3680te4o;j4ainreaching 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 e(y4j8/ .rsvpb3b1 p iadx v,ymuddy 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 yir,/p xd.v4 pb esjby8v13a( upon emerging?   

  A city planner is worki vv*obcu,845zh jbny8ng on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that evy5hu* nvj8,8zbb4v ocen 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 thv3e1ja .hl,aruw8d 5.o uwl h,in piece of string while the jetliner she is in takes off from JFK Airport (Figl5rw3o1h d ,u,8hwa ev.j.alu. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps conne . 7m i3iaxp;7mgzv9oucting different paxm7;vi7u aopi3g 9zm.rts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using thekx6td6 4ce2cw d4(zw f pulley apparatus s42zcfd6 cwe(kw4t 6x dhown 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 accelera6 u .b6v2eor(er ug:5ocfxe1m ting at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-reslc;6c(kyf m+ 9 ;kvqfwtraint chair, an engineer considers the following set of9 6cml;;+fwk q f(kcvy conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass e 5.w:9yn6tdjhoya d*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 ropmptj;/lo +2 fdes 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 /jdl2;t + pofmin pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel 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 boatq /hq 8:99fkfeis5fcegaj94 h 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:kt/;v he z0nt 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 f7 x5r),xo,qwin a+yg are roped together are ascending an ice field inclined at 2,ya rg+oq57xi f,wx) n1.0$^{\circ}$ 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.