Why does a child in a wagon seem to falmo m59xv57kidy58 1- srpvu ifl backward when you give the wagon a sharp pull forwa58vi5f7xp1i9rmv s - moyd5k urd?

A box rests on the (frictionles( 2n g; gx8rlr0uij8(sheicr-s) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Dghe jsrci8;r(0rxiun28l-( g iscuss 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 an object is zero, are no fo a9 0m*6q8f, uh844mkddelv e tssh-wmrces acting on it? Explain.

Only one force acts on an object. Can the oyoo*0k vh+u+1nou ; blbject have zero acceleration? Can it have zeu+hl+y o o*uko vnb10;ro velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is ah6y9obru aq*p0kc :f 7 force needed to make it bounce back up? (b) If so, wh f*70b9karo :6qcpyh uat exerts the force?

If you walk along a log ksqc r ew8tzycc-c+h1+ 3q 4*ffloating on a lake, why does the log move in the opposite dire-3yrc 4ckh z c*cst+w+18qqfection?

Why might your foot hurt if y-u 38srynf,g *i.cssdv ;ea)nbm1yhq ob:4 b3 ou kick a heavy desk or a wall?

  When you are running and w72j ;0qbvfn5b6axi :w9 mgu hcant to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to comewq70 b9icjh6;u5vbm2gxaf:n to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of thc cx wbt2l)d19e same thread dangles from the bottom o91 2b)dxwctc lf 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? Explain your answers.

The force of gravity on a 2-kg rock is twi4 au v(+ tytjws:tmn-*,*u oqvce as great as that on a 1-kg rock. Why then a*nvy4-st+ttqvmu(ju*wo :, doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate re-,c9 nrpncmuh2k l(b;sults if the scale had been calibrated (a) in pounds, or (b) in kiloccn l9kr-;uph,2b n(m grams?

You pull a box with a constant force across a frictjj te a68bxf p9.x7zy;ionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the p yx ftx8b679jz;.aje table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the id4bpw ; 0lw+q*ugo yd:6kge0 rnfluence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object+*;rg 0kw pw 0yeuqd bdg46lo: 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 ar -8 lostuax)v5qn6+ cle on the Moon with )ut6ca 5n8ls-x qvl+othe 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 Earth.

According to Newton’s third law, each team in a tug of war (Fig.:u yj eu-p20pj 4–37) pulls with equal force on the other team. What, then, determines which team wypju0j:e2 up-ill win?

A person exerts an upward force of 40 N to hold a 0v)c 8upj(kcs bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on8vkjpc 0cu)(s what object it is exerted, and (d) by what object it is exerted.

When you stand still on the gro m(3n7ak 2zpehn+ry.zund, how large a force does the ground exert on you? Why doesn’t this zre nmh7a3 zyn p.+(k2force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vict 5kxnhzj:y -mj6:sinw( kp. 49wwbbi6im’s car is struck violently from the rea. bnmx69kh i4j- (kwp 6bnwj:5zis wy:r. 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 of a flatbed truck. When the truck accelerate (0-v uoufjl-v(ite 3nu cam02 yc38cys, the crate remains where it is on the truck, so it, too, acceltfv3u(-oy3i 2u0(cc0 j-nmae u l8vcyerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. i 5ac:wo4v j() cvr p-yj(zxe:After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on4r:5(i:xc o(ejypazcw v-v j) the ascent. Why?

What would your bathroom scale read if you weighed yourself on atx/bj w +:e( 4xsvro)sn inclined plane?r/wess)t :xj x4(vb+o Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled uv; sm:2j(qdy at 1.25m/s$^2$?   

  A net force of 265 N accel i)g: ;mng2xrzerates 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 i:pb9kgs xtmw/.j45s pf 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 x.u2xlg :eh:s $76-\mathrm{kg}$ 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 requmuwv8;16;kf) qeb6ql t*r5bee w 7aflired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h?wb 5wba *l)mt8 6 r1qekfuee;vl ;f76q -  

  What average force is needed to accelerate a 7.00-gramu jjcrh2z 8b4fp,o /*wzput/1 pellet from rest to 125m/s over a distance of 0.800 m ro p1fbczz/8ht*/u2 ,4juw pjalong the barrel of a rifle?   

