Why does a child in a wagon seem to fall backward when you give the wagon a s)9puoi )lq8 ibharp pull fori8 oilu )9q)pbward?

A box rests on the (frictionless) bed of a truck. The trued)f- swfrt 3.ck driver starts the truck and accelerates forward. The box immediately starts to slide to- )fet 3rd.sfwward 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 forces wxo:onede f/g ,d5.z+ acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratio:pvwmf, u9x);c:oi qo n? Can it have zerwm) ;f uv9ipc:ooq, x:o velocity? Explain.

When a golf ball is dropped to):rleu( +bgl96a4ie, lizddk the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what ebl, g +a:)ldk (ze4r69iedulixerts the force?

If you walk along a log floating on r.ezpg; )b w,)h,yp0xnb)o es a lake, why does the log move in the opposite direction?p yohr;g,0s )be w), nz.x)epb

Why might your foot hurt if you kick a hed*tvy k:ik;m8:enh1 yavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickqrcmo7w++2 hak4s6x v ly. (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 rom2awsq46rk+hc x +7 vunning at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, andtq0.fm s,i6j u 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 omtq6i su0,jf. r 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 cn a 0(rgc5z)2u7ng 9wzsq1uegreat as that on a 1-kg rock. Why theeur12ng sz5(a )9 zc qc7gn0uwn doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resultst ms*f3 jdmm 0 w,pxcd ri*y:4ctf)-jj 1/byy, if the scale had been calibrated (a) in pounds, o /b0 sm,*fprjtiy4) :cyjxdj-mc1mdy*,3 wftr (b) in kilograms?

You pull a box with a constant force across a frictionless table using an aty. ea xiyhapv29 3n4;ktached 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 box (a) remain the same, (b) increase, or (c) decrease? Explain.hk2 vy;.349ye apxni a

When an object falls freely under the influence of gravity there isjnu)d 1wpha19 a net force mg exerted on it by the Earth. Yet by Newton’s tpuj11)hn9dw a hird 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 a 10-kg obj3:a sqol d:9svect 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 aqdvs9o l3:s:a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of am0bg) sa1-o dwar (Fig. 4–37) pulls with equal force on the other team. What, then, determines whibm )s -a1gda0och team will win?

A person exerts an upward force of 40 udzuoac i+ u2b1 u2k:1N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, andu2 o 1u+k 1acuuibdz2: (d) by what object it is exerted.

When you stand still on the gro gyqdb*8epi. (und, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the a ibp(8. gy*eqdir?

Whiplash sometimes results from an automobile accidrt. 3rc:.eljzi -(xohd9i1l bent when the victim’s car is struck violently from the .cb .jl 3iioelx1rd-:(9ztr hrear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the be 9 pdjrt(w cqau,f-+1ud of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, +1 -dctr a 9fuwj(pqu,too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After t4rtdzp3k(yv 3b9/xq6 8b/nz)vkpvtmug6 q t/he block reaches its highest point, it slides bx3m 3yb/ v/bvrtpz 46 k 9/kuzdp8 tqtngvq)6(ack down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale rea s-5b+ch1ifi2osl0 e gd if you weighed yourself on an inclined plane? Assume the mechanism functions p gslfic-ei12s h0b5o+roperly, even at an angle.

  What force is needed to accelerate a child on a s)zwso m.ozo;:led at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ;oo o2 bot(f3mid1x-3hhnap5,* rxwr 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 wiz+b cwrb4 a7t* ,n;cljx*ce-tthstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight odv6n)bp;( h4j .gt rcvf 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 8.0 s if(dyidv ;apv 86 the car is traveling at 95km/h? 8(p6 daiy; vdv-  

