Why does a child in a wagon seem to fall backward when you give the/i: lcz9h-xcy* xza-o wagon a sharp puxoaxc -9y z -c:z*ih/lll forward?

A box rests on the (frictix4h+p 53d/xt yv icf)ionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary stan5c/3vyxd) hit x4fp i+ding on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Expla68a,ohxl7zv1j) ghp vv (lcx -in.

Only one force acts on an object. Can the objda72ceqg ny9+ect have zero acceleration? Can it have zero27qnae+9c ydg velocity? Explain.

When a golf ball is dropped to the pavement, it bounwj /;:u -8szflkt 4cfyut0bfh+6. pjn ces back up. (a) Is a force needed to make it bounce back up? (b) If so, what ec fh u/tf0btw 6 -j4f8k yznp;+.ulsj:xerts the force?

If you walk along a log floating on a we)h/ ,wra1mmbhiq49 lake, why does the log move in the opposite direction9iw)bwr , m1/mhq hae4?

Why might your foot hurt if you kick a he ,tu t-uisvz+pj22ad v9p8iv2avy desk or a wall?

  When you are running and want to stop quicklybcr.-1(w6 q s:crint,6gqce r, you must decelerate quickly. (a) What is:c ri nrwb6c(csq ,6t.-g1eqr 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 come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceilinjl) )gf2h(z+tkyu 0 fsqq7a+eg, 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 dgfy+h )ksfj)0a q (e 2qtzl7+uangling 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 twice as great as that 6;zze yedh hs;vl y,lo-kbwl;v /2 ;5yon a 1-kg rock. Why then doesn’t the heavier;-l5hs 2yl/ ;e;dyozl; zywv6ke,vbh rock fall faster?

Would a spring scale carrjjjj a-.q) ,yjied to the Moon give accurate results if the scale had beenj.)jyq ,jj aj- calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force7rbl8- a6pcv ic1s( nz across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (61vcicln -pr7a8 s(b za) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravityo -.6*+ nrhjbrcxc67ly lmj x/ there is a net force mg exerted on it by the Earth. Yet by Newton’s +l76n oly/cj6-c xhr x*mj.rb third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-*f jg0d vcdu,0kg 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 hor*fdc0g,u j vd0izontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a sig h+duwv1.nv88i 1 ztug of war (Fig. 4–37) pulls with equal force on the other team. What, then, detei1. 8n uhvvwi1gs+d z8rmines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe 7 f lbn7 9e-frm4e3yc mxobm.6the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) lr embb67xf4 ocm.9y -mn f73eon what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how lz.,0+5mk lydkps jid 5arge a force does the ground exert on you? Why doesn’t thi zilk j+5m 0dpkd,s5y.s force make you rise up into the air?

Whiplash sometimes results from an au:u imt )s q0czl--sus5tomobile accident when the victim’s car is struck violently from the rear. Explain :mz-l)uqsc i05s- ut swhy 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 flatbed88k *rvihu afex1qklh +() j2t truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. euh) qjlx+(8fh *i av8 1kk2trWhat force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blocg0,9jmbztv/ q n;e*t 29np5m) wgnpqzk reaches its highest point, it slides back down but the magnitude of n99;*m / z2zqgqn)nbvm, t wg5pj p0etits acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclia 0v:y*76v)xzn+ qq/u oj zjbnned plane? Assume the mechanism functions properly, even at an avznjqb7/ x 6 0vzn*oqya:u) j+ngle.

  What force is needed to accelerate a childwz-xa 6ckmm 07 on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike andm2 *gylx *72q8 :jra. oyavimc 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 f;yr1lmk 1f;w5kt)mrf 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 3 yfl 68c1ev 1u.bce*ksa1jx,-uq x fz$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the t b7a-(q+n ojrcar is trave +n(arjotb7q-ling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from res: fxc3sxuz+w:wobc 36 ,zxu 6mt to 125m/s over a distance of 0.800 m along the barrel ow36xzu mxbuz+ 3c,o:fscx :6wf a rifle?   

