Why does a child in a wagon seem to fall backward when you give the wagon a shqg 0*t f;n0lxxarpnxq;0gl f0tx* pull forward?

A box rests on the (frictionless) bed of a truck. The t j. lt47 wvx*ahn/9-azic5ija ruck 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 box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who iwax4/.* jz av ciji5t-7n la9hs riding on the truck

If the acceleration of a f) / 9s9oj.ky3lqvbcin object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object hav-5xxx*ci xy4 ke zero acceleration? Can it have zero velocity? Ex x-*i 4x5kxcyxplain.

When a golf ball is dropped to the pavement, it bounces bhd1i,+ha a4miben-by* u -c- aack up. (a) Is a force needed to make it bounce back up? (b) If so, what eu4hanayc1e,* b-+ -i-d ai mhbxerts the force?

If you walk along a log flu hmg * 6g9jpl8gkoo9 h0)bm5foating on a lake, why does the log move in the opposite direcfghmk g8poo9 m9b6* )0jglu5 htion?

Why might your foot hurtok-s e(6h)l w31 ap5tiuwn jgx j7mz,)wis;-u if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, yo;y jam4c8lzq3hv/ st7u must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experiejlc ;hz y /vt7a3m8sq4nce) 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 ceilinc:f6lntyodk l(/c 1gf b 325zpg, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a/6bckyf 3p ldg 1l:ztc(n2f5 o 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 on3om n -) tn0xmc6mtlr- a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall f nmn6t- lrc03xo-)mtmaster?

Would a spring scale carried to the Moon give accurate res:jo-q y:miq bq22-xjlults if the scale had been calibrated (a) in pounds, x imoql--j2::2qqbyjor (b) in kilograms?

You pull a box with a constant force across a frictionless tav u5u3 ci0f -avib/z;.2wdnuuble 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 the acceleration of the box (a) remain .2vfud iv 0u- cu/z35uaiwb;nthe same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gram(i19uindc,(4 a s isbvity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law ,bin9siu1id(sma 4 c( 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 10-kg object when you auk/md5gyw,xnu0rn0xe -3/kqre 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 oyde 0gxn-3m,ukk05ux/w r/q nn Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls taj3) - wb1kjasn1jzh:ui a9 ,with equal force on the other team. What, then, determines which team willtb-z ijhk3a9nwsaj ,1 u1):ja win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desiihp7 awvk94lx5/f a/cribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what oblwx5/f h/aip9 7avi k4ject it is exerted.

When you stand still on the ground, how jxwm/2sfk4 o;tdy,1 i large a force does the ground exert on you? Why doesn’t this force mako;yi ms1, 2/wkj4 xtdfe you rise up into the air?

Whiplash sometimes results from an automobile accidektfq.( kz7dx0za;wn/ r gni :6nt when the victim’s car is struck violentlyzwn r zk.qtgk 0fx(6;d7 :ina/ from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed hmm+xy 94 -hqoof a flatbed truck. When the truck accelerates, the crate remains where it isqmyh-4 hxo9+ m on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up i6nezy:bdv g::t7en9b6k 8l5k7akzddff + x5a ramp. After the block reaches its highest point, it slides back down but the magnitude of it :t 6:df5 alefkk68zg 9n:yx5k7devd+z7 nibbs acceleration is less on the descent than on the ascent. Why?

What would your bathro ka12-jo6s mhg,,mywojc(ug 1 om scale read if you weighed yourself on an inclined plane? ,jg (m au1swmkc1h,2yo g j6o-Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m.k-tib :*+8rbml tlxz /s$^2$?   

  A net force of 265 N accelep u6ts g,3rucr6*4cnv/ne/r prates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to ack1tdb/yjf)(6s buq,yle ro4+ celerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a cyk; 9f)kp xnt* t42ewg/ h+bm $76-\mathrm{kg}$ 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 s eg +n +g8;0,vndkdd u4i3zrpn3m8 givtop an 1100-kg car in 8.0 s if the car is traveling at 95km/hd8g g,+4vi3vngnuk+ ;emd038dpn r zi? -  

