Why does a child in a wagon seem to fall backward whe0w+e9h5as)zgytn 8v en you give the wagon a sharp pull forwaragw8) 5vt +s0h9yzene d?

A box rests on the (frictionless) bed of a truck. The truck driver starts the t+( j0 ac yt; vexoi.q,d3me/jwruck 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 theo;yc+m it/ j,( vqaw.xe0edj 3 truck

If the acceleration of an object is zero, are no forces acting on it?v7z5o.-oo-o9ulzmw go zd 31 gh2bdm6 Explain.

Only one force acts on a3a. mdc kag(5 mon.j6 h*qk+etn object. Can the object have zero acceleration? Can it have zero5 .e*.aj6 (gqk3hnmd +ocmtk a velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back upqu:2kc u0 s1syd5beh+ 2mr*h e9.c a+z ggy)mb. (a) Is a force needed to make it bounce back up? (b) If so, what exerts they0hscu9.dgu)+ 2a+5yzb:mh1r2 ekm *ecbq s g force?

If you walk along a log floating on a lake, why does the log move in the opposi luu c dhqq*jxgi(e 1fs62*4k7tl c(e *udj6h71gxqs4u*iqf2k e direction?

Why might your foot hurt if you kick a heavy desk or eo uhxd, 4pq1)a wall?

  When you are running and want to stop quickly, you must decr l8u(hmv33c3drap7h elerate quickly. (a) What is th a(738uv3 rdlc3pmhrh e 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 ceiling, and a section of the same threagn14oox )zfua0s2 pu 1d dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, wh 1s u2o)nox4zfga1u0p ere 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-kg6vzisn /ogc 5pycane1dy. *2 6 rock is twice as great as that on a 1-kg rock. Why then doesn’t the * 6/vz6gcnyis . p2oyn51deac heavier rock fall faster?

Would a spring scale carried to the Moon give ac 9nfpo+3y 9i xh2.:nm pts0zkf zbm)c3 *)ysvacurate results if the scale had been calibrated (a) in poxcpm.tohi n)p*z0a+ nsyvkf 9: 3)zbsfmy93 2unds, or (b) in kilograms?

You pull a box with a constant force h;igoaa;0q rx9;b/ut pcdmt 5;9n m 8zacross a frictionless table using an attached rope held horizontally.crpa8bm;od0izq xau 9 h/;;nm5 ;tt9 g If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely u vd8f:4x6ib optr(dwf)z6,owy,/q cznder the influence of gravity there is a net force mg (/: yq) ,zw 6o,ixrzd4pbf6ovfwt8 dcexerted on it by the Earth. Yet by Newton’s 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-kg object when you are on thwyb.m+++16 bxy fdaq(wjx) noe Moon with the force needed to lift it on Earth. Compare thbwdmbj++ (y6n 1 +w).o yxqfaxe force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each n0 2:9k,pfunwpzwyk ,gfvr5 . team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines n5fk0 , rf ,gywuzpw2p vkn9:.which team will win?

A person exerts an upward force of 40 N to hold a bp8 qs/2k/dhde ag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on whasdp8 e k2/h/dqt object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, h; 6ef5h.che rqow large a force does the ground exert on you? Why do ;ee6h5q.cf hresn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vtqtix .f26wy7k w/802ajx0 rnqfr g2sictim’s car is struck violently from the rear. Explain why the head wgq7s 6wnf/ .qyrt2x20ai 08ktx f2 jrof the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck j7 qv5-xgkv;n. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to xnvqk7g v j;5-accelerate?

A block is given a push so that it slides up a ramp. After the-g /a(xj 2uxez block reaches its highest 2a/zj -g (euxxpoint, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale re :y-)viod0t:msx cv; kad if you weighed yourself on an inclined plane? Assume the mechanism functions properlmoi-ct svx) : :vdy0;ky, even at an angle.