A fisherman yanks a fish pqmp-l/:iu )i vertically out of the water with an acceleration of 2.iiu m)p/: lqp-5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (+ wz0e96r /kedrpqkjyh;wf 2 (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratim3yth* . iv1nvon is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppory h v*m1t.n3viting 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 mot 3,7n1 khfxsp7gyqfr -ionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acce 7nhqkf7gpx- f3,1 ysrleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevatfzryh ;9*5/u otsh.z vor has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevat r. / zs59ht*zyhvf;ouor without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 1b7ysjh:b 934 h,+k 6nynvl mdw32 kg including parachute) when the upward force of air resistance is equal tohl39 wkbbd:y+4sh6vjym n ,7n 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. z7nun,ox *sy5When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 n5o*, nxsu z7ykg, 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 ta09kznnxv. )jsble. A rope tied to the box runs vertically upward over a pulley and a weight is hung from 0kx9n j. zn)svthe other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball f1nrmuq.+ oh uy n(4d)player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is d44zvd rv8(cg hit by the bat, and again (b) after it has left the bat and is fly (dvg484v zrcding toward the outfield.

A 650-N force acts in a northwesterly directio28xj( vfuw-mtmzsk+,wg; j / .egvx8yn. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illus;uxvz(8m. -wg ek xfg28smj,w/ j+yvttrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizoglz)k /;1y;kzsz f78gd de.vrntally between two buildings 10.0 m apart. The sag in the rope wh kgyddgrek;/zl8z f7;s z.)v1en 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 by a massless hayl6+rtku v*a94 g1xzxz7( h 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 14.09;bv1/qakg7 sgpgn - f$-\mathrm{kg}$ 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 locy38v.i s,g e6s 0vvxqkation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fe,qs. vsxvgv ki68 3y0orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 carsgn *d.3bu7i* 8aywj y4z:adei of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling bedwdjez3a7a gyibui 4*:8*yn . tween the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the buct 5rb4 l d 0wce.f(ykc5w*d,.c s5fvhiket-pulley apparatus shown in Fig. 4f h, 5yd0c5v.kdbsec c. 5*i4rft wwl(-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, avznn ,2agucx*4.d) qw 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 (m ndh,.b4v):wf djg r 5wozvc(:ass $ 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 a2yurxe(6 5 mjk ,gij.)enw rx*re in contact with each other, as shoj ,2xmi5 eegn)ukyx j( wr6.r*wn 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 1.80a,;f(3 xel i c0+;rdcdx,ncl d m above the ground, and t,c+dil r,xe(fa dc dx3;l;nc0he massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionles7 wu,kpmn9xn(s table are connected by a heavy cord of mass 1.0 kg . Calculate the accelepmk xw,u 79(nnration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a umi15;a9k0 (6vfqjliz u6os;/theow 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 start a 5,tjkzr ws shs.u,, d+).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 traihe *gvi+l6e(.1 ody.dy io96v)y g ynysdj08pn accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor h*pv189l sode y +0)nve(ydydygogjy.ii6 .6if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffx6d+xgzrgp j7c8+: myicient of static frictionc p6d+xg z87m j+x:yrg between the tires and the ground is 0.80?   

  The coefficient of stat(4ej5fy/a 6jd), kkjdy.e md kic friction between hard rubber and normal street pavement is.4m kea)kd, dkj (y6jjfy5d/ e about 0.8. On how 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 nb(hm3vif k16 at -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 30cc j91s hxw)4g$^{\circ}$ 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 contqn(-nb qol )fz .5p-ugact with an asphalt surface have a very high coefficient of static frictio- 5nf-n .blqo(gzqp)un.

