Why does a child in a wagon seem to fall backward when you give the wagon a+eqa7k 56qd -g.9oztnqzkokk*amz96 sharp pulzqogk7m 6z* kqon5-+aqt96dka.e k z9l forward?

A box rests on the (frictionless) bed of a truck. The truck driv)u t7d540/djw(3a tnaryv khj er starts 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 beside the truck aa(5jrut3 hd7 0wya) /j dtnk4vnd (b) by Chris who is riding on the truck

If the acceleration of an object is v5s:cai4 3. uievzt-vzero, are no forces acting on it? Explain.

Only one force acts on ann 8c y)(6rgdsn object. Can the object have zero acceleration? Can it have zero vel r)n(d8n6ycs gocity? Explain.

When a golf ball is dropped to the pad+kyg v k9 :p8j/bi:ollh3e/jvement, it bounces back up. (a) Is a force needed to mlkkb: 9 veh/g8+dpy 3/jj:iolake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does0j2jw u0h--.tkre qpjpo o;, x the log move in the opposite direction?q0- ;e. -jjophpxuo0t2, rjwk

Why might your foot hurt if you kick a heavy desk or a wa yhecri 99 po,6jn76uben9b (kcpw n0;ll?

  When you are running and want to stop quickly, you must decelerate quickjuj2i; 8sq*,d / dd puaqac 0l2)or2bvly. (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 persodq,ap;j uuv2qb ojl2ddc8/0ar2 s )*i n running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sesc8nsju(yx g6o/0ee + 5q ms.dction of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a sloycg (e 08ssm +ds5u/ 6qoe.njxw and steady pull? Explain your answers.

The force of gravity5zz xc:-lmmt s-3rrj3 on a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesnj:r3tsm-zx- rc 3zlm5 ’t the heavier rock fall faster?

Would a spring scale carried to the Moon give acch,nucj ritj,czq:00 ki b42+ jurate results if the scale had been calibrated (a) in pounds, or (b) in kilograms4q,bj 2+c0, i r0nj thcuijk:z?

You pull a box with a constant force acr(p9 b1vg0nxd h ;sef9uoss 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 td f9gshu01xe(9vb;pn he table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a nbr) 4. j.ifcazet 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 doe.j)rc 4abfi .zsn’t the Earth move?

Compare the effort (or force) needed to lift a 10k1eky2eg :bgw* 89 ayl-kg object when you are on the Moon with the force n b9l8k2 :y aeggkwye*1eeded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a t.9 i(vecmyz2 qzl89kkm/ 4zlbug of war (Fig. 4–37) pulls with equal force on the other team. What, t4b kmzc lm9ki8(z/z9e2vl y.qhen, determines which team will win?

A person exerts an upward force of 40 a;b:nhkc ly91N to hold a bag of groceries. Describe the “reactib9hl:yc1; n akon” 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 onhtwvis xbr31e18el 8( the ground, how large a force does the ground exert on you?3b vtwe18er1 xhs(8il Why doesn’t this force make you rise up into the air?

Whiplash sometimes resulty i8qjv2;z:oyfec -h (s from an automobile accident when the victim’s car is struck violently from the rear. Explain w2y ivqyzhej(-;cof8 : hy the head 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 acceleraxvns o,a xi5e5qhv20w;eaqu;(: cnhj1,qo( wtes, the crate remains where it is on the truck, so it, too, accelerates. What force causeu;: a;(1qawqi,, x5hno0qvc o ns 2w5jxhv (ees the crate to accelerate?

A block is given a push so thd:k2o3c t3mzuat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its ackd 2utomcz33 :celeration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on +ue+-hnuf ;,xk n:xte an inclined plane? Assume the mechax+ekuft+,n :e;h uxn-nism functions properly, even at an angle.

  What force is needed to akca aa xiktmq(:6vv.8 p6,8s mccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bs)q*cjf)wz 8 zike 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 withse:q9h p:(dul6xrvm brq8kbxy .e;9- ztand 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 x9dx-0d( 4,lwglvo hp $76-\mathrm{kg}$ 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 stogb3 +rkqgedyap5n 7)e :xr:j/p an 1100-kg car in 8.0 s if the car is travep+agg:jy7r):k eedb5q /xrn3 ling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to /9(x xuq 7ol:z;mc b9yz k.fqe125m/s over a distance of 0.800 m along the barr/ckq: zeblx7xq.fm 99y;u ( ozel of a rifle?   

