Why does a child in a wagon seem to fa;y411rje 6hrxpd5x znll backward when you give the wagon a sharp 5 xnhpyr d41r6x;j1zepull forward?

A box rests on the (frictionless) bed of a truck. The truck driver s ,ll2.dd q;3exjan*ppu:en -u tarts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground b p ,e: eu*q2-xln.3ldjdan pu;eside the truck and (b) by Chris who is riding on the truck

If the acceleration of *taf)s ,ab1 rtan object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object ha9f5v st3hpcn) +fpg;o id*kx6ve zero acceleration? Can it have zero velocity? Explain.dp)nhct6f+;5 p s fkio3 *xvg9

When a golf ball is drobtg ebdz0ka1 454z vv sz.ua2/pped to the pavement, it bounces back up. (a) Is a force ne/vk4e2z vt g aaz4b.sd1b05zueded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating ow,e g ss+wieib:81 yhv(-z;ks n a lake, why does the log move in the opposite direc:;-zsbhs(ye81wig +v,iw k setion?

Why might your foot hurt if you ki.j 3 z6 xqiu+*k6ysn*+ s1mpaelm1ocbck a heavy desk or a wall?

  When you are running and w+ds ,-,v ga6uvq4jqegant to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own exp evq6uva j,-,qg+s4d gerience) 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 threa3ze 0nb ceo1r mt;1c trrj n0v52+gdif(rq4)vd 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 above it? What if the per03z;(i 0n vtc4rorv11c rnmqe )ge d5t2f +bjrson gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Wa*is)m n +0;kd cj5bfshy then )0n*+a ijfds; 5mskbc doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon gi/awmb4htm1 w9 ve accurate results if the scale had been calibrated (a) in pounds, or (b) inmb 4m9wta/ w1h kilograms?

You pull a box with a constant force acrout9c1x r6 +djb z8ezjxou-6 d*ss a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an anr6 djz xeu-8c x6jdu1+ 9o*zbtgle 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 und7ytv*18- bidda h,gx ner the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth movedyanb,8-g vht1d7i x*?

Compare the effort (or force) needed to lift admty;ibn1v+f 4)9hlp 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 horizont+ yh)di ;bp1tlvn m94fally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pu 0yu32 ppgrgcuvsr.q(malk+t:;-r r,lls with equal force yr2 gqr map(:.ls3,k; rugtcp0 v-+ uron the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. D6pqd;2s 2nshca1 lj -bescribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction-;6 lsdq1 as22cpn bhj, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large h/ v/ytxtrv4padflnk3 s. zhz9o244 +a force does the ground exert on you? Why doesn’t this force make you rise up into 34hy v/vtrz/za k9pds4l.x+4o2nt hfthe air?

Whiplash sometimes results from an 2-pvu ,b z;ljdautomobile accident when the victim’s car is struck violently from the rear. Explain why the headvlz p2,-u; jbd of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flat sgw(m81we / 48zn9spyfnpx8qbed truck. When the truck accelerates, the crate remains where it is on the truck, sewng19qxn 8yps8(w8 mf p /4zso it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slidest3dlu4*;v4g( opcgd5j9jo csyf t; 0x up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its accs dxcy9ftogljv;5cp*g(0 u o;dj43 t4eleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed x*,w,j,+pavpna,g bx. 4uua qyourself on an inclined plane? x.a qu4, pb, upn +vwagaj*,x,Assume the mechanism functions properly, even at an angle.

  What force is needed to a -;ed.q ba opxb6ve/2kccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceler5(bgzvd8j /wpates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if i lno-9udq 3b-kt 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 o hs*dxusm9u yn96.;ir f 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 the cqv0 e0ek,pm ab04khj/x.0gj car is traveling at/kvme0xpj0h be4 .cgj 0 qak0, 95km/h? -  

  What average force is needed to accelerate a cs/ 9oonxq.; j8mc(8 ,o mulkm7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of o; qm om9uc. o8,xs( /cjnm8kla rifle?   