  What force is needed tommajsqx6qqykuvs :/ 8 . ejmkf04y)d4 6 *qrh/ accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a)x +jjqy ax9 8.wc:vqb kyz2(cnd 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 w54dlnwhdolh4,u dwn eo.shs71 wi3 j6l.v6 *aithstand 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 of a ar u on3n4x zsgj.62k6 $76-\mathrm{kg}$ 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.76g 6ool g8azl0 k7u2drfgtv in 8.0 s if the car is travelin d6fru t67glzglo708g.2ov kag at 95km/h? -  

  What average force is needed to accelerate a 7.df 98zlki(tys c6w mchk8.z0200-gram pellet from rest to 125m/s over acsh.dzw8 ( k 2ytf9i0z kl8m6c distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a f7anc, 2yil-rt 1vlmn6)vzk3tish vertically out of the water with an acceleration of 2.5 76ymct,knai3z1t l- rvl) 2n v$\mathrm{~m} / \mathrm{s}^{2}$ 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-milr ef+pl* 2bzi.e 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 t5gzm zf m90fd:hat the maximum acceleration is 0.0680 g . What are the maximum and mid fmzz :0g59mfnimum 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 el4oijk 4rky6xb 7ijd /2evator. When the elevator begins to move, the scale briefly reads onl /j4ok6jkbd427iri x yy 0.75 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 m*y /h(f)p2ti0xv*s yooyf/gelevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevato )*y/m*osy gyo2h p xf/iv(f0tr without breaking?    ( two decimal places)

  (a) What is the accelerei,g2vz9s-ll -4 nlbzation of two falling sky divers (mass 132 kg including parachute) when the upward forczs-i9l z ,vb-l4e2glne 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 roof of a houser +oa k q1ad6k6/8jaws 3.9-m high. When he strikes the ground below, hdo/ks6ar+k61 a8ajw q e bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the bo6n7fwr-z .k5a bzah+qx runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine thzrw hb-f6kaa+q75z. ne 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 playe2cm/x ldak+( zr
(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) ap *wzzq.xl(cr 9 iede9bcg)32t the moment it is hit by the bat, and again (b) after it has l. )qgpbr99dw ecx*zc2 (ilze3eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A secobmf: fj7a3s)c j:.:e iab7crrqoi y73nd 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate you )7ajecf b73.roiq:b sja mi7fcy:3:rr answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontal dlo/6 28ftgtmly between two buildings 10.0 m apart. The sag in tto/f6ldmt28 ghe rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from another 3.2lumook x.25kz oj+-x e30 bb8p8 glu+u$-\mathrm{kg}$ 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 1492bnxuz0e wu2xl o7o6k 8q y)g.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 housingxao/xdm,tzf)sq ;y/ :: nz *jm unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of thz*/sz; jxanq mdo/y,x):m ft:e 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 pullingod fu5jnnu n s h2o06m2f-f(:y two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between odnfn( yf:0fm 2 6u-5nousj 2hthe locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-p-q7 i 0sn(knmd/a 7wkpulley apparatus shown in Fig. 4-48. (a) How hard must she pull ( /- 7pqn0iakkdsmw7n 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 rac2 *j8ix mt++iwr pqya6e began, 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 (masnnkw7 mle045 7oo -qckw /l-rls $ 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 surfacey(fw -ea qsc2, 9br) 5:tpouvf are in contact with each other, apyfoq cue92s:r fb(w,tv )a5-s shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown /(ag..f ur 2zpdhpq,kin Fig. 4-52 are each initially 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 its velogpp uz(f q./2r.,dkh acity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cordc2 oi5g8lcz a1q4s:st of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the co o2:cqas4i8zt lc 1sg5rd, 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 u,uqccv0cl8 d, a.w2wkinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to sta04y*wpd,3+eg ;wyhj aug str)rt 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 f ehr *5 w72xaanb4kolij470 gab 2z9bon a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feea kozgb2i9blwex b7 474 jr5fn*ah2a0 t and the floor if you are not to slide?   

  What is the maximum accem*ni7rzb o t,;x/v9myleration a car can undergo if the coefficient of static friction between the tires and the imx 7n/ rz,t*b9yvmo ;ground is 0.80?   

  The coefficient of static friction between hard rubber and no;y75d0 io qzvsrmal street pavement is about 0.8. On h07o5i;ydz s vqow steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate ;hl s +kosxumx3g17,bat -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at resc6 7of( qr5ibnt on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coe9x18t a2 +n cq;shy+ ikltqoq07kyl,lfficient of static fri s9xyc1 hai ;q7k0nyqo8lq ,+l2tlt+kction.

