Why does a child in a wagon seem to fall backward when you give the wad+dn:g in 8*t l3pgk;:li ie)ogon a sharp p;gl+dple *o i83g :nnik): tidull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts t:tbwy bts/y 8)he truck and accelerates forward. The box immediately starts to slide toward the rear of the truw): ysttb8yb /ck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of /wx cb;.nmz6can object is zero, are no forces acting on it? Explain.

Only one force acts owc.nrv ,l64 lgn an object. Can the object have zero acceleration? Can it ha.cwr 64n,lgvl ve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force gn9f40 gy8+ hyey7gh * k iframll8(k0needed to make it bounce back up? (b)yef*4 ( 00hr98glgkfh8g ayi7y lnmk+ If so, what exerts the force?

If you walk along a log floating on a lake, why d (.x*ndas4t raoes the log move in the opposite directi . atn4s*drxa(on?

Why might your foot hurt if you kick a heavy desk or a wall?tjh*+0lfrjc9gvt9t2 4 cnf o9

  When you are running and want to stop quickly, you must decelerate quickttadcyfk v( 6s54 6xuh- uzt0:ly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usintuxuz ctdv6ah6 t s:5(- kyf40g 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 thr2spjt08d:x- : oyuo z-u6 xkcjead 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? What if the person gives a slow and steady pull? Explo y:-2u6 ut xd8sxj0okzj -p:cain your answers.

The force of gravity on a 2-kg rock is twice as great as thatk,m;m9yvbsg3h w 0u ,;zu:rhx4wy e6v on a 1-kg rock. Why then doesn’t the heavier rbv;,gw :khx,;0uw mu hmez3y6 4yrsv 9ock fall faster?

Would a spring scale carried to the Moon give accurate results if trmhcr/7vb 4-o- : kmqdhe scale had been calibrated (a) in pounds, or (b) qdrr/-b m-h7:kcmv4 oin kilograms?

You pull a box with a constant force across a frictionless table using an attacnc/kq1rl s1hxt e )8zvm.*:crhed rope held horizontally. *:teh)n .c8 1mr/srvkql 1cx zIf you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely unlycz)b 5* 4dnpder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposzy*b 4 pd5c)lnite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed tbsx-ma)7*qlc 6d au7io lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Ea7 7s)uacx di-blm*q 6arth.

According to Newton’su1)1 +feklgad third law, each team in a tug of war (Fig. 4–37) pulls with e1eg1udk)a +l fqual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag83pkwoar ; *wx of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, aw8 *xwa3kro;p nd (d) by what object it is exerted.

When you stand still on the ground, ho awow c*)f)vyh:/gh2nw large a force does the ground exert on you? Why doesn’t this force make you risvo2ygaw:n) / * fhhwc)e up into the air?

Whiplash sometimes results from an aut9bgh(n31paj t omobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this sit193j( gt hnapbuation. Is it really?

A heavy crate rests on the bed of a flat i-8)iyv hwn;abed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelera) i8yni vaw-;htes. What force causes the crate to accelerate?

A block is given a push so that it slides up a 8ignoljxnfb2p8 z7o5n p/f02ramp. After the block reaches its highes7n /2 pgo5nbon8f 0xfzlpi28j t point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom srbc*u8kozz ,bsq .i88knv: u1z3l;ua cale read if you weighed yourself on an inclined plane? Assume the mechanism functions pqa8n l,uzrs 8o v;c : b.ki38*buuz1zkroperly, even at an angle.

  What force is needed to acphy(jrkzr* 7b l, b7s3i+ ryzkm68rrj3(;fbdcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridezvq) jze**-rxiss hx ne10k3 9r at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a r-jeb-mif5n-y .- ax 4ny3kbgtope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a bn bjhnvsjl-b9-52 +c$76-\mathrm{kg}$ 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 11008crpl/l+o x 1g0q so9e96 mqtt-kg car in 8.0 s if the car is travegp 8s l9 6l0xo+o9tcqeqt1rm/ling at 95km/h? -  

