Why does a child in a wagon seem to fall backward when 5elz hn70 7*doiy5obiv:au t+you give the wagon a sharp pulo7et0+zb: 5hu o*iva7iyld n 5l forward?

A box rests on the (frictionless) bed of l. fa w9fu ce73trg4a ral-w.-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 standing on the ground beside the truck and (b) by Chris who is ridingwf4tlwg9 rr3 eu.l-. aa7c-af on the truck

If the acceleration of an object is zero, are no forces acting on it? Explain.8ono- *t szcjb6t7 dt0

Only one force acts on an object. Can the object have zero accelulp qmh3208 nku5z5qk x8n ,pleration? Can it have zhm ,53q2q5l uxk 8lu pkp0nn8zero velocity? Explain.

When a golf ball is dropped to the pavemen45fo y uox/4(lh sdfax6j y08rt, it bounces back up. (a) Is a force neea/456 ouyxofy( 8hrf0l4js dxded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, wxsy 9.d,y,x/y h)5mgq pb j;jrhy does the log move in the opposite direction?gyj9h.b,pdm5xjqry/ s ,; x)y

Why might your foot hurt if you kick a heavy desk or a wall?x5t9t;p1y( n uozrcb1

  When you are running a gy*nf3,x7l7d.z .o6gilvhlr nd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causnvg l3g7yrf6hldzi .7o, l*. xes 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 ceilingzfdg1- l(;yc (qnbv b3, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slo3zl-vn fcy1b ( gq;b(dw and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Wh ka4q.-k v)kyoy then doesn’t the heavier rock fall fao-kv k4ykq.)aster?

Would a spring scale q-on dw yr4.tg4-rw lx5 i2n-om*exy/ carried to the Moon give accurate results if the scale had been calibrated (a-m qn4x -/x-gntw*. yr2 5rilwo4y eod) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attac gn9ax-+gg ,k)5th wvj(9jzpghed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat ong n5- vt, p 9z(+g)gwhkgj9jxa the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is m4hxnyab4943k z ,f/dj4 mpove oc;:d a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal a /43doef4:vackx49zmn,4dohm;j yp bnd opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or fodwmi+9s6a th9rce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with ai9wdth69a+s m given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug ok rxl+o2yq5 zk-nh:(ep(, fnxf war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team wilpkx5n:q(ore+f2zx y( n-, hk ll win?

A person exerts an upward force of 40 N to hold jqq +x.2ofu lv+o m8i7a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its ma2qf+l.xv qj+i78moo ugnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on+vim;z4q6 -uuqk( ege the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise4mz(+; 6-ugvqik qeu e up into the air?

Whiplash sometimes results from an automobnn)c(i8 efc fdfy r1-)ile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be i( feccf18rdy n)f n)-thrown backward in this situation. Is it really?

A heavy crate rests on t/m7:7 s5*/ hptz sy jd/3s y-jnbwpqynhe bed of a flatbed truck. When the truck accelerates, the crate remains wj y d p/7mpssny s*3why7- /t/:jbnqz5here 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 the b5 (a bu n9crolrq(.v95j 1 hwlrhoim87lock reaches its highest point, it slides back down but the magnitude of its acceleration is less on ll(5(8 voq9 c5w1i9aonrmubj r7r hh. the descent than on the ascent. Why?

What would your bathroom scale read if yos86pmb e-2ch j(;i 20yxkefc eu weighed yourself on an inclined plane? Assumehc0f8kb jm- i62pc; xey( 2see the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a eyyr(3 rn *:yksled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 27ollv59tcvt k wz2 w*5.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstar4 * w60e:ccz)cbl.pf 0ifqj jnd if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight og2o :ye6 wpri k.u)viu3 ;.fdqf a $76-\mathrm{kg}$ 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 *wi*x b8v.ox5i2g llu car in 8.0 s if the car is travlixb x guilv**w528o .eling at 95km/h? -  

  What average force is neede-i71kc uryv;d/wou h1d to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the bayr1o ; 1-udihv/cu7kwrrel of a rifle?   

