Why does a child in a wagon seem to fall backward when you give the ub/.nt kg4 q of1zxn4j;u 4b/bwagon a sharp pullun to/u 4nx qjbkfz/.b1 4;b4g forward?

A box rests on the (frictionless) bed of a truck. The truck driver staap sg 9,(m6 3ozfi/a6jksfy* xrts 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 is riding on the tr pfo3,jgysf9*kis /m6aa6(z xuck

If the acceleration of an object is zero, are no forces actin6e2 f1/jbxspuc1 ) rveg on it? Explain.

Only one force acts on an object. Can the object have zero e 7gkd pnk(z97acceleration? Can it have zero velocity? Explaipz(9g7ek d7knn.

When a golf ball is dropped to the pavement,lb1;gky oah.(v,dg c5 it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what e( hl.y vocabg g5;d,1kxerts the force?

If you walk along a log floating on a lake, why does th5yo6r +xwu 8jve log move in the opposite +ujw8y6 5orvx direction?

Why might your foot hurt if you kick a heavy desk o w )0f ew/jy+m7dbu/zyr a wall?

  When you are running and want to stop quickly, you must decelerate quickly. lj(5)jl+vqq+ :jjco+ ixdr9 g(a) What is the o9x+( +j+ qi c)qjvldol5 jgj:rrigin 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 fixm4o 0.wzx,b pne thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–4.xmbo, p0w xz36). 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 roc x 2aw zq hy667hv5yllp;h:rd5k is twice as great as that on a 1-kg rock. Why then doesn’t the hearhylv6zq7:l2xy5 6w ;ahphd5vier rock fall faster?

Would a spring scale carried to the Mi9bp/ m y(.-c irh6vzkoon give accurate results if the scale had been calibrated (a) in /yr9(c .6mhipbzv- ikpounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table usingr u oe+p+avim1* d6;d.hgq6qd 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 +h.umdodg;i 1 rd*pvq6qe +6 athe acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the 2i-6pqs4q(a g;wxaap influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on t2w4a;gppa6sq xa( i q-he Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift 0mzm1lo wz:,w w85ka ,um+cjpa 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed t5,zmuwzmj1,+la0wp8mo k w:c o 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 (Figg0y3mlfk g /0iw8: ajeh xmbec/-b+g -. 4–37) pulls with equal force on the other team. Whkch/08miaejxf3 gwg+ b/e0: -bmlg -yat, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desc rgwob8pgtnvuf.y wy 7/k:,35ribe the “reaction” force (Newton’s third law) by stating37yn:w.tbo5p ukf/,8rw vyg g (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a rx b todsz4,q)zd)7d2f oq pfh-uu og(;9,ks)force does the ground exert on you? Why does(drs7thgf 2o)49pdo sbu)qo-)z k xq,z,dfu ;n’t this force make you rise up into the air?

Whiplash sometimes results fr0( rj,zxmq7a 4p( d qf0m4tekrom an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim ,r(7m(j40fqx0ztr4q a kmd peseems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trud-)tp4na;l c wnxb9;tck accelerates, txlw;)t4t;p9n cdn - abhe crate remains where it is 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 a ramp. After tho2arpi3xh:jaad mt pq84 ,f 4sc6g+ak7w.ec*e block reaches its highest point, it slides back down but the ms7o4,268a: p 3 *4rjtek+acfq.a xp gdmh iawcagnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale readvk8/lrr yco(+m8p po7 t;olh7 if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even +rmv8o7lyr7ok o(p;cpt lh/8 at an angle.

  What force is needed to accelerasssr8:rm(p-zzws )ro eg. u3/ m6db :mte a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelera dzgm(ldz(p( i8m- p,xtes 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 accelerate a k xd9qbq7t+z 7mt 12vc.la(qg 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ,5fc of. +y1care)kwr $76-\mathrm{kg}$ 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 requirsn i,08ct:g a-7mtjljed to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h j,8 :mlsi0-cn atgj7t? -  

  What average force is needed to accelerate a 7.00-grlgy kx+. )kzj6am pellet from rest to 125m/s over a distance of 0.800 m alj6+yk)gzk.x l ong the barrel of a rifle?   

