Why does a child in a wagon seem to fall backward when2j s36wb/ cdpz you give the wagon a sharps2p6wd 3/zbcj pull forward?

A box rests on the (frictionless) bed of a truck. The truck drivs,pi;7t/xf;o wyiu 4fer starts the truck and accelerates forward. The i7s ; ,txio/yffpw; u4box 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 forces acta 5 llhoasq/vl*90db a df/5:ding on it? Explain.

Only one force acts on an object. Can the objeclm tscy13l h89t have zero acceleration? Can it have zero velocity? Explain91cymhlst 83 l.

When a golf ball is dropped to the pavement, it bounces back up. (nykdl-/zb /l)a) Is a force needed tody l/lz)n/kb- make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposizev3hx19/ y jct r8f:y6ztd. pte diretevz3j rcp61 /dxt 9z.hf yy8:ction?

Why might your foot hurt if you kick a heavy desk orzzynm)7t6tpfl 23ogwoto , 3* a wall?

  When you are running and want to stop quicke/2bpd2dfpmrls0*q7i dif 51 mj2lh0 ly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (u0i/i1l70lp*sfpb2mqf hd r 2m2 jedd5sing 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 same tud )e(zvxj 7izf7eb 68i ntv x7ug:u4.hread dangles from the bottom of the stone (Fig. 4–36). If a person gi)7e7: v (xf7.8zxj4u e vdi itbnu6ugzves 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 a nf t/+tr2.tbrock is twice as great as that on a 1-kg rock. Why then doerta/2 tbn+t. fsn’t the heavier rock fall faster?

Would a spring scale carried to the bn6a majipg2pl4)( 3r Moon give accurate results if the scale had been calibrmj2l6ppb3r 4i n()g aaated (a) in pounds, or (b) in kilograms?

You pull a box with a constant f.g 1s+ luik8c/h ,cnapvx.m )aorce across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of thmaa iu. c/p.hl1) g+ ,nsvx8kce 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 forcei) (zqiws/zaj9 e*lmu l) :5vf mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth movji* zu f)/ :lmvwaieq9lzs)(5e?

Compare the effort (or force) needed tof1tm-e k/b 7a7cgeu4 z lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the forc/ka1 gfmtbcuz e74e-7e needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third lawe )a3f,lu.0 tjza4 xix, each team in a tug of war (Fig. 4–37) pulls with equal force on the oth xt,ae0a)43z u.jxflier team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a baai8 js pq(1; kja/r)5rpvn-zlg of groceries. Describe the “reacti-5j irs/a8 j) vpn(r1plk;qazon” 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 is exerted.

When you stand still on the groizob+)zhh - 3kund, how large a force does the ground exert on you? Why doesn’t this force make y+ z3-zhibho) kou rise up into the air?

Whiplash sometimes results from an automobile accident when the vicy, 5nuqm hh9o7tim’s car is struck violently from the rear. Explain why the 9u m,y57ohnh qhead of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acc+8krifb/ qub6z ;av1felerates, the crate remai ;qb+ fv/ 8fi61kbarzuns where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block rep5 yx5e,ll8v*-fd7kqvim6 tqaches its highest6qlvmp l5k5vtq*f-,yd ix78 e point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scd8t-qs t*cfz -ale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, evencft s-8qd*t z- at an angle.

  What force is needed to accelerate a child on a s b8sf 8v.ge3l3+ slzecled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a 56ou3zpt1 otvvepu;( nd rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rop ev9a xs.o-u0wb/m7kme withstand 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 of a a. 4ytngm01 sx $76-\mathrm{kg}$ 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 pdfgp,4i fu: o+b.7or adr,2man 1100-kg car in 8.0 s if the car is traveling at :g4 dr2fudfp o o7r.+a,,i bmp 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelro7mcxh/ 6qae62swv xiig-bt dg*5o0 ,yp1+ elet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifeixrc*d5v/ge 6i6qxh,myo 2+ow sbg-1 pa07tle?   

