Why does a child in a wagon seem to fall backward when you gozhuh1f:9 +cm ive the wagon a sharp pull+huz:f 9com1h forward?

A box rests on the (frictionlebqo ag9 3,ey5.cijsw. ss) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the b.bioq5 3 gs c,yj.e9waox, 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 actib fx3d c)hs9xlg8-4n kng on it? Explain.

Only one force acts on an object. Cl: jc l/k-czd5an the object have zero acceleration? Can it have zero ve5czl-kd lc/j:locity? Explain.

When a golf ball is dropped to the pavement, it bounces bacf-iy*v -2wjhqk up. (a) Is a force needed to make it bounce back up? (b) If so, what exertw2-qjvfi * y-hs the force?

If you walk along a log floating on a lake, why doe81er4y 1 xiii,3qgnwt s the log move in the opposit4ixig 3t8 qew11r,in ye direction?

Why might your foot hurt if you kick aw.s(f5pr4rb u heavy desk or a wall?

  When you are running and want to stop quic5zr /eep, qto4kly, you must decelerate quickly. (a) What is the origin of the force that causes you to /o5erz qp 4et,stop? (b) Estimate (using 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 sect9e :;0u9sxu r shx,notion of the same thread dangles from the bottom of the stonx:09ous ux eh9r;ns,t e (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 slow and steady pull? Explain your answers.

The force of gravity on a 22hdhx 79wqzv3lk p7mj5)( a ss-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rm(5z39xdqhsjv) as7lpkw 7 2hock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale had eam-jh 2f8pf; been calibrated (a) in pounds, or (b) in kilogra-28jaefp ;f hmms?

You pull a box with a constant forcefjql ycp:iv2 ,9hya2( 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 fvi(ap c29yqj2,hl: ythe acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freeufesdae3zz gh+ xm:2 wp34c5 .ly under the influence of gravity there is a net force +fe.3g 3hmd wcea: 5u2szz4xpmg 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 move?

Compare the effort (or force) needed to lift a 1;uc8 f 6kx:uevob.yl50-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 obje.v8b: xloe6k5uu; cyf ct horizontally 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) puloxdc8kgoo; d5q2:l n o)m:w9 qls with equal force on the other team. What,c qdoln kq8m);o:w:92ox god5 then, determines which team will win?

A person exerts an upward for. (0ztkdbw -iorg;(n6khoki g0w(8gece of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object g.o;0n60gkht(ewwk rog(( 8-bkid zi it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, e;) lf)dj gp7:x70oo cbswbl.how large a force does the ground exert on you? Why doesn’t tb )lwp.oceo7j;bx )l 7gdf: s0his force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the a3os;4ezzzykv : 2 7ukexg/u 4victim’s car is struck violently from the rear. Explain why the head of the vi/ ;s2g ezvazkyoe7kz: xu43u4ctim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on ti )6 ( xnepmoa/p/k-pqhe bed of a flatbed truck. When the truck accelerates, the crate mx ae o /)(q/6pipk-npremains 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 s*itn46v9wdr f2:ti h it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than 2s4*rhw dttnf6iv9 :i on the ascent. Why?

What would your bathz8 gppzk- 4,bproom scale read if you weighed yourself on an inclined plane? Assume thezk-, pb 48gpzp mechanism functions properly, even at an angle.

  What force is needed tdeaoir9j dbvxk5c5- -xv ,28,k ug i+to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a,n*(u-j;w , kmay9x(mejzzxknd 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 it is used to accelerate a 968y0 ,1p1pftwy2 akiyv0: gpbwa- b sy,0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of52e8 q7i,jruv a i7zke 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 car is tr5+0- e5tm( e,f/byz n naov:,dnydtlhavta b fy5v,l0e , nmh5dt:z+o/nde-n(yeling at 95km/h? -  