A fisherman yanks a fish vertically out oflln1s,z*w( 5 6gq zlne the water with an acceleration of 2.lwgl nnl6*( 1z,qsz5e5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cov f1 gqdss,/w 3bhe3-8y3bj xqnqi(d3:t1 mypcer a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratix/ iblfl0qjzy, 4rec6yi (.x/ on is 0.exczfqb ri4l,/ /yl6j0 x(yi .0680 g . What 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. Whe e.j9z;3t-ijqxid/vrb7rjb -q o ;jz *n the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the ajq bodv;z/j*;-ij-tz7iq r3rj x. eb9cceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a ma.. tbfl+f6m wmximum strength of 21,750 N. What m6.m+ t.bwl fmfaximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 13z be27lb3uzz kt :nb742 kg including parachute) when thzl3b ez tu2bk 7z4nb7:e 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 r4kydyjji8 i :bxdci.f)m:o:4 oof 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 distad 8 )ybo4jmi:kci fxiy::4.jdnce 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 t2b:o88 j*t6j idvsa hq3fkbw7ied to the box runs vertically ub3vktawh*o: 8dj 6f qi28bs7j pward 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 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 nc csik94:,ct 5xa5kiplayer
(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 isdou-l i+2;cqp8 h0vyk hit by the bat, and again (b) afth;8 -duq pocli2vky 0+er it has left the bat and is flying toward the outfield.

A 650-N force acts in a northr/n 8h zihd+6c pql,y /a9hn-kwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points c - n9hkqnhr/h d /al+8ip,zy6westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high d:;w .,dstyifbam9w 7 wire" strung horizontally between two buildings 10.0 m apart. The sag in the ropei,s7m wt;.9d:d yabwf 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 buc 72 ,wmz4fqexi c+nz,mket is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1ufv/ p1 bblpu(;3;vp u4.0$-\mathrm{kg}$ 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 yu,-je(qyj i2location at McMurdo Base, Antarctica, a2(qyey-u jj,i s shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass b-s* o/+vb( qzs7z e fqys+c1jcal8 (gwehind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fi8qyw( s-lqcv*a/j7s1zcbfo + sz+e(grst 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 appar/ij onsu(f7 2fatus shown in noi/2(7jffsu Fig. 4-48. (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, mt 3coj. y4 5upqwa:t;a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block r3g l/mn6prw; (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 fricti mzqg 6td79+mdonless horizontal surface are in contact with each other, as shown in Fig. 4-51. A d97d6+gz mmqtforce $\overrightarrow{\mathbf{F}}$ 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 thepd jy ft4c+i:-sox/p+o:k o6q 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 its velocity at the moment the heavier one hits the ground. This isi:o:t q4sok y6cpx+/+p jfd- o its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frict5rmi ,obx.k2 kionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of eac .mikx5rb ok2,h 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 friczitsm ew .,4,ction 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 st7b: ysf-lfnf x8k)d (lart 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 minw0w/ie:6fe dbc 8y6ifimum coefficient of staticw 66ef:wei0yfidb 8c/ friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum p 7p-vt+fqm2 iacceleration a car can undergo if the coefficient of static friction betpm- v iq72+fptween the tires and the ground is 0.80?   

  The coefficient of static friction betwee1p 4 + r1ru9l+ tjwwycs8mw.pun hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle)t wlycj1 89+p p.w+ru4m1w usr 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 -4.80 tl7ng)f4g h d)$\mathrm{~m} / \mathrm{s}^{2}$ 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 ac 4d; 1drqbop gm a():jk,(gai 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 an asphalt surface have a very hf/qivj1xu .b:n;i 0u6m.zvgzigh coefficient og16v ;q mb.x i.u0njf:v/izzuf 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 kineli-rtas . yg1s2h 9mu-tic 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 (Examp-nyv* v8afop. le 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assuf-.anv *8povyme $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor.ud0accy-dl)3 How far will it go, given that the coefficient of kinetic friction is 0.20 and the - c)u l3yc0addpush imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizont3v,w o rs7g:o(t2f zunal surface (Fig. 4-54). A 620nt 7g:32uz s(wrovf,o $-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coef 25qgamlv k /ez:va5lj71g cu*ficient 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 *27q5 ca :v lavke1z/ggumjl5 still avoid having the crate slide against the cab of the truck?   