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 friction fow: k5fed o+e9d8u 7pzzt2bk y:r 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 masqr )j5hi5 e;tfz4tb, /ju*v- hv cf;ffs would box A have to havrt55h,;qiufbf t z * ej-v)j hfc/;v4fe to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acros 1uly1mtqm1o vc;1fa+ s the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impa mcua;t yv 111qm+flo1rts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kox)yvf) agnxt*n- qch yw ) *z74nz;p;g and 110 kg , are in contact and at rest on a horizontal surfaacynzxzo 7-x )4;tynp g fhw*)vn*;)qce (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static f54uchxo 9:t niriction 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 havc 4n59xit:ho uing the crate slide against the cab of the truck?   

On an icy day, you worrpb4u0 2b oup hj,q)wdm o q;wjd75r4+ay about parking your car in your driveway, which has an inclib5)+buawhom p,dd r7owq jju0q;2p 44ne 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 slide with a 28fbxcou;1al wl 8v(w7 3xf2 7md$^{\circ}$ 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 at a l/ftcn ft.qpzqs. ; f; 171qv*nxkns ffy:)o/n angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of n-dqf+satx:5le tr4s ): kyi0 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 stee5q 7f,6bs9tire3fz4twz af,t pest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by an6.n r m,e:r,kony3ka:sda2v0 qs; csomeone pushing on it with a force directed upward at 282n;:va6kcam d,k,e:aq3 0 rrn .sny os$^{\circ}$ 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 projectkdf2ql3 tsn 1, e2v.m x6wukim s)a;6jiles as they melt. Consider a c1 t,sj ad2ui.mes mk) 63wnkxql;v26fhunk 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 traveling at speedffdvuq 7fl* 2+ v is equav2 uf+ldf7fq *l 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 foec qpq2j * +gpcekacd-f,s4 1:rward on the dash when the driver decelerates from 4gcje :c*k,a-2 4q 1pqec spdf+5 $\mathrm{~km} / \mathrm{h}$ 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 given5n70r emmi-w p 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 filled to the packii+h.xf no,/w+mir p m4ng station 11.0 m away. The belt is initiai,+o/mmp x 4 +hrfwni.lly stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, 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 betweenhx6nt1mvtg0yd.-f2dr1o ( x y $m_{1}$ 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 th5q d zxkt.u4q6 /ufmn0e 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 may-6+*pya v k d.xr/chodel of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fra*xpv .k6cd y+r yha/-om 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(hn/u 9cud-e5//0x /u3uuunoqwev c v of surviving an automobile crash if the deceleration is no morhnu u09/ev xc o (3ucw/quude/5/nuv -e 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 is a , and if an objep, dpl0c /*o+na ejr)rct is going to "hold *0+ncpr j)ad /lpe ,orits place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident ink:0pzcsx *v: nvolving 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 cx*z:kpc:0sn var assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-u/f j9j ( s4www*nfmm,in-4 means that for each 4 m traveled along the road, the j(wf9msu j/4,n *wfmwelevation 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 Tower of Pisa and fal- 5szku 4 z hi7pq/aj9w1:z rf*ktvpr-ls 55 m before reaching ksk7p5z1w*zt 4iv-fz9prq /h-urj: athe ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s burvsp5+ )uol 0;14ep zh(hw luxt enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without huwe1 u;04h llr vxp )oz(5+shpaving 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 redesql7 m u0; g 9zj7jm/qjp+tdux,ign of a hilly 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 wiqmzu0q9 m/+ j,dpjl7tj7u;gxthout 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 experimen73d e.z gwz)pu/bo c9ggv ,i;fts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices thatcw ;/zd,i3f 9)gop ve7 .ggzub the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting diff 1jczwjilj)7 :jkxhz*;ksr ,2erent pahzlksc jzj ;2w jk:*rxi),j71rts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M )h4 uns6k )ajp6/tak 0l using the pulley apk)jal6u0/a s n64kpt hparatus shown in

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

  A jet aircraft is accelerating at 3.5 r6wo5 xo1jtkdv s4c91 $\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer cobhpow9d 3 am(0nsiders the follo hwa90 m3pbod(wing 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 (660,000 1xf6(n1olat qn4(arf $\mathrm{~kg}$) . 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 andx6juhvso.k5 6 )j1+eixusp d( Karen, use safety ropes of similar 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 rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a for(j1pesjx+ u.) ov 6i6sxhuk d5ce 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 i : xk7tehd--qugbyr0 4y9g2uxs 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 maximum speed of 3.50cml (:k2 xr.cotd9 cg $\mathrm{~m} / \mathrm{s}$ 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 ascendi3n. gnpu /0l,2 nhaexkng an ice field inclinx n/ pnh 0l3,ug.ea2kned 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.