  What average force is needed tasefygj2 8szc9m( b6 0o accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of 9(me f 2c8gsa z0ysj6ba rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratio2mfog29:nlbze2 +f6obb :+oeuyvmr;n of 2.56uom :l f:b9 2;2fmeno+obegv 2rbz+y $\mathrm{~m} / \mathrm{s}^{2}$ 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 covef o17nwj(k1;nbec k b8r a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratb(ner +-2imyy ion is 0.0680 g . What are the maximum and minimum forces the motor sh y2ry ie-m+nb(ould 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 texc;k g ,2 hoi2;m/zfzhe elevator begins to move, fc ;/hkg22zz;x,o imethe scale briefly reads only 0.75 of the person’s regular weight. Calculate 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 21,751; rdagmo7/4vh6x fr l0 N. What maximum upward acceleration can it give the 1gox v6dal7; m/r4hrfelevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sk(mo2h(s,n z v0fuye llvwtvf/:)xb ;;y divers (mass 132 kg including parachute)2xzf vwblhemto,)(n;ufy 0:( vs/vl; when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground 5oe 9yl/ m3* .-.itnfparjw t*l+whvebelow, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding lwm-tl3npr 9vi5ol ej. ft+h*ya/*e. wegs) 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 tv8ze:ko)x(1nxl rd4qe2 ;+uej3 k g tkm fk3)uhe box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tablejkr )fk31voxnek m )uxzu+ege24q3k:8(;t dl 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 diagra gkyi l7:lae3 d.taf 593ndmw7m 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 diagramal-uitk-x ;5 w of 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 owxta--li ;k5uutfield.

A 650-N force acts in a northwesterly directigj q:vrj;(c-hf nx 1-ptkd75ton. A second 650-N force must be exerted in what direction so that the resultant of tht fjc75qpvd1j(h kx -n-:;trg e two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acros 1pl 4lm;*ru*uborzwa46: fhos a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midp r fohwlar*bp 64ou*mlu4 1z:;oint 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 cord fp.q4(y qs7 4u;ui uya)zrk hc*rom 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 14.04j:wgo9:r at,6 hto nc$-\mathrm{kg}$ 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 5elsj*y /6ohxr 2kd y7via/htdz3+s9new location at McMurdo Base, Antarctica, as shown in Fig. 4-46.63xts heh/ir5dk+ v79/2 ol*adys zy j 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 pulling two cwpo38lf/hi f 2ars of the same mass behind it, Fig. 4-47 . Determ2pffwhl38i o /ine 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 usis dh)io g7;h5*nvva r1e0tfk (ng the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spev571*ovrt) a; (s ehikh0fdnged?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6/tm()k-ub w ktl/ 0e)ye.a tpv5$-\mathrm{kg}$ 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 (ma0ygdi ;xgpbw2o01v al(2 - r9mxtz-fass $ 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 areyah ssrd 49vf b7mp 2;c2;e4 p*ftd+np in contact with each other, as shown in Fig. 4;rh+ csbnf2t 7p4smpd2v49ypde* ; fa-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above/+xhz*pefr b )dfgkpcf3(m - 8 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 thc/g bde (hzf*p+r-xkp8m3 f)fe pulley.]   

Suppose two boxes on a frictionless table are c;+ e ofz +/+cojzmy1zeonnected by a heavy cord of mass 1.0 kg . Calculae+/fomyo j ;c1z z+z+ete the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction ben,dsadr7lez l .4fe1fx/- p3 ty47jdatween 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 star qoj a2(twx0n-r;szc 0t 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 i o;.yf++ebl12g* ej ja* sfbsat 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if yo ;e+sfbsf+ya** go1 i 2lbje.ju are not to slide?   

  What is the maximum accelerati j lal5a(6cv0dh(b j uoqtp50jm ,z)8won a car can undergo if the coefficient of static frictionl6h0bzv5 ucwjjm 0((lj d q5at8 ),apo between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemen/. +y6pg pn4 pd,v2juh p0lkdet is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?d dnegj.kv,p0/ hup4y6ppl2+   $^{/circ}$

  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 -+0 kibd gy;pg04.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 30 -m1y m4fv.v(m.elh kx$^{\circ}$ 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 vgzn.o- qn/k1wqhtpe( ob +g )3ery high coefficient of static frn.w k gzbo 3q(og/nt-+ph q1)eiction.

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 fri +a+ mvsrk:9bcction 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 larg.e pv::abodn, e a mass would box A have to have to dnvb .o,:eap:prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fag*x7tr7wkqr cb l5x buf :l6zww,;m.;r will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an iw rl7;lrw:t gcxm w ,uk;b67xq z.b5f*nitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rec3jo6tth us2ccs2 0j5st on a horizontal surface (Fig. 4-54 2hcc5us 60js3otj c2t). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of st+ffa-et sk k5 sj)x.l,atic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerat sfl 5fjt)-skk+,.aexe and still avoid having the crate slide against the cab of the truck?   