On an icy day, you w,fsf11 q*td)al 1ayeuorry about parking your car in your driveway, which has an incline of 1ef)d,11*y tal1qf sau2$^{\circ}$ . 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 jko6 mg;/kpg e63)w/nl*qab8 fvulx* slide 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 tiltedju)vul(;jfh66 q mrs7 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 ml/14l(s9 ydvsca9wtil 59 ol speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed ofse2rx.2oq c z: 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 2 j4r;h c7t,kued2)facwwiv .by someone pushing on it with a force directed upwarddac4f2.i7 cj twkw2;vhr),ue 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 t+0p oegu zj+m/hey melt. Consider ajz+gmo eu+0p / chunk 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 for an automobile travel-lcfw zc706fn ing at speed vn-cf0wcf z76l 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 dashmjyq;q u g/hd*+kt1 /iboard of a car slides forward on the dash when the driver decelerates frq* /+m /1uk higdy;tqjom 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 q +b,1 -q7p ol-61n v2mw+qmos kxyq;xvu(wgwm 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 zp7/erl6w qa n.tzg8 j5k8)skthey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zgaqn6l8wk zk r. ps j8t7ez)/5ero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction bet-iz)l+7 pga/ at ml:f;zo.qkdween $m_{1}$ 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 coag) k8y kaem*e:st 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 mammb1+9mhnc9sx:16hq jyo5 l t ajalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 mx9lqco:sa 6y1t5 j1 nb+hj9h$\mathrm{~m} / \mathrm{s}$ 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 surviso9 kqe,mdkbwpg4yp f ;to +n/)/l)0cving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force lgyw pesq k4mdt;/)9o,bco )p/ kn0+fon 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 earthq., n sjy*r5y:q xto/v r-yd.umuake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fris,uvqj-.:. my tyrdy/5*nr o xction 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 accidenlwm-gu0g-kyx 6n b 07ut 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 bk 06g nuyx-wmb7-0lguetween rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for ea;,a9ff /v.mpr 9srql tma:zj :ch 4 m traveled along the road, the ,m9rfalj:s mvt9zf.qa ;r /p: elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning To;7(sgso p0uem wer of Pisa and falls 55 m before reaching the ground with a speed of What was the average forc (p0g;7e uomsse of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a m a 3s8apd/36sa vq4wl0fkt* j7 m8npcan/s1neuddy stretch where the effective coefficient of friction is 0.60. Willaf8p/ svtsjne 13p3/7*0 dqn 8a l64nsawcm ka 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+8 f5 s2v spt) wn6hh7bzkqeukw0n 7e. redesign of a hilly portion of a city. An important consideration is how steep the roads can be so tha 8 )0uee.7hnt5ww p2f6b+khssqvk zn 7t 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 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 experimenngfd+ (/s96kpx up;q*xz s.byts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Figxy6px* d;puqf+sb(9.n/ g ksz. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connectinww+x6m wwi4vp0o 5af,mw1 l)jgal .z:g different parts of th.wm4zw0 )a+gal jvxmf wo6 i l5,:pww1e 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 needek*s1cdce lbcl *+tx8-rr. cy/ d to lift the piano (mass M ) using the pulley apparatus sho*c r+k ds- c1l.b t/8cexylr*cwn 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 accfb:ycu5hctdb4i n/.9 wd; i,t elerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chavklfqlfd0: 7 /ii-1moir, an engineer considers the following set idqiv 1-:07 fof llmk/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 metric ok0yog n;n1s9(nr 0(ptu px -ttons (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 mxxie9-h (nwgvki*3oky,2g h os:z5fol9. r )length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the ro5kw o ,(:*)s3zn9l-khooimh ex .2xyi gv9gfrpe 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 usin f79eo.t0ai,h *zop7 u*wmoxbg 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 xx +t8jlxa cot g8mdkr4zv ys*1j*-./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 a6, pxjr9,2md ,nwwz1oc yy-z dn ice field incline,zmp,wyocyw d9-xn ,6zrj d2 1d 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.