  What average force is needed to accelerpzgr64h 5q2 mgk 7n8saate a 7.00-gram pellet from rest to 125m/s over a di4kn5q8 2pha6sgzmrg7 stance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration r .o +2cziywafgm)0 e4u0q2/yvheti 4 of 2.5 iiev)ty emo0.40cfqg22h ry+/ zauw 4$\mathrm{~m} / \mathrm{s}^{2}$ 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 avd ovrh s+6xr(r/y6l. 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 t dutae 9umww;4co7.1 oo be designed so that the maximum acceleration is 0.0680 g . What are the mawtum7au. o;cd91e 4w oximum and minimum forces the motor 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 bathdzkdpz70a(2 p4j3 us +nno;u oroom scale in a motionless elevator. When the elevator begins to move, theu p27d3 0(okosun+ ; zdnpjz4a 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 elevators+iyq zg: p0h7o1b-pn xwqr m(o8e 4a8 has a maximum strength of 21,750 N. What maximum upward acceleration can it give xiwp8p:m s 4e8qqg-7+ayh orb1o nz(0 the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falliw;e h2i24 vkthiz /*-smocm. dng sky divers (mass 132 kg including parachute) when thedcmsh *;t.i hiko2mev/ 4-wz2 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 (y*;g7 smwv ovm21 )cszo a4ekhe strikes the ground below, he bends his knees so that his torso decelerawcg ky24)oszaemsm v(*;7v o1tes over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests qb7+6hslr ad5 on a 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 the db +ah567qrsl 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 basketba.wl d4n t3rb9s l:i-izg/ y1iull player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body ddy - :4rfxd0zhiagram 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 thd-f 4zxhryd0:e outfield.

A 650-N force acts in a northwesterly drio 0ha0lipv(uy *7k uu1fb .7irection. A second 650-N force must be exerted inh7 7a*uoir0uyfbl0. kp1vu( i what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally jxpjko)r,7)z8s 2 pqkbetween two buildings 10.0 m apart. q,)pzo)8pr2j x 7jksk The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket iso ky jauxy17:g5we 4d/ gu6/pg hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 148s-7u)7nk, kx 1ljpiy 0htyxu.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, ecnf)bp/5,eiy,w 3gq Antarctica, as show,gfywb/ 3qcip ,)e5 nen 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 pulling two cars of the same mass brv/eu0 id 9ra;ehind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweenu r9e/v;ari d0 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 tu zryva2o26 , bx3y)gx.emg:a he bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed:y2,v a ozube3 ymg.xgxra6 )2?   
(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 bega;u zr++peo0 zajc-jo7h, lfn1n, 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 (mass 59alu5 f*r lkb t32zyl$ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact withyrnd* wcpe / *4je2t*z each other, as shown in Fig. 4-51. A fec2n4**ydp/ twrj*z eorce $\overrightarrow{\mathbf{F}}$ 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 thei6t9co ;g h4 x;/dfgopx y/:hj 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 the6; idx4yofjgxo// ;t hgc9 :hp 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 ardnf3ns xde:n uy-mr.fyr32 +2e connected by a heavy cord of mass 1.+uddr.nn3f n- frmy232s :yxe 0 kg . 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 kinetic frictiom xt1 1tw arjb2p,e5-wvnd*l -4 x9dljn 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 requir (j74gyot(dd ogv +r-led 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. Wha0 49xoaxyf5(p n6myslt minimum coefficient of static friction must exist between your feet and the floor if you are not to slide y 4y x5l(x0o9fspm6an?   

  What is the maximum acceleration a *iyb wjsq iq*6/5j.tc car can undergo if the coefficient of static friction between the tires and the ground is 0./ 6wqb*ii ys*t5jc.j q80?   