  What average force is needed to ,5 uk+ ujuvh.urw(cvhg7*t t1 accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.*+. uj,tc ug rv1uwk5v7hh u(t800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water wij4 1fldm.cm)skob04c th an acceleration of 2.10cmlj 4mks.d f)4bco5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile track (401y9bba w-kql, 2 $\mathrm{~m}$) 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:) ,cxhb8ism;jo/ya i that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppo c: hx/aij,bmy;s8io)rting 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 4ys s1)mfv0g tj-igi; elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration v)0ss ;j4mg1yt-fig iof the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg xjck verv 2l;( : 16vkas72vflelevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breakikfer;s2v l(xv:j67vavk l1c2ng?    ( two decimal places)

  (a) What is the acceleration of two fall2 ev k)wg fn.-z0mze0ling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth ofg00n. ev-mzzkl 2 efw) 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 sx-q k qdt qb(6xil- :4.3vijnhe strikes the ground below, he bends his knees so that hisq qsnxdq-4kx(3tvjli- 6i b. : torso decelerates 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 on a table. A rope tied to the box run9pv-kru*vuxcw v..e0*pys ;ds 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 box if the weight hanging on tc0*u- .v. xyur *vd9p;vpwek she 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 basketball play rfc6 lh-z6 i65i(dbiopy (n.xer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a basebu4v,g - p;nm x:a7.gegr :jreuall (a) at the moment it is hit by the bat, and again (b) afterr:. r:nmevpxa4 -g7,ugu ;ejg it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fkh37lzsv *bzv 0 l9 w+mlt1tk.orce must be exerted in what direction so that the resultant of the two forces points westward? Illus+0wvl7s llbk. 9tz1*kz3mt hvtrate your answer with a vector diagram.

  Arlene is to walk acrozz3g+sh(bav: u; pgx.gui+lqr *p8q4ss a "high wire" strung horizontally between two buildings 10.0 m apap uxlv*pq ;b r+ 4g+ zh3aug8(:igzsq.rt. 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 is hanging ch odt-2x2xwf :;futp.u7j/tby 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 1q10wvp kb;9fo.zqb)i 4.0$-\mathrm{kg}$ 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 r+m2 j2in ml:wat McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the i m:w2rn2jml+ 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 ih9( mq jtl43 7b xnxslpqjh9)g 7c3.yds pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the 74j9xqlgdx()ml7.9h 3 yjp3hbn tq sc locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus sho9 tybwx/:mw 2oj(a/omwn in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at const:mmj2 (/o tw9b yoxw/aant 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, a g4)g( i37ydnq4yz eqz 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 (e v ;gxxa3w rs5ry,e(2mass $ 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 surfacewhn;i(dd qm ( w7rdsnlpzo /*c+5y,/l are in contact with each other, as shown in Fig. 4-51. // (rwnom dil7s5pnhwly+cd zd,q*(;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 the ground,),q j 7z 57hkrk h)nojtgw7)qx 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 determ7t jq)x nwogh)7rhk)k5,zqj 7ine 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 z6mw)fxl gi3/u4c-c s cord of mass 1.0 kg . Calculate the acceleration of each box and the t3ci 4ug-csw/ m6xzlf)ension 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 kine c0t/b94)gt5ss y tgdntic 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 b5fhxelm9 w7-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 i t7 icpzt p;1o,oze747zr-hqon a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your f7ez 7coot p ;7 ,r4phzi1izt-qeet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coecmzxxvh: 3e2, fficient of static friction betweenc, hx:m3vzex 2 the tires and the ground is 0.80?   

  The coefficient of sta4u .)2(ew wyy avtw+hptic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximhy(utw4)a eyp.2v+w wum 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 at se qiyujx+f5,x .s3 j.+r(xtg -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 oms:aojw /euc b4k 2/98sfk7ajn a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with anbx-y u;6igz/,xkn bd- asphalt surface have a very high coefficient of static frictixu,i;- /yxd-bg znb 6kon.