A fisherman yanks a fish vertically out of the water witqtijfkoivas *kh+sx0* uk.gw: 2n95d a8sb*4h an acceleration of 2.5 u: vw2j+ 8 ox9f.*gkqsh5tk40di as**s nabki$\mathrm{~m} / \mathrm{s}^{2}$ 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 d5q 6 s,omj5u r5ehc7i (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 ji8al ft e5qvf8xw)3 9be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum foraq5 xvilw f9)t f8ej38ces 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 inh3ek)f3wx+n -h- hig c a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleratioxw)nhhe--ig+3cfhk 3 n 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 21,756f-;x 9pcraa 6dwi v7, rle4zp+kk(o z0 N. What maximfz9pxwizk;- vc,aea ( 6pokr4+r 6dl7um upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration-lfl g3a6-05 zt, ,wbw2vq thmysg ho9 of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth oty593mwhgo ,, b6wlfls0-vzha g2qt- f 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. Wh:d5ur84urxi td qe-tq ),2ateen he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mas,t-:reu5t qqrda) utex 2d4i8s 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 sbc( 0 -bi/go4 ba bqifpg203za table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tabl ibbp4ca2zofgibs30-0q/(bg e 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 player /z2p/uup 5 hutw/bct,
(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) as .jassajv/o(247n onw*n n7biih48t (ii p baseball (a) at the moment it is hit by the bat, an/)o.(o7in2sat an8s 4* 7bjiinv 4ns(pwjha i d again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forclyf51h((uxb)d.seui +nh5l oe must be exerted in what direction so that the resultant of the twol( h5e yixu)hfd+15 u ls.bn(o forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizon-yq n9ieu,h9pdbxk97 aau(w,tally between two buildings 10.0 m apart. The sag in the rope when she is w ek,9xdp99qau7hn- iab,y u( 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 cord fro4r:2a 7-xi2vwltb fhxm 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 1sb / o 59ssuf*yhc nwq.j4i7o*4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unita7 u4u .zdngm) to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-44duz ).7 guanm6. 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 ozj 3;nns (zp(x1d 3nfnf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firstjz(n fz;nn 1p33 dsn(x 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 apparatusu,go8kj3-k) r6k k fzytvl 9 (la*de+k shown in Fig. 4-48. (a) How hard must she pull downward to raisked,jrk gl(v 8 aou 9fzt*6yk) l-+kk3e 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 e,2s/txu wzkzvp)1hbt-z;a 5 ;zsf8 i6ojcv/, 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 xfi(+ *wnnl- ixg l*u6(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 are in c7nm ;-p,lfl eyontact with each other, as shown -l,fmnel7y; pin 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 1.80 m 6fx/5iu uh(kpx7z3 x qabove 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 its velocity at the momentz3quk6pxhi 7uf x/5x( the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy corjt/ q:i-khh-:es(hy oq;;is4ieq 1az d of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end (zi-t k:qs;qahh1qeo hjies; y :/i 4-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 betweejc so+b,ph4 5gn 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 staxwg+qf +/:we, nz-rn drt 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 akpgd oz gp9gqr 2y84*:ccelerating at 0.20g. What minimum coefficient of ggy8o2g:dpp kqz*94 rstatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergc4l)sxr; skq/ o if the coefficient of static fric;scrx l 4/k)sqtion between the tires and the ground is 0.80?   

  The coefficient of static friction between hard6qk: i+xn hsx4l e:imh7qkz- 2 rubber and normal street pavement is about 0.8. On how steep a hill (maxiq xmzik:k eh: h+nx-4is7l26 qmum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4+f fs fgy3*ocvb4s;g4+ t-acpmng5q , .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 rod(4tgdg1i6u+2v3 mbigk k goo-ghg8vr8 20 aough 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 high coefficie(ir-r/o 2(nzrdnh9vyfhx ;/nnt of static fryho /-xrfnh29d/(i rn(z; nvr iction.

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 fricd uy/v kzm 7 uhd0z7s63c01rsntion 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 would box 6h(-am:kcynhp s r*c/rv1k8 ytq88a gA have to have to prevent any mo ks (8 v6t-hnayq8gk mpc8/yr:*1ac rhtion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far;ny,sdw/db d/(mmxm rr j:f )h6b+gb 4 will it go, given that the coefficient of kinetic friction is 0.20 and the pushbgm /w b/rjs(:d+fy xdh); dbnr,6m4m imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kgv-m ;gutp-l3q-w) qpdpfzjd. ;vc: ,b , are in contact and at rest on a horizontal surface (Fig. 4-54). A 63vd), wdbfm;up tlvc. p-gj p-:z-qq; 20$-\mathrm{N}$ 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 1tqhl2y.wt,ru,kewc: 5fs 9 9kbpa(r 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 crate slide against the cab of the truhqp r2,(,le:.y5 bfattku1swwrc 99 kck?   