On an icy day, you wovl y5)j: dproa/2w2s crry about parking your car in your driveway, which has an inclin2dpy)2c:/5o wja lrsve 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 sl9+g:cfzlv fxi1y njutb:/,;xide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an angler)ufs 6dmm13 r $\theta=22.0^{\circ}$ 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 3.0o,3m u8.p sm)c4oxr xv $\mathrm{~m} / \mathrm{s}$ 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 ti+6p u4y zj gf90iede e.gl1n 2;s8otphe 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 agai s.;z1za z cvb,ll.ynfvrv7 +5nst a rough wall by someone pushing on it with a force directed upward at alv; bl7.vs.nzyvzf ,rc+z5 1 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles asj: 0 zek4mfkw-6-lq(+/or1g 0; a rx scxnnaus they melt. Consider a chunk of snow at the ridge of /q l rwnkms g(k-00cx61-e xu ;af oszan:4+jra 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 di0,p o3 idewl/f-rm/rqapzo+5 stance for an automobile traveling at speed v is equal to dwo-z0oq +/i5,/e3mfpalrp r$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 forwi+vf:y pa0/go ard on the dash when the driver decelerates from agyp/fi0vo+: 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 sx wq4hdo 46+kmpeed $ 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 koin3.ui 9*xa6/w.- sqb taeo filled to the packing station 11.0 m awa6nb xu- .wo*i qso3./a9 atekiy. 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 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 frio)33:; j;wsxuxyt-wsnr p d,fction 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 down a 6n(g hr ca3bl-+ u b9k2 ,x/fm*zk8pudx.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 heart, at each pulse approximate8pxkfgnd0r c r2q 9afqj(,n*9 ly 20 g of blood is a rxgq0 (8* 99dpjqa2,nfcnkrfccelerated 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 osf vi dct7ync4(/)3 pff surviving an automobile crash if the deceleration is no more than 30 " vsffc /ty(icp43)nd7g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthqgy,m-* e2 njhi ,)gqmhq( )(yuraw.l auake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of statigq (iynh gm,ahqy(,mj2wl. -ae))* ruc 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 an05ejh. bj u0bs fnq8u- accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficie .5ue0usn -8 b0fbqjjhnt of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fo9s+0oal:u 2 fyl9hahp, a3sf er each 4 m traveled along the road, the elevation change is 1 m). How fast is p f+2h 0 yas93,h9souleaaf:lit 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 the top of the Leaning Tower 3 hr--)u-l*8 svx kb dhwmclik; 0y9okof Pisa and falls 55 m before reaching the ground with a speed of What was the average force of vsm -*ro wl-dc3 0bh ku;9ykhi8) xk-lair resistance?   

  A cyclist is coasting at a steady speed of 12m/s but entersvh dk oo o7u5912bs6g7.d okwj a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without ko do 1wov9o77hd. 65jbg 2ukshaving 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-qiqd i1i ll7+kyybe21vm+ f - hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get q+ikylf il1ed2- 1 -im7qyv+bup 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 wa .f0 m-t5vhqd+2la ra)zy ev(ytch from a thin piece of string while the jetliner she is in takes o-rv 0l)mtf2e(hzay qv .+ay d5ff 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 sbw nq9 412 fnz( a;fkhhg-,vdreveral ramps connecting different parts og1h9(nkfrb- wq ;z,2v and4 fhf the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass Mgd3 mmsjwt- ww93t/+l ) using the pulley appar tsd3 /3wt wm+jwlg9m-atus 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 axa0 p+ 9hqqhss3f 4s(qt 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 engineerm too/p8o : 31 2*n1sy1wbanjxbd/n a5vw.jmv considers the followiosj/pm :w b1m tav5j2xn1wybn*vo n 1 o38da./ng set of 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 traiu4l -nsvne:f yt,)ww;n 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, use safety ropes of similar l 0kvee::j *eck.i4:n7srnmgfength. 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 w:nkrifje 04mk:: evs7.ce ng*eight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-oybx,4.bgkch o3g+h 51 $\mathrm{~b}$ 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 bvzccc(u,*j 9a 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 arew2 n ai8yiuy/;x+a yas 21eaj4 ascending an ice field inclined at 21.xae ian14+y/2uayyw8j; asi2 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.