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 kinetipfqkl1i-97wcgfbn-k0bcz* b/iv e 82 c 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-m r95nb(j,na5paz d v932 (Example 4-20) how large a mass would box A have to have to prd,a5 bn95zr(n pmva 9jevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it n3ub. f y6kaje:a,gm o.-tno8slides across the floor. How far will it go, given that the coefficient of kinetic frictie- nfk ma,u tao6 o:j.nbg8y3.on is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg wl yg2z ceqpfi73+ *p:and 110 kg , are in contact and at rest on a horizontal surfaceycw p +l2*pf3gz7qi:e (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. Thq.,u h2y*jtmve coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the dr*yh q ut.mj,v2iver 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 in your driveway, which has v y;vwfal0z0ggw 7me ,yc56t0 an inv00c5 ma,6ge wz7l wy gy;t0vfcline 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 sl4 hl/cl ,,f.lww rvipfct6v+9 ide 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 ti2 t1-h4lbu 5lhc 5ibpjfyl+ )dlted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial sw u7ww+u- ;qbipeed 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 steepesldf9sf uj4t3e4 1-;6u n-c tk5q frdent hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it wrrd335*u ugt q1mx t/rith a force dq3u /3*5 udrtrrxgt1mirected 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 pl 8lv hi3;ylqkt:w*h+rojectiles as they melt. Consider a chuit l3w;8l: h*hlk+vyq nk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance wk)ek1dn(h7 r for an automobile traveling at speed v(kke) 1 7dwnhr is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drive7mhyn- + d2z-.dv tfz1a d/xhaomx/v/r dece/yfdzt.d h av-mxhxom 271/ vz-n/ad+ lerates 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 38rpltoz,dv3 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 conveynq k; n4llfl*6sds.z1cjbj1 9or belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static fb 9lj*1jn6l;sl1n4d kf.s qczriction 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 dw we3z/fhkvs7)s(7l 4 s jiv-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 (including the bicycleim:2udo.ha,m ov*q-o) 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 eacia5u r(x wx/*)nhvb t0h pulse approximately 20 g of blood is acceleratedix*wnu/ x) vt5hbr0a( 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 q85j0z s .veksof surviving an automobile crash if the deceleration is no more than 30j8.5z 0qskv se " 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 z1e r8t: nzvw).vutohzc33 a )produced by an earthquake is a , and if an object is going to "hold its place" on the ground, sovvh3rwz )z)ent u81ac.: z 3thow 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 ac:8xc1-5m*vn jh l3jt3hhq evqcident 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. Estimate the initial speed of that cq*8t5je ql cv3hm1h:v - n3hjxar assuming a level road.   

  A car starts rolling down a 1-in-8l //.thxas dlhml03n4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it h3. slx/ ntad0hll 8m/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 -lj vt,ne-sft:h df5+ vmy3 f/i 4rxj;ctfj7( the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What wrsv,(e-3jntj:f h v;f 4/ftdi-y jf xcl75mt+as the average force of air resistance?   

  A cyclist is coasting at z (-r1akkf2dya steady speed of 12m/s but enters a muddy stretch where the eff1z-fayk2k (rd ective coefficient of friction is 0.60. Will the cyclist emerge 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 portio6ocx7 dovvv iw+)bai;:( ub:i wtl:i. n of a city. 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 level l )dwiiv:7ti vba .iocv:u( xo+ wb;6: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 experiment+ m3mr 4x99vey/su)vl4 hsafuixez;(s, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the stel; xm u4+shmu3ei/(axv )y z4s9rfv 9ring makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting differ flq)mi5i 174ul: cxnyent p7n fylcm4 u1)i:x5liqarts 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 forc1g s ixewo6vsn 6yd-a;(fuy3)e F is needed to lift the piano (mass M ) using the pulley apparatus wxudys-a6iy 3 o;sv(f)6gn e1shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3.5 vy3)jluv1suz x*j4 :v$\mathrm{~m} / \mathrm{s}^{2}$ 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-res,og:os pna7 zspvq 1(5traint chair, an engineer considers the folo:z(5g qsa7opv, sn1p lowing 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 train has a mass of 660 met3cwc-j(7 gubj +0vy;- pefqylric 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 Kare,t60lf n7t:nbvn.(b ywm/h yln, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climyvnb.h(wl ,0t/t b67fnly :nmbers. 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 x;4+s 0hu/ay cjtvnz u0k)b;y is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall buildi9 e-a-x-bm n1ua8woe63 j hjlyng is allowed 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 whq05u+ bgoeryqlc27t 2z/b:i k*.mp oz o are roped together are ascending an ice field inclin tuorlbz7. * kqz+eig/yo2:b2 5 m0cpqed at 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.