A fisherman yanks a fish vertically out/0if 7mf )qlar of the water with an acceleration of 2.qif )a0 /frml75 $\mathrm{~m} / \mathrm{s}^{2}$ 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-cuzo+ap rj*r an.449w mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum aco p6y-scr7pqq*v + 1bnceleration is 0.0680 g . Whnb q1opr6+qv- p*cy7s at are the maximum 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 bathroom scale in a motionless elevator. When the ebix*0ggu ah- 8ygyb/ -levator begins to move, the scale briefly reads only 0*yug-hg0 /ib gxy-ba8.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. lbq -aaq eltcc , 99aju/gv*-0What maximum upward acceleration can it give the elevator without breaking?0* qcj -e9u9lagt ,c/va q-bal    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 k ,t4egeqhry-g ci ok ej*w5y:w ts0*,(c-,cjkg including parachute) t ye4kt-i h r sgcej**w,yc(: ko-5q ,ejgw0c,when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roo q tqyrv14l3f7f of a house 3.9-m high. When 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 vyrf3tl 1qq74 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 rop.ph4t-(wbw a sor9 qe0e tied to the box runs vertically upward over a pulley and a weight is hung from the other end -eq4wp w.hr t0aob(s9(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 basketj 0tgme)3pm1s5 qz dx:ball 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 ((f; l/oz9grzqa) at the moment it is hit by the bat, and again (b) after it z(qfo/9g;z rl has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A /h3e5+: jlsh9si sao ldh7kk 3second 650-N force must be exeek9as:3slild3 j h 7/kh s+oh5rted in 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 betwm zkr7y68 4qdmeen two buildings 10.0 m apart. The sag in the rope when she8dmy6rk7qz m4 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 coq ah6k e9dy dzudb-s2; jbmkcf. e54/9rd 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 1423kw5iqcp/zp-ih +xb .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, Antalodt5b8 ktg:oz,b jqr8q40 fo -;wsw 6rctica, as shown in F5w 8qslofqtd86;4 -jog rbbk:ozw,t0ig. 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 bep3ci9 m.(ywqghind it, Fig. 4-47 . Determine the ratio of the tension in the co3wqm.yci(p9 g upling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls h/qf;j 0:txiz4y 7d adrerself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull d7ti jz:fqr; 0x dy4/adownward 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, a(w d79efxfab,vcxk 41 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 block1u n,9p3wks3im 2uwb(bqzk 8 kk8eub) (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface d b/ ll;ars.v.are in contact with each other, as shown in Fig. 4-51. A fo /.rvldl;b .asrce $\overrightarrow{\mathbf{F}}$ 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 injv9. fuii7y8qitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then iifq9u 78jv.y 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 heuppp+ ;23ta5o4gc iyiavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, uopp;3ay ici24ut +5pg sing 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 5f3 fim-o;qp 87 hs gng0pxz2n35$-\mathrm{kg}$ 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 g47kdo.y8xweq,g i(t 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. What minimum cof zr,9*p qljn1rpy;+b7p3d pmefficient of static friction must exist between your feet and the floor if you are notnq ylbdzp,* 17 p;p9rrjfm3+p to slide?   