A fisherman yanks a 4*y) nz5ci2nsel 0tkofish vertically out of the water with an acceleration of 2.5c*l o t 0n2ezky5ni4)s $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (4nckhsdm36 t83rkb;g /j y9/frm y-ic502 $\mathrm{~m}$) 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 des bd,w ,dz vgih, *fzn3eoei4+;igned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablee,i ,3zvf *gizbdod 4;,+nwhe? 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 motion.ll;zr 4e 9y j5ds)inmless 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)in;59l.elysrj z4 md the direction of acceleration.     ----待选择----downupward 

  The cable supporting a:8hir-, +jdcjw4rnzz 1zdq-j 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elzwc d, dqr-n:jj j8-z+hr14izevator without breaking?    ( two decimal places)

  (a) What is the acceler mcghbi4a gg(q0b/*be/ s)o* zation of two falling sky divers (mass 132 kg including parachute) when te/gqb/a zobc 4*isb(m 0 *)ghghe 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 house 3.9-m high. When he strikes the gro xqq:hb-3r :zi.o,r sdund below, he bends his knees so that his torso decelerates over an approximate, o:x-rz sh3i:.d bqrq 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 1,uk xea *h8d6f+ddqvtable. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fq1* da,6+d8xude khv fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for 8 k7c iyjl-8cpa basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a basebaf* 0hfai++1ohl8 4wbiw c9vg fll (a) at the moment it is hit by the bat, and again (b) after it has left the 4*fh +fowa90 1ihi8w gc+bfvlbat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A sect u0/plrq :o;wond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer lqtop; w0:/urwith a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildin6:1lq ( rw-queoww,u jgs 10.0 m apart. The sag in the rope when eqlrw:j6( -1 uqowuw ,she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cordr i4n2xbj8, to/r7pn 0m zv+rs 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 14.0nk 4jyx 6 c(5lu+dnec;$-\mathrm{kg}$ 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 Mck9upi93osmy* m 8c h)rMurdo Base, Antarctica, as shown iny3r8uk9)9mos hp im* c Fig. 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 pullix1 c.g5q(a-r,u oqp oqng two cars of the same mass behind it, Fig. 4-47 . Determine - qo,oqgp(c5 q xa.ru1the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls her*jgz4)88vigqld k5 sft33w osself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise jvf4k i)wt8g d l8gsz3o s3q5*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 begvmp 0.;x3/tkutvp abk :md/wrm58a+ran, 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 blo ck*bfc;a cw p2+nzy74ck (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 hocibh e49tge 82rizontal surface are in contact with each other, as shown in Fig. 4-51. A e tg 849cehi2bforce $\overrightarrow{\mathbf{F}}$ 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 (f1l-5 ;vryv8i0q9bofpdqgm each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and tvfgry-0d98;(1vfmql qbo p5 ihen its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a he6t*sg98vl2 y wwrlxo03lo a0 9yxfpl7 avy cord of mass 1.0 kg . Calculate the accelwox rv283 y0wlf0g7 pll a9ots *l69xyeration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a r:/sn po2nx6z 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 ren27di+ ukp8c 9tbp aoyn)i( .squired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on aq.t0k( ioc8rc train accelerating at 0.20g. What minimum coefficient of static i(c.o8k0qctr 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 coe fs77;,+puu;whtusj 5l8k)pf :frb *aept4orfficient of static friction between the tires and the gro8t:ka5shr w, 7 op;t p+ 7 r*)ujbffpfl;e4suuund is 0.80?   

  The coefficient of static friction between hard rubber auxofmd3.y,g6 g3 )kpbnd normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkeg,d6f3 o . x)3gmupykbd?   $^{/circ}$