A fisherman yanks a fish vertically out of th;bj ngax5e y 4qm1ym(*e water with an acceleration of 2.5 e j*mn xqyagm;(b51 4y$\mathrm{~m} / \mathrm{s}^{2}$ 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 0 otoh) ojg3gq ajd+,3dld07ptrack (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maxif lf 9oy/hy(51d bg3xgmum acceleration is 0.0680 g . What are the maximum and minimum forces the motorggfo/bxdl53( h9 yfy1 should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When tha,hdb -5pl87vjlv6h f e elevator begins to move, the scale briefly reads only 0.75 of the person’s regular webl7v6p,h-lad8 5jhvfight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 3; awf.i1n 3s fz dglqb5;uv-a2125-kg elevator has a maximum strength of 21,750 N. What maximum u-l. a5;vdab;1szn 3wfgifqu3 pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fal3 9epwqa x)77cov;amdling sky divers (mass 132 kg including parachute) when the upwardoq v3cx9m )77p;a edwa 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. Whenr-ebwuw( e qs9) d/tb, he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excludin(9, srt/ d) qebub-wewg legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically eq-izvu;v4c k:e(9(xw*mijf, 1 eln gupward over a pulley and a weight is hung from the other end (Fig.vii: g-, z1*49q(cxwe;f vunj eml(ek 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 ag2ldrnd itp l:m:+e0w8 p0 rm- basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momentcj,q5:wt/ /y xtwgea 7 it is hit by the bat, and again (b) after it has l5:wtw qyc /ae7x/tgj, eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directi .tu /1u.zkzo)g.ghxlr4( ycqon. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diag /qh.tz rczulox.kg(u.1 4y)gram.

  Arlene is to walk across a "high wire" strung horizontally bup2yub 598 lyoetween two buildings 10.0 m apart. The sag in the rope when she y2yl opuub598is 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 hangiq6mb7fg/5o k9ou*oy/ c 3 fqnang 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.u zvs,sou)0sq gy,77 y0vh9et0$-\mathrm{kg}$ 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 McMurdo Base, Antarctica,kuc/k +a-a 1ys as /a c-kaku+y 1sshown in 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 pullinu ms7q/dy (fa7ro+u x.g two cars of the same mass behind it, Fig. 4-47 . Detxf 77+/oua(rqs d.muyermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus shown igr+nz0sr/(- dpv )j brn Fig. 4-48. (a) How hard must she pul-p/rsrng j(bz+d 0r)vl 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 begai)c (,6m3y jsolo+ huoutgv9n6*dit7 n, 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 (9h0ja*8sin xu gog1:k 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 fric9vqw,t) o5nmfoepr 9q9(b86hsi v tn7tionless horizontal surface are in contact with each other, as shown in Fiw 9hb, m)7to5qie8vrf vpo( sn69t9qng. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially uvq8y0t8in - aa;g(k.yi.e fk 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 velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pfyi.(y8at; gn0ukqa 8k -ev i.ulley.]   