A fisherman yanks a fish vertically out of the water with an ac *pkm0,qin*0 dhadvj/ ub (7hwx9 -dgrceleration of 2.5 *uda7xj pvd*-w ng mh(hk/ bqi,0d09r$\mathrm{~m} / \mathrm{s}^{2}$ 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 trnb+bsn8/;k ai v9f ;y q:nch8wack (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 +wai).;h xt+ ;j fdmvlbe designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suiaj .xlfh+t;m d;w )+vpporting 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 motij :-(0/p d(o udeb )jtykq bg:k.biq)bonless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Cal beqb:k0u/)kj(- b.yi(gjt: qobp )ddculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,75 4jdaspqx+hb4(- s 0aq0 N. What maximum upwar+ 4a dxqhj0ap(4s-bq sd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inc0i,i i8x-ho /n.itzf mluding parachute) when the upward force of a i.h80 /xm ino-ft,iizir resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the gron+o a tvru1/8z etb68to o* .t:n-fwzbund below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding a t+881noub fr ./otbwz6vn-*toez:tlegs) 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 run o 6d1asb4p6ijs vertically upward over a pulleya6dsoj b p461i and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diag /ejx(souh 8v(ram for 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 jb andgaav/ 7l.kmke 34;:t;h a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfi. 4:lkt vbmn a73a/g ;ek;jadheld.

A 650-N force acts in a nor48wlox,bjd * s*tgms.thwesterly direction. A second 650-N force must be exerted in what direction w sl 4m8st g*.xd*jo,bso that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across sxj03r-vz cq4 a "high wire" strung horizontally between two buildings 10.0 m ap 4zs 0-vjrxq3cart. 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 buc j2xlkwqt8s (;ket 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 1dp6gk wy,8 pyulw(1i. 4.0$-\mathrm{kg}$ 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 w 3csmli.gcfq+ya.-8 new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces .mcw.g asfc3ilqy+- 8 $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 pullingws(xe r60pg3 q two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomos(wr6e0 3xpgqtive 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 theut1ow s0(hs *8klhj17z-fnvt bucket-pulley apparatus shown in Fig. 4-48. (a) Howh(stouwk7 1h 1lsznj0vf-*8 t hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race jb)cl-syr, n( began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (massbkqi/)3 ugnpzne/*c*lym 4f( $ 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 with each othwu-( dr92ehcqere (rwq9ud2 c-h, as shown 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-lh/ 8 qyr1,*tfe,xr af-ecpx initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its vel1 a-l,* e-cyr qfxe ftxrh/,8pocity 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 connmxi/54nhbt t7ac y 0drm *y:g,ected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagram *bn0x,y4dy7itrm h :m/act5gs shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction be* +2rvc, vcrkctween 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 5.067zza/zju dkw3bn j03$-\mathrm{kg}$ 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. What minimum co.3dz:k0zywxb nsda + -efficient of static friction must exist between your feet and the floor if you are notx ds:nz-z3ak+b yw.0d to slide?   

  What is the maximum acceleration a car can undergo if the coeff2ek v(aw93nx wx3n9hnicient of static friction between the tires and the ground is 0.80nnea93 w xh (xvkwn239?   