  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;tp m/( q6; l6v /o4dg jpeg/tnlf+tdg -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 a rough ,*,v2v+t,k ilwx jb+:ew7e.w,lagt i/ zr fbi30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface h36fd6uqvei - ( a9h7dh0ybhlnave a very high coefficient of stati fd-duhi6ha(lh qve9yb63n70 c 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 frictiop gh,v*bo29/uq(h zk dn for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A have tow8sjka tq gb;ou yv- z7dd;m .t,-sj-+(7pocq have to prevent -,g mq;vcysotwku(7jdjb; -8 -s zt.7oadpq+any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fa q0ls,tqxau(o;gc/lw sb 78g8r will it go, given that the coefficient of kinetic frq0 cgxq(,a7sl s8guolwt8; /b iction 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 in contact and at restj xa93,pxk*sch4nr.e 3:cpwy on a horizontal surface (Fig. 4-54). A 620p ,cj *xh 9e:.ak 3nxy3psrwc4$-\mathrm{N}$ 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 frictionxp:f 3 6x/etvpy xee;. between the crate and t; e6:evp. xyte xxf3p/he bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you wor5 wllzpzug9 o*k9,tj- ry about parking your car in your driveway, which has an inclinek,lo zp9-g95w*zl utj of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 204 fvyxt8ut ytn dvew;+if4 .+8$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane v /qg h b;27hscni0y 92bqts+ltilted 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 3.0 9awwh o)gri0 tx1jq 1:$\mathrm{~m} / \mathrm{s}$ 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 reach n91ard gwf9+y d*0ukopmbi0) es the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by so:e8zup9m; hw 6sqi 1fgmeone pushing on it with a forcp :wgmqe1h;s i8fu9z6e 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 dangeroussfl66d 0wfin2cqf)3 t projectiles as they melt. Consider a chunk of snow at the ridge of a roof wil 6nwfs6c) ffidt203qth 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 travelingzt4dxd ) fk-7g at speed gt k)fd7d4z-x 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 dashbo/phmc7p( y lr8ard of a car slides forward on the dash when the driver decelerates from (lh7/p8rycpm 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 gi.lrv/wr;9 e jcven 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 aa *erfpe/45b q)7 dtvunn:4onm 8d.sn conveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distasn5n / neae)844 fu:v7rodtqdpbn*m. nce, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic frq)0rn wihd:/x iction 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 9p (aqk8x3m .nw pxqz(bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian h.unn7wc( slf:fz -hcd 65tjp, eart, at each pulse approximately 20 g of bluc- j5h.lf: fn t6n, 7cpd(wszood is 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 surviving an 4 ;k4wvdabyr 3*t1q zqautomobile crash if the deceleration is no more than 30 " g 's." C4k13z w ;tyq*varbq4 dalculate 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 acceleraty9y q: 8d-hna5vgd(kq, a6 scnion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that th n qgn:qdys, dav8hc65 ya(9-ke coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two cars, mz8g)yvp vs rr ,l1bf1.easure 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 pavement is about 0.80. Estimate the initial speed of that car assuming a level r1vpbyrgf v, )81.rzl soad.   

  A car starts rolling down)za5-sjn y/9yq)uo lpt c t-4w a 1-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) Ignorl/wsjyc a)q5p tnu9-zo-)yt 4e friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dro.ho(3mv4 l7 vtqf7zmdpped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average fo74dlh3 .ov7zqtf(m v mrce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but 4m pfwo-thg;3 )byq4ou /fv2xenters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mu 2x4pfv w 3t/bgmy)4 oou;h-qfd lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign o : ,pos./rractf a hilly portion of a city. An important consideration is how steep the rco/r:s ., tparoads 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 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 experq0fnh +v0uwaun7h7 5 piments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes a 75+07pvwuhq 0uanfhnn 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 connecg /88mmu 4mi2:widln ating different partsd88: uil2gnm/m iaw 4m 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 liw/k;6l02* g iqa xhkqyft the piano (mass M ) using the pulley appyh 6akiq0wk qx2;l*/garatus 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 3.vykh 4m0s 81t 0a,ymv1mfekf 15 $\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer 8ld nuu287ccq5 0rsqb considers the following set 8bl cusnqu278c 50dr qof 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 (yx d i):stohr358i-dc 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 ropes of similar len .)n) imoe, hga+osse(gth. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purpoihe+,e. na) somg)so(ses 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 9uusn(:lcyfbb0 3 :/d 5xdwaxusing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed t :x;rm7kebv g09+x,*5sdydhb yk j5ato 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 togi gxfo t8b/vvix7* 5 b q.;awsl6;wva8ether are ascending an ice field inclined at 2b b5;ai* a /gs ;wq7wtvvxio8 l8v.6fx1.0$^{\circ}$ 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.