Why does a child in a wagon sqebk-o yoy f1e-8gd02 llqr5c1oj jc o+.p-g7eem to fall backward when you give the wagon a sharp pull forwa7ok-p- j1 +20odecrlgf yooe q- lg1bj.c5qy8rd?

A box rests on the (frictionless) bed of a truck. Th j eb cdq(pv94,:v*tale 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 bovl q*dvtba:ec p4j 9,(x, 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 obj v6( o2h mxxum4zc:x , 8tbse9n4jwc)zect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the objectzdtm fuz f4)y*xu-lo3n4t tcth040+ g have zero acceleration? Can it have zer3ctt t df n+l )ghtuz*0f0muxz4y44o-o velocity? Explain.

When a golf ball is dropped to /2v(a2 p(kh2j ycdmp lthe pavement, it bounces back up. (a) Is a force nee2j2laky(hc d2 p (mpv/ded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why doe7n 4kfna52ue:cahx. u- .cx zms the log move in the opposite direction4:na 7znu. . kh acmc-xx52euf?

Why might your foot hurt if you kpu wpmv-9l2 (aick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceq,2u upa0i js,lerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your su i,pj0,a2uq 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 fin+z( uu+(ahsw ye thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it?a(uzwu(yhs+ + What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kay3 c-fwe a5k7g rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rocaw- fc ye573akk fall faster?

Would a spring scale carried to the M x rn1gx6poo.o eukne.(la. b/72 ;jyioon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kipen .u oix(yrj .geoklan 6b/7o.;21xlograms?

You pull a box with a constant force across a frictionless table usi lt2mdym:z99q ng 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 thdyq lmt9m9z2: e acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity ther5qgm34j688ckch h k dve is a net force mg exerted on it by the Earth. Yet by Newton’s third law thec k84g8jd h5ckqv6h3m object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (3fa3ck9 f t -ji.o0m3txmzih 6or force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it a0jz33-3mih9 fttk f xi6m.oc 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 tug ou.f c71cwl9jpcaa8-3ba mfu 0f war (Fig. 4–37) pulls with equal force on the other teamajafl1c8-7mwcu a.bu 039pfc. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desceotc w um02i7(k)l4sn ribe the “reaction” force (Newton’s third law) by stating (a) (c4noemi7kwus0 l2)t its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand stillt q-77z 7aplep on the ground, how large a force does the ground exert on you? Why doesn’t this force map 7el p-q7taz7ke you rise up into the air?

Whiplash sometimes results from an m (6rnm.yj +1pwuy h(qautomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backwar+ p jm6rw(qu1yn(.hmyd in this situation. Is it really?

A heavy crate rests on the; 9mg dwqouf;7 bed of a flatbed truck. When the truck accelerates, the crate remains where it is on theo7;u;qf 9dgmw truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the (l a,f2cu,fd * fkrijfnk8:jb*e30 exblock reaches its highest point, it slides back down but the magnitude of its acceleration is less on tf,d*a n2xj8 ui0(j*f efec3 lrb:k,kfhe descent than on the ascent. Why?

What would your bathroom scale r8fiy cb6 b hih; nynxr(i0,ukt6)3,yt ead if you weighed yourself on an inclined plane? Assume the mechanism funythn6(uii06ti xhnf)y8,rb3y b, ck;ctions properly, even at an angle.

  What force is needed to accelerate a child on a sled )8bcqhg.4qq6t3zpzp 4 hru. z at 1.25m/s$^2$?   

  A net force of 265 N accelerates a * s.w g 6dihww l6a3w14iihk.sbike 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 it is used to accelerate a 960gt 7 jv;gihm+yx9xo46$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of avr)a/r9 1ptta*b noj* $76-\mathrm{kg}$ 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 requirz o.+lqd r4d;.kib 2psd *jg1hed to stop an 1100-kg car in 8.0 s if the car is traved*4d.lo. 2rk d1+j shgq; zbpiling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125 ;a 1nhab8sbc5m/s over a distance of 0.800 m alon5 a bsncahb81;g the barrel of a rifle?   