  The coefficient of static friction bdlhyk e8,2 kja d3xcrymb 4px7+wk.: ,etween hard rubber and normal street pavement is about 0.8. On ho3pr7+jd 2x y, m, xk:eckklhaydb4 8.ww steep a hill (maximum 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 atug 2.6 shntabek,-p i2 -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 rox:ftl12z5)ocf s+8jms rzq7 df ug41xugh 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 a12 q9 ss+v w-kvciagj7sphalt surface have a very high coefficient vgs12kaq+9 c7jswiv -of 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 kin04idp339iyr uh , flznetic 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 4-20zortst5gf w2m73 lcnu.2h 55r) how large a mass would box A have to have to prevent any motion from occurring? Assum.suf5to2l3wn5 tr7zgr5h 2c m e $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will ool u* wba-l5*it go, given that the coeo wuoll*5a- *bfficient 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 horizt4 k:lio1tkb2dl0 go,ontal surface (Fig. 4-ttol gkb,k1:i4d0l 2o54). 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 njgh;r(1mst +klcd7 /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 driverk t( 7 r+cn;gmlhd/1js can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car uunyl522 ft. odk 92cbin your driveway, which has an incli 52yblc.un2f29k tudone of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a twj z:5 s,e30ydsrh,urlm e8, 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 /m-ulifl) ct9 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 x uf+r x5lr1kmy: c2+pspeed 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 bwr ntljk*70jn7x g9)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 ind*cc nr ,v3 8ypchw0y,- w;opt place against a rough wall by someone pushing on it with a , wo3cctdwch0y; y8-ppvrn * ,force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous proje;xd 9ongfgl 33ctiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of93 d;gnfl3o xg $ 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 aute e bj37; y/vg0syvk(bomobile traveling at speed v is /be0ykg;vs(3 ve y bj7equal 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 6ti tncvhy;y )7w4) cna car slides forward on the dash when the driver dec6wcycni4h )n7 ttvy;) elerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speehrtd/2 a5;n7r2ph7.dt p 0n ,cyufb hw3ubm-ed $ 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 ared8;o4edrcqze*0ts- c ;.zr fo 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 the 4;frct0- ; .*ez8dqzoodesrc 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 coefficie6)k lbfm *bls.nt of kinetic 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 (includaof -ax sajy/53;o3gz3. qpm xing 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 modu5ub7.6vq xs7c ve4rfel of a mammalian heart, at each pulse approximately 20 g of blood is accelerated qc6s e 5rvfv.x4ub77u 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 automobile cra/r5w ae8 uk(xlxck8f,k-tk h,sh if the deceleration is (kth8lekcaf ku,xxk8,-/w5 rno more 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 produced by an e- 3iq 9gzkf ug. 2fk7jvms4:qcarthquake is a , and if an objec-9v 3s.cqmq g2:ufj gz kkf47it is going to "hold its place" on the ground, show 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 investigatorssni5), i md0tp, examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estiii0psn m d)t5,mate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means tngkfv skyct ()r,p j2fw3k)u2a7 :k 8that for each 4 m traveled along the road, the elevation change is ,kf( 3t 7 pw kf8kc)vngy2rsj:u at)2k1 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 T;f9x8t8: p 2(mhpd1brh nzrwf /ou p7lower of Pisa and falls 55 m before reaching the bp( h hm :p8lr 7ox 1np9f/d;r28tzwfuground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at 1ltrm9lq 7.beibc:y0 a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist ee mi91qbl trl c7:y.0bmerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. tefs4l ;g(mfyh6v)/ n An 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 small car, with a mass of 1100 kg , can accelerate on a leve)g/hn ty ;sfm6(lefv4l 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 physxas+ w 2,ligp4c4i9wsics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes offa2 4l+p4sgw,c9ii x ws 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, thce:9b -s ;,fbvoip vf(yc 1r3dere are to be several ramps connecting different parts of theeifr(:sf39 dv-,c; c py1bbov 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 liftubokyd jk5:1 55 ,absv the piano (mass M ) using the pulley apparatus shkv5y 5bs ojd,u:b5a1 kown 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 accelerac+ss i1 n4pz7+l-fum)pot 7ngq*jv .rting 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-restraint chair, an engineer considers the fpo.ly5:f wt;so8** duald ;s rollowing set of condititodaf8ou ;ys:s ;pdl**w.r 5 lons:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660ksdmeca:a/, (0 l u,u2mze)sn,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, use8ps69 pft jlbi1yi4: acc ;lwj,v knj0oh/8k+ 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 hicl :yf8, v/n0k sjaip4t8l 6ih91 kow pj;j+cbs weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is a )gymzcm 1 uco20:p3rusing 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 all9ry, t ot*xqb,49s zrqowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an iceyo9afw/6lp4n field inclined at 6l/ wp anyo9f421.0$^{\circ}$ 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.