  What average force is needed to accelera ;;kp5vdm+ ormte a 7.00-gram pellet from rest to 125m/s over a distance of 0.80 o+;m mkdvp;5r0 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelera- u)ht d:-s5 t/pks;5i2b yozb:ciqnx tion of 2.5 tzk)h y s2b:dxnq:c -/ o-5spb ui;5it$\mathrm{~m} / \mathrm{s}^{2}$ 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 trln is ),93)mbah+n okyack (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 dea p.l)1hvttymi- o 4f4a7;iyey:) rc qsigned so that the maximum acceleration is 0.0680 g . What are teiq 7c4y)-a1:l.mtti4;o) yvrpyhf a he 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 ibvc-moe3 c d-6n a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weivob6c3c- m-de ght. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting o pttsr1;2u 8ka 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator w28urtkst 1p ;oithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inc f)0c4 l;om)w nq0hkiyluding parachute) when the upward force of air resistance is equal to one-fourth of their weight? n)) oh m0q i4cwy;l0fk  
(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 h42a kcgaae;n t9(t q2h(2d+kj(jnpzwouse 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximt(( hndg+(2j;ka wte a4zqkn2ac j29pate 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 boxu-zpw65nrx w5f ,w9ad runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exert9 dfr565waxuz ww,- pns 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 ba,5cs9+r kandc sketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-bodyo,tk3a*v+-chhnxq(r w j m,u* diagram of a baseball (a) at the moment it is hit by the bat, and again (b) aftenaujq, v(cth*wo-r3 xk*,mh+ r it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be e ) jcty;fqfz8 y,sb9j(xerted in what direction so that the resultant of the two forces 89jtjyy(cfsfz;) bq, points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildin) vb,y:(b 5x apc3rmxggs 10.0rm(x3b b)gyx:v cap,5 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucke94((r5gv m) eymin)sltv);vrtij a d3t is hanging 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.ml bx/le3(f u (j3qhj.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurzt6.pws i/ .0ypvrlv0v8 vnd3 do Base, Antarctica, as shown in Fig. 4-46. The sum tvz63vvs 8rinpwd 0y/ lp0v..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 to9kbg7+o f1 mmwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and tm+b mo1kf9go7 he 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 shown in1wo5o8uyrt4tl rd/7 v /:gfjro f ;lmdh:u; k, Fig. 4-48. (a) How hard must she pull downward to rai ;ttdu;ly4 o :wmuj8,frrdo7rlgk1 : 5f/v/ohse 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, a 65zlm1ab/ uqh* pj5b p44$-\mathrm{kg}$ 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 h+fi :8ypak v)8r vteah b-)at-kq98s (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 con9wvdrywj 3o; xu ,rv,0tact with each other, as shown in Fig. 4-51. A duxo,v3 v0w w;y9j,r rforce $\overrightarrow{\mathbf{F}}$ 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 aboveg(q4 o*obbbsmq3 ju/ 9 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" speed. Assume it doesn't hit the p39 s*(m4qbo oqg/ ubbjulley.]   

Suppose two boxes on a frictionlesse fr mov ajo7fr0 )beg4fvyovf( -1+9+ table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the ter14) 0evevvfoarfm-oy j(g9of + 7 b+fnsion 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 frictiobjh(fv /dc7k esy5.q3)5dic bn between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a -zs/+n,z eecwgf86)rhu6/ zt vf,wxp 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 0.20g. Whrjvc5+9 tm2whi xyg:zd (y52uat minimum coefficient of static friction : xrijh d55yuzt92+ (cwv2gy mmust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car 3 zg538 v8kwzc63nkhach kkq/can undergo if the coefficient of static friction between the tires and the hzv8kakz/k3 k83 cgw3n q6ch 5ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pa8xe b.hc 9cx8lo5qu( svement is about 0.8. On how steep a hill (maximum angle) can you leave a car pc lcs5h89x(e8q.o xb uarked?   $^{/circ}$

  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 jy0z )tq,rou, mcf21u8jt8zhat -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 92rh bb ld;31ldxi1 xxon a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with at045-rpa1d9v jw-1tg z zturhn asphalt surface have a very high coefficient of static frictionzgt1rphja45 0z-rd19t w u -tv.