  The coefficient of static friction between hard rubber and normal street pav78 o/s091sss e j xd/e5*f)j) uhmljrd6oqwax ement is about 0.8. On how steep a hill (maximum angle) can you)5sswuamdje 1xjh7e o/9)s0 dqsl/fr8oj x6 * 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 v n1m1r(e)hvysf,i 5/ ih2zyb-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 ,9. wcczsbe6z3 s8wavon 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 atlj(/sd g+obo-f)6 ztn asphalt surface have a very high coefficient of statit-+sbz)6ft/ (oodgljc friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction f4qp,i* mw kn5hor 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 (Example9j-bdk.p c lt5n/f0 zl 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assubln/clpfdzk -5t.0 j9 me $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesra0p uw:ywfoo27q)cs4gd 3 2o across the floor. How far will it go, given that the coefficient of kinetic friction is 0 :w 7w4u2dya3 r0)gfo2osoqpc .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 in conau964vgb7by)f/ali fisq sh9 bv45 k;tact and at rest on a horizontal surfilf)ssa6/yqb vb9gu a5kb4fi9v4 h;7ace (Fig. 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 az1c((mweor- 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 hmeca((r ow- 1zaving the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your dh y,k*34z;xtazag rc5 riveway, which has an inclin34 atxzyz rk5h *;a,cge 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 wit2qki8ydl5ny06 /ujk k1av(t th 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. 4-58r0u f6rk6vd- z su6bgb 2wyo*5 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 jj,3(ypwhy5,in4v ae h/q *uiinitial 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 steepest hill with a speed ofsl8rn01t- yf x 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone (fpm,l ylamv8 b zf..xs:6wyk 84omv 8gh0y6 wpushing on it with a force directed upward at 2 y .yf88phw4ms(,l 86b v.k gywmz aflx0mv:o68$^{\circ}$ 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;vjnx8nle75 * bbn)/ m cvhpn+ become dangerous projectiles as they melt. Cox)b c7+m hn/nv;8 *jv5nlnpbensider a chunk 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 automobile traveling at s x, jbs38,j8l u)cqz8 3njgaicpeed v cjscqxjn8ba3lij u )3,8z,g8is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of d4 h,yc/8i9(hg hjapua car slides forward on the dash when the driver decelerahg 9/ dy(h,achp8j4 uites 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 speed:cavc- u3r ix. $ 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 to the packf8 n) 44uo)mjs9y moh4scha.jing 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 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) s8 4.9ho)u4asjj4mnhmyo cf 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 k6k 5cng:t e,qji bh:)finetic 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 bicycle) c+ jxe1ft+49nfk(*d+ mld uaitan 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 heq yo:,/g olfyhsjq+)7art, at each pulse approximately 20 g of blood i j7sfqoq+)yo,/y hlg: s accelerated 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 g+ol :. *orcy(k;sc3hd:esg o surviving an automobile crash if the deceleration is no more than 30 " g 's. l:*ogd co.3eoc;g+:ky s(rsh" 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 producedk-m18 w)s iac1e* b rkmy6d(gz by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static ie cdwk 6-r81b m*yg(zkams )1friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the 191vi o om7rpjscene 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 ofm 79p1vr j1ooi 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 19t7yqmgy* k74e,gv7qigv 6 +lvsjby mb7: 6e i-in-4 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 traveling 55 m? (a) I,kv46+t7geisg ybmj7q9m 7vl*eb yy 7q:vg 6ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped )isi 8tqi 9k:wf a9c6gfrom the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the avek)c aii s:f8q9g9tw6 irage force of air resistance?   

  A cyclist is coasting at a steady speed of i 2lj4q8s ec 0vwi(zk512m/s but enters a muddy stretch where the effj4el2iq (zwi8s5cv0k ective 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 rednsq2aux)o9 sc5gfs a7 +(s)ufesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars+a2)7()9os5quxu fc a sgnf ss 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 fb)1kjpm/-yfh ad :a2trom a thin piece of string while the jetlinedf/k1bhy -)apmtaj 2:r she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connectilfw 5h y.;dle8ng different parts of th8yf5e ;wlh. dle 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 pig* .quj5bnp7g,i6 ionano (mass M ) using the pulleyjp*quo, 5g6ibni. g7n apparatus shown in

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

  A jet aircraft is accelev,ola2. yf z5urating 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*rtq,.k2d uoarj 8-,m g 3(z8f hnufuy child-restraint chair, an engineer considers the following set of condition3 a2gof y (jufm 8u .rq-h,r*utnz8dk,s:
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 tr4f) ) b+nt qk (fk-p4.svtsursain 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,cogos.c .b8o,z;p6 oo use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not c .b6;p8so. oc g,zooorecommended for safety purposes in 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 boat is u1r2 x hhhhxj1hb/.qh1sing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allo 34wmnp9fy/f7mhl +/: xccdrt wed 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 ar-kn c9kh 4d7 v;ab-mgde ascending an ice field inclined at 21.vgmk-a7;94 dhdck -n b0$^{\circ}$ 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.