A fisherman yanks a f8 pcvhrz: v 3k/cqb2.i hjj+i:ish vertically out of the water with an acceleration of 2.5 8icz3 q+ vi/h2kr.h :pbcjvj:$\mathrm{~m} / \mathrm{s}^{2}$ 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 covebt p+/1(8 5 /gjazjnfj;jcxj qr 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 dev,pq9lyl z5ixxby rt * 4k*6)b;tb ai)signed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max 4tly5zbbvb9ilx)y ia r ,)*;*x6 pqtk =    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 or b+zqr+x,dn nm.x)9 in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleratir+o,n.n m )x9+rzdqxbon 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 21,750 Nhzzh sb2;dzjh 6 (7qt8. What hqsd6 (7 2zthh;b8zjzmaximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass8vs, u mx/t6nyux - (m,j8mr,ln x1ork 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of t ,kn/rrs(8x ,ujn utm lmxy8,61om-vxheir 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 groun nwq)5.t-ktnb* kf8sg ax j)h9d below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kgt n8-kgkfqjh *wx)5 .bnt s9)a, 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 : 6f-/gql u4szhzbk c0a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on t-qc:fz6k g/uhl4 zbs0he box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a gjre1 qf5 51txx,.wrc 7cr7llbasketball 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 o ue8g*v*w,a vq;q :bnvf a baseball (a) at the moment it is hit by the bat, and again (b) after it has lv b8uq; g*w aq*nev,v:eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. d/u h2nj20rtt)lie +zz :h8qs A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate s +02iht)2 nr:8/djlzqez th uyour answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally btrr au +220zcsetween two buildings 10.0 m apart. The sag in the rope when she is at the mr+aur2 st02zcidpoint 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)f 6tomudp7.q9+w nd g/b5fck 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 14.0uaimb* 9)qvwn zo3,grs)x : 2e$-\mathrm{kg}$ 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 Baf m sjmlh3**d5se, Antarctica, as shown in Fig. 4-46. The s*m 5*jshmd l3fum 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 cars of the same mass behind it, Fig. 4-47 . z1jwa ,/u.gfn/jp b5aDetermine the ratio of the tension in the coupling between the locom/pf1b5,aj z/.jwug n aotive 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-pullehiisi 8wh- 3i*sng5 d;y apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raisdins-iw5; 8i3hg*ish e herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, :icx/mq5nbc p2tn i;4f inw3qxt +)1oa 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 bv r)3kr2 jhxr-lock (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 fricn1i yn8xkj 01ntionless horizontal surface are in contact with each other, as snykj1xi 018nnhown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abj,u(qjt x 70-odve x9sove the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height x e9- uq70jvt,(sdjoxdoes 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of m*hl 4tos*-yzjue3ia3a8 2fg yass 1.0 kg 3zy gay4fjt*2 a sl u*he-io38. Calculate 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 kinetic1c vtc3,eou 7gj;* xec friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to starqn3vjfkz) i+2+k by, at 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 acceleratin lx+g59bpl *dtg at 0.20g. What minimum coefficient of spdx9 t b+g5l*ltatic 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 coefficient of sdg*2 ilg ;uubcgz46l1ut2 i1n /1qibjtatic friction between the tires and the groundin l1 qjtbdi*gu1 b 42; /21cgi6zlguu is 0.80?   

  The coefficient of static friction betwe5e/re1q ur 7azen hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum qrua/5r1e7e z angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate 7t:3s bqqoebt( qn-2 j9t;jc jat -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 )m+cx*q 6j bup 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 coeffici 3ri 8votww8ccq56f/z ent otirz/5c3q 8w 8o6vfcw f 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 kinetv.roaq 603g paxt,;q pic friction 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 bohc.llt:brdlt-xrx 8(n -d2w4x A have to have to prevent any motion from occurring? Ass84rlb-wxdc xl-l :d (hrt.n2tume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the :qa +i-7o7es4h ydq2wjwy y5nfloor. How far will it go, given that th7qq745y:n2 oywe ya shj- +idwe 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 , are in contact and at rest on a h6vch,-k o5 rldorizontal surface (Fig. 4-54). Avklo6rh5,-d c 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 static f05s ikchne2t4 riction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoihkn5 ci2s4te 0d having the crate slide against the cab of the truck?   