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 fr tl9tom)t/ bc ,c0un(ciction 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 massyv7 0u;inx3od would box A have to have to prevent any mo0uvxd 7niy o;3tion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it goa8p+pn: g(* (ntem 1yg lke:aw, given that the coefficientk am::+1(p (an8wg p enlgtey* of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in5.gn23/ipa l qya5slf contact and at rest on a horizontal surface (Fig. 4-54). A qfgsn5yl/.35 2i paal 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. Thlr,2idds2n1 d e coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum r 22nr1s,d dlidate 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 ab * ijz(nt4flpp..ixy-5 cqe0 rout parking your car in your driveway, which has an inclinf4i5yq ip 0z* jc-..t (repxlne 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 jc2(w yzn/ex7ex (ex, a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a planrqt(,3zox j-l e tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.,pgkffw9 z -t nr ape9a4w c)m-)s(/9hpvjs1j0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a 95 cqd6pyrmzh8q-owrs/ +ln/ 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 ag: ip ,e hosuyh44k)on2ainst a rough wall by someone pushing on it with a forceo ship2ne y4),o4ukh: directed 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 dangerous puv*ag wjkt -kl. pxv2xnsw-wn+4 (.o7rojectiles as they melt. Consider a chunk of snow at the ridge of a roof with os*tkl+-7nwux4.j- pw(gvwvx2an . ka 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 automobile traveling atf7 ki,4h9oh)o6l/ qolbtlhd0 ywy8-t,jls6c speed v is e, yyl 0wq9ftdlbo 6s- h,ci oll/4tj6hkoh87) qual 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 when the dria mvr lz5wj4.u(6tx)bver decelerat.x5t ljba)wrm(64uvzes 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 i9 l8xg+dro ls;u2(0avf8 bk xes given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they ar zg3x2* a aeis9kghs2x, 2+nxxe 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 ohx+gka3 sxxi2xng*z2s e92,af 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 betwe*; zvmnmox.5 nen $m_{1}$ 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 k clq6hi1(no:)uhag 84fxou,sg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model 8ij6nd madg: ,of a mammalian heart, at each pulse approximately 20 g of blood is accelerated frg ,j dm8nia6d:om 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)0s7 hegw r-mk surviving an automobile crash if the deceleration is no more th- r0)gsewkmh7an 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 earthqua5xto,gd. we6 hqu5f w/ke 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 must be a5t w6,oquh/5xefd g .wt 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 sce agbiah4.k*5kne 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 coeffh* 5a. kag4bikicient 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 meas0j6v bpo nar e-ci5g(w .j0x-ns that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reacc vj-6r05aw0i-. xegjons p( bhes 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 from the top of the Leaning Tower of Pisa 6 0 wt2i9weq;n.tkvh 6su 2hswand falls 55 m before reaching the ground wituhwn0h ; s.tk9 wv twe66iqs22h a speed of What was the average force of air resistance?   

  A cyclist is coasting at ak *j.)euh,mq*v62nkfgp xd:n steady speed of 12m/s but enters a muddy stretch where the ef*vn kg e*)p2nd6xq,:mjk hu.ffective 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 emerging?   

  A city planner is working on the redesign of a 5v9je 5xv3qxmp aay0) hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can acceleratj5v x5ameyv90)p xq3a e 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 ca4f9qwt9ovh7k zx 9jaes;(i 0fr* 2ipiece of string while the jetliner she is in takes off from JFK Aox c(j rw9a02qffk z;*ste a h9ii974virport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps con ,t50 zlu1bkqpnecting different par05p bzl,q uk1tts 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 the p+0x3 dk2z+towwc mnsas uv +p33 8itn:ulley awtdt+znkcv 3s:p 3s+na mw0+u2o 3i8xpparatus 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/v:gy:fc lylizg j07so z0)+j 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an enginee:xus r/+po81k omgs :r qr(+thr considers the following set oh:u(8r1 xs+mo / o+grp:kqtrsf 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 of 660 metric tons (66tg at2v)e:/:s7k dkj j0,000 $\mathrm{~kg}$) . 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 Ka y8ugcvo-v*7 dren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about goy* c -vuvd782.0 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 is using a " 7 a 9hx+v2ec(y-bisx68q ot2izc wzo. 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 i cant,gwy -qv6d(0q (ld mj6p/s allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field incl 9b0 ii7/ni pp, ic.ij*xtg(yivqx.o2inedib 2qj( i,vi. i g*cxt70/.npioxy9ip 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.