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 kinetxwkf.du.w,8l; 6,3zrvhp uuuac89bl ic 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 wogq w)(i.5faz0f)n hd fuld box A have to have to pre)0dfg q(w.fnz i5a) hfvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across d/3gm,i-p,e0 kfxbgg the floor. How far will it go, given that thekp0 d, xggbe/3f-, igm 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 1c3nhr.wa(i vu wv* +2)y yo7ab10 kg , are in contact and at rest on a horizontal surface (Fig. 4+y(b2.w3 no7 y warc iv)hvua*-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. Th5kn;eg vvg(a16ha g+ce coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate aa+51hv k;(g6ggec nvat which the driver 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 f8 m+ .pxv:uu.o8f xegin your driveway, which has an inclin8: f u x+vo.mexp.8gufe 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 .:4p swc 0a yu;d4aygjslide 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* v3c4ap yr c*zoup7p+. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of q uk58m*nknv;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 o4j--5yoaqw ch f 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 fk c; nrds-g ;)qj1jg*wall by someone pushing on it with a ;1jd*; fjrc s-gnk)gqforce 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 projectiles as they meltu/,k*,q ;2 vv(x/ymrjzurw pq. Consider a chunk of snow at the ri,/k v(muurwq*jz qp;x vy2/,rdge 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 minimum1+ygrmo k mci3dp7ik4-:up9 l stopping distance for an automobile traveling at speedckd: 1prymi7mo-i 9 p l+k43gu v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a ca:fi:0d,tqv 35ol 8vup cuwei )r slides forward on the dash when the driver decelerates fe vi:,cpl8f3d ):0 o5 quwuvtirom 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 initiaf9yor67xz(l9o0ke s s9z oahaigg+8 / l 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 whe226n1a lzxx 4ne8 krsvre 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 friction between a box and the belt is 0.60, wxas1r e 28xl n264nzvkhat 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 frica3nfx0aan d5 -s2cdj:tion between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a egaa-h*;*e- aa y 4; zdmkt/e-gk(tjr 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 approximmo3i bkbof3q 5a1a9.i ately 20 g of blood is accelerated from 0.25qob5 b.13faai 3i km9o $\mathrm{~m} / \mathrm{s}$ 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 crash ig4, wjfznx0w 4-aub2w f the deceleration is no more than 30 " g 's." Calculate the a2 uxzn-4gw4f 0 wbw,jforce 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 by01m1 wp w23h. p ldcx-*zl/lv hbhsx1p an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at lea -/.l 3cp*1hvh1m 0lbsplzp ww2x xhd1st $\mu_{\mathrm{s}}=a / g$ . (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 p)( e15s uuj4r)lsj xlof an accident involving two cars, measu )s14uxjp(jlre)ul5 sre 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 car assuming a level road.   

  A car starts rolling dj 1wtustb,ab 8lu aetuje 3,7,-8x9reown a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after ,s8rx e7-aubbjuutw1ae9 e 3t tl8 ,j,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 81py6.g-gyijgl5o xq sp5wy /Tower of Pisa and falls 55 m before -gqjp/g681 yixl wo.5gyy5s p reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady spg e28k8o):vl 8eiz nwdeed 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 mud lasts for 11g2i)8 zd :vlek8owe 8n m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a2k- na8sd)v mgwq*.dsoz6 s1v hilly portion of a city. An important consideration is how steep the roads can be so that even low-pd1qa ns-sg. 8dwsz6k*)m vv o2owered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piece c4s/mal0fwlm w --/iv of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She noti m4-wmli/a0v/l-cws fces 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 ramps connecting d)u* +u uab/bzo yrza:3ifferent u+a:/r b *oybzu)za 3uparts 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 to lift the piano (mass M ) use+49slaackpo. wk,-kxb9 ad+ing the pulley apparakx., 4o wcela+kb a+9apkds- 9tus shown in

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

  A jet aircraft is accelerating -el+1 ibb7 drxat 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 enyt7:9 g34daq;;b z)lggi p xhzgineer considers the following set of conditions: ltg hyg) z47dxpag 9 zq:3b;;i
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 o/eve7 2ebm4y ) zbsj;hf 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similarc1 apf.3. d1hbtx7xm ,m.witd length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended3d.1b,.hw xt1t fmxm7. cpad i 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 " 10hei6y:o 3 ie*v-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 h( bx /hhk5)udbuilding 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 who are roped together are ascending ac-iif(u ce4 i1:h3h agn ice field inclin(h ch1c eiif3gi4: -aued 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.