On an icy day, you worry abou1y 4t/suzu+-y*xhuzhf7 + ibrt parking your car in your driveway, which has an i-rzub hix4u+ hzy1 su *yf7/+tncline 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 withe5d gem6lghkng-/ bm3en2g. m4ko77k 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 oys-mh/.cpe7f n 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 inicg ewa r.(n,j 87 h,o5bawl-aztial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of iv2a*hu 98b 7 c4jkzko6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone push/-c6d/2t gqmc tgh +gjing on it with a force directed upward at 28 gm6j gdt/q gcc+-/th2$^{\circ}$ 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 as twjjs si,drkukb* 4on10u)l*3 hey melt. Consider a chunk of snow at the ridge of a,i kw30 ujknud)j1bl *4rso* s 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 474ec i *om)fqtzwee-aab o* 4speed v*4iwa 4c7oe oeqe)ztma-b4 f* 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 dashboax-d; ifvp6.pild14ib rd of a car slides forward on the dash when the driver decelerate.-i ld v1ipi4xd6;bp fs from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass;b(ql*d phq nav7hy3 ,57 fjgf 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 they are tylx gs) n,4dx 7+efy: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 tteydn4 yxsgl,xf: )+ 7he 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 friction between *nqr+rk9t+zkq hv6waro .u- 1 $m_{1}$ 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 (incizg,+4tb+gtla )w.g v luding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse appr z-s.lewgx6l w7,,n8dfkv 0qv oximately 20 g of blood l.s6 wvqnvg0,dexl ,8w f k-7zis 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 aui8y*gu8c2vweu tv ,xl,z+ 0ymtomobile crash if the deceleration is no more thanz0y+ ,,cu*txv8 m8yv2geuwl i 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquakepx-ymk5t0 ,/s x/ pwyy is a , and if an object is going to "hold its place" on the ground, showy/x,w xy-0yp5 tskp/ m that the 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 in 9ns).lxjfxz0 volving 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 is about 0.80. Estiz.)flxn 9 xj0smate the initial speed of that car assuming a level road.   

  A car starts rolling down a 19f e8k2j wim /96gtxdt-in-4 hill (1-in-4 means that for each 4 m traveled along the road, th9t ktfx9jg w8m/2i ed6e elevation change 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 the top of the Leaning Tower of Pisa andq a7n 20f5oudd falls 55 m before reaching the ground with a speed of What was the average force of air resisd u 7fqna5o2d0tance?   

  A cyclist is coasting a8no0; hnobg *m) gnrf4t a steady speed of 12m/s but enters 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 )ngg;o mbo8nf hn4r 0*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. Anxd:m+5m - gogk important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular sgmog:-5 x mk+dmall 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 e0+4 xame d/pmfiss-y,xperiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airporfsp- ym /0+dxa4emis ,t (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramp 8ub( sw,d -3pzo+iszrs connecting different pbi+su8owr3zp,( dsz-arts 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 t t-5-wmwy8-t dfn)gt qo lift the piano (mass M ) using the pulley apparatus shown inm-wwg-df5tn-)8 yq tt

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 acceux:oal17cwhw-x*y;+z p pr7blerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraibz; 37*6wsbzazv9 fxqnt chair, an engineer considers the followis*q3 z6b9vz7b zw;x fang 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 Ir4sotqmuwi 59k6yp30*gx - grtalian 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 Karen, use safex+wz ov/;jqy mcxubowq38,21 n z7he +ty ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climber+xzuq;we ,qc/oh87j+m2wvbznyo x13 s. 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 climber is more likely to be hurt?

A fisherman in a boat is using a " 9ajfikm f(.z 6k6p v1h 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 e,b a8,g2a3 ftk gjnp;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 togethermu ewtcr 95 ns.:g)a-;kqx 3vc are ascending an ice field inclined at v9u)qca- ;xe:stkmw3.grc5 n 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.