  What is the maximum acceleration a car can undergo if the coeff5pcm;: qitm;t icient of static fricim;: ;pm5qtt ction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and norm dd)-.jo qpm0fal street pavement is about 0.8. On how steep a hill (maximum angle) can you lefqjp. d)-do m0ave 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 -4.8qs-p5a o9r2pn 0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 :si /jfd1svv5na v-a530$^{\circ}$ 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 wi:wp)dx2;b;w8v y7wkn pn 7 wjcth an asphalt surface have a very high coefficient py;:pc7xk)nvwwwbw8;j7n2dof 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 kinetic b2ra piu;al47 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 (Examy5b*of(* upgx ple 4-20) how large a mass would box A have to have to prevent any motion from ocyp** b (uoxg5fcurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so thag)54ea l :ojg 0 84*iz si:x4cgcbfvvkt it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.2ksvbx4)ga4g*lg jf 5o 4civc:0:e iz80 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kgtra cf0e, s765hhmf0 5:cwned and 110 kg , are in contact and at rest on a horizontal 5 e0a ehw r06tsc, cf5nm:fd7hsurface (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 carr-i/ypj2p vu.l re fy.z1oa6j/ying 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 driver can decelerate and still avoid having the cratezol/yy e vpuj.-f .ia21rj/ p6 slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whic*v.3u eto-im7z lwf d2h has an inm z2fu iow-t 3.edl7v*cline 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 sl* wydt/b86wxvide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted a2wgubyg 3)u *x2:9 hc;hjiwbf t 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 2 . i*qjhzk*uuof 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 stj, *lvnt0v; ol5f g5w7qr 3w j1m(yocpeepest 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 tk.r6fo*he7m place against a rough wall by someone pushing on it with a force dirf.6k othemr7*ected 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 can6j7cyblbn n6) become dangerous projectiles as they melt. Consider a chunk of snow at the66 n nbl)j7cby 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 fo kgu ephan zmc881,65qr an automobile traveling at speed v isame1qh88nc5 6 g,pukz 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 dasvfjpey/;s2it w+es3 1h when the driver decelerates from 45 2 fsjvytepe; w/+s3i 1$\mathrm{~km} / \mathrm{h}$ 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 :*ij3za sq,kr8tx0.li wt-zs is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are f4je (be bm1u3rilled 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 accub e4mej1br( 3elerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic frg s h+6ce -yzsgx jav)1+c/oy4iction 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 (includi:pgi1 fvvv0 t/ng the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at eaza)xno/ 4 mp 5ak dx1bp-5c6rxch pulse approximately 20 g of blood is a 5zb6px/x ma1d)-4 p rak5nxcoccelerated 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 survivi(blr ,km z7base3xe72 ng an automobile crash if the deceleration is e3z77bb(,kl 2smaxr eno 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 earthquake i;npab ashw08 kuu6)s/ kpy 6,ks a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictih a; u8k06 6,sw aspkbnpu)y/kon 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 the2 nonacd,xcdfx l676(dh/d 3l 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. Estimate the initial speed of that car a/2clx 3nc,hl ndafd o6ddx 7(6ssuming a level road.   

  A car starts rolling down a 1-in-4 hill (2cmxgk cxqa c+*2yr:9;rzr- y1-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 bot;c:*-mz kc 2cqyg ar +rr2yx9xtom 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 te:23i+w0clim m-khd l he top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resist2e0kidll-+mh m 3:wci ance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch whernuruf1 v1y6t051a ta 1qeiak, e the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedf611 r1a i tuaeqt,u 10nyak5val 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 p a:di-zfb jvz:.1i:r-g gksd*ortion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up th g--vd fa.* rd:ibg z:j1kzsi:e 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 ff7 k7lizxo 6z6z xadfa.;de53 rom a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle .6zxofx6k5dzeid37 azl 7 ;faof 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 differe;ea f(r3 fm(ipw24h ryqs.ag) qg.2es(a3ar f4m;) yw(ifpr hnt parts 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 myy28g w.b zhr4h;mp/ M ) using the pulley apparatuyhz/w ; y 4mhrb8.2pmgs 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 acceler*;x4 zxuqgf.tating 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 mvpi+8bm+e c -child-restraint chair, an engineer considers the followinc -+be i+v8mpmg 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 Italibdbln6 r p)2:man train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's5ai8ngtyx v5z)u 5c*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 tgc5zvausi 5)5n* ty x8imes his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is uc74 dz9 zl8dtqsing 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 allowed to reach a6*xxfl :vt og0u0 4ymr 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 ascendingl-lun 3c*b)u 6yjd5en an ice field inclinceu5 3yln-)nd6bjl *ued 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.