Suppose two boxes on a frictionless table are connec:pqp* v;b ecplu p t+2j9y-*hpted by a heavy cord of mass 1.0 kg . Calculate the acceleration of each boxp lv2thyq-pp:* b+c upje 9*;p 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 friction9: sh5 wjh6xix 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 re80ijkz m mb,q)a ydhlra kpd;9:fw+2,quired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What mxjby;s9 ()2vl n 7u4y4dj ielxinimum coefficient ;x slxd(l4y4b j)jve72 nu i9yof static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if tok d s.er5lt/8he coefficient of static frlokt d58.es/ riction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber4pbg*fs *of+ 6t ow h:rc(nk5z and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a cas5*f 6h4prot+bn :ow*zf ( kcgr 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 pp+t z,k9 -7cc0cm, m1fdz5qr mlprz5 -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 on8 esg1 :ol/qku 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 an asphalt surface have a very high coefficic9mtb:x(x fw +ent of x9xbw f m(tc:+static 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 frica2*cnc6 te sth mbvt-p e-*5i5tion 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 w9c v3i x;ry(ssould box A have to have to prevent any motion c9rv(x3ss; iy from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across mm ,y2ou)o-gf ;x hen;the floor. How far will it go, given that thex2-;hfyo gun,);e mom coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , as,x2r bq9 b.jvs*7 mxjre in contact and at rest on a horizontal sujq .j*s7brsxv9b 2x,mrface (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 carryingi m9fo h0tn.j8 a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver c 90.tni 8mfhojan decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which hfr4p xl3ygwj95dol13as an inyprd jwl39fo5g1 43x lcline 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(kb/5 j ukp3gqod.7-ceim* od 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 o g)yjg7e o7wsm0u -gi9n+2bhmn a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spezi 3s0y azv/1ped 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 t9fd twhlw 5+kdf9xr7-wz v2* uhe 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 so1)ad.ee+ hprzw n/60d*h gnk+vn ug9emeone pushing on it with a force directed upward at +dpzv.hgne)r n *h0ekdung/9wa+ 61e28$^{\circ}$ 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 projectilzjv :uxdyt7av3/nc* pu r h040es as they melt. Consider a chunk of snow at the:hpatu30j0x4z nv y7rdc/* v u 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 spee6 ez3/w r tkx:jn0yw9ad ken3w96/:wta x0rzj y 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 dashboard of a car slides for zn(t*7)ps. gysf0dd wward on the dash when the driver deceleratestsgdzwy 0d7 *pf.()ns 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 mashb)5-+cziq6 jkl):oyza*jgg rppz 04 s m is 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 thj.v8jfgv-h25 j-ria ley are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is jrlif2 vj5j-gva h 8-.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 kineti f72guo4q-whvmno.9v c 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) can coast dfs8:xp3 7ea rwown 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 *(mo+gxyh z o8kf0c 8va mammalian heart, at each pulse approximately 20 g of blooxc8 vh*o+gz om yf8k(0d 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 reasonabphf / cu,i uo+5k,+(ja oretg,le chance of surviving an automobile crash if the deceleration is no m+,ohk,pucegji a/t5 +u f(or,ore than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration pwir-cstr .;hh/y7 ot/9j5g g k8lc/v yroduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the/w87-t/r.yghtyj/s c ikr; l 9 vgcoh5 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 akc ldf (x/xv)p/2kx l(n accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement/xk xk/(fcv2(l p) dlx is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 (t 9-xcurs/vqq 83nvnhill (1-in-4 means that for each 4 m traveled along the road, the elevation c9r/vns(8u nqtxq -cv3hange is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from thuwan 11hk4 3chhf f4co.d89r;zg ffp+ osa18k e top of the Leaning Tower of Pisa and falls 55 m bekco3+ff8rf .z 1p h4;1hcsgao8ua4hf w 19kndfore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but uh3 p,v h*0tcuenters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy s0vcht,3uhpu *tretch 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 hilly portion of a city. An imporz .t;8ftek 4vqueh06lo4/ nb htant consideration is how steep the roads can be so that ev en ho.tf8;4 /60e lqubtkzh4ven low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch fromxs)o bir 055qt a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that t xqst r05o5b)ihe 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 connea d3)cy; gn4ngcting different parts of the stordc ngg4y3na);e.
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 ) ugi8a3bvgytmyb0,jm7 /b (tb , sing the pulley apparatus 3i,bbb(tm78g,m va/ b0 ygtyjshown 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 d- /2y8 xkh(xsj6urz w8 vz1zzat 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 engineer considers thev5;xr wz( a k2nv:rn,l following set of conditions: 5na ; z, wxrn(vlrk:v2
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 I9e gq21e p6 r1 z67ja9j i31rai0cced wc3mfuwtalian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and K,p o wzd2dgul0cr )i765w qt-uaren, 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 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 c )g0tl6q5oupu-2 rwz,widc7dlimber is more likely to be hurt?

A fisherman in a boat dxz9oqy +bg5+6xt veez aw29z:j y* .yojr9q2is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed odc0 quu3*u+hp f 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 k9 ogb0:k,yex an ice field inclined kxe0,:b9 gy okat 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.