On an icy day, you worry about parking your car in your driveway, whi*q b dxo (pjyp:kg/32ych has an incline x dypp:gyj3/qk2*( b oof 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 gk2: y14 eg9q *.jfi/ekwmezlide 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 tlj8 b7kpo6)h xilted 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 inkk g; sze:66zg4 qxe3uitial 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 i,*(xb4u bbg f/ i,yapa speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pun j :a)gc 7uzh)4aekb.shing on it with a force direke 7hu) ja)bgn4 z.:cacted 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 cac+xmqw.5* xbp87r jlfn become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of afw.x*x5bl7jm cqp8r + 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 traveli)zs1x 6jmgt;p ng at speed v is equal to x)t6 gpj;zsm1$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 dash-7u t ;my swxhw4r( 9dya,9jzgboard of a car slides forward on the dash when the driver de zy-jwdu sx wt49y7 9;ahgr(,mcelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial sw8z ufko gp:rt qh2 xe2z;9cl;+at-2 ypeed $ 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 conveyorz-iqx7 h o..:cuqblwjcc t4 ,8 belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished it c8jb-.ih:o, c. qwxcq7zlu4f 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 oxfi oxdpm/d64f6g.t uf-m2 (gf kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (includir-x kftkjrhn g6 hy +b;64a1evz; fo0,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 eapqr .a iy 4* p74 3pklbym2ie5uo6t-igch pulse approximately 20 g of blood is accelerated from 0p lr a. 7y2bg*ip34uty5oki ipm-q4e6.25 $\mathrm{~m} / \mathrm{s}$ 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 9uvh5hc+cr h 0surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the f u59ch h0r+chvorce 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 is a , a -txudms(px0*s1ukz8 nd if an object is going to "hold its place" on the ground, show that the coefficient of static friction wudusz1 s0mpkxx8- *(tith 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, e)-h03ge uc gkixamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and t ick- gu)0eh3ghe 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 thcm)-2.lp w ml.gbs0seat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going wblm. sm) . gwls2-0epchen 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 Tower of Pisa and falls 5 3h;l/uzuci2pl2 qzg 6n3z k-w5 m before reaching the ground with a speed of What was thnh-z/z6 p3;l2 3k iwgzucuq2 le average force of air resistance?   

  A cyclist is coasting at a steady sp-vd lha4tl7o*j mi b7.eed 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 7hji4ltob* .-la m7 dvmud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a .2 htw6tfi8rvuy ;zao9d5 p(j*urv7+ cdhv5hhilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest t ;t2 hjr 8vufv+zc9y5v dop6rh5uaiw*d(7t.ho 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 exp k, nh. :aoxs0x4jcv-o ta6r6geriments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airpng,ko4svax 6a6xc0hor. -t:j ort (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connectimk fl-i68)4app f5 iatng different parts of the stm6l)fk ia58a -ift 4ppore.
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 (masnu+d :(e.jzrb xn:t9ltn n-/. -swtus s M ) using the pulley apparatu.xtet:nw/. s l+u zs(tbrju9n-nn:- ds 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 ac8kdi0 c y(.awxcelerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engia07hbkyab4hf ; l/p,b1o va -dneer considers the followin,d- pa; ybb/a a h4k1flo7vb0hg set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,000hu p9z0cz +stl: ,env( $\mathrm{~kg}$) . 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. Karej1of,* qi*sq-* itz uon'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 distancjt o- *,i*z1osqiq f*ue 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 i34(/xk2 ffx doxilt+*fz2ewk s using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximusg /k7m)e5rq6mdqk 0km 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 aomimvb6+.ewwq;g 0x p6 ,a bs,re roped together are ascending an ice field incline6+m,;oiwbv.egb s mapxq06,wd 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.