Why does a child in a wagon seem to fall backward when you g++j amtt0tft+ive the wagon a sharp pull forw+mt+t+fajtt 0ard?

A box rests on the (frictionless) bed of a truckm*b 2hm-upw8m.h+cs y. 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 grs2cbh *m-w .m+py8h umound beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, u6;4pu7t) nmr o/emsn3fkwz 9gyn ;f0are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it*xal ig-q5 qona2-,f y xfqn-* aq5giol,y - 2ahave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force 9lvnhk9e 6 ekq67h c)dneeded to make it bounce back up? (b) If so, whk 9)k96 q6l eevhcn7dhat exerts the force?

If you walk along a log floating zliej gwrv.7hn127c / on a lake, why does the log move in the opposite directgjc/12 7ih7.n wlvrez ion?

Why might your foot hurt if you kick a heavy deslk ii/w c:cb5sb. -cq9k or a wall?

  When you are running and want to stop p.)+:ptvpjj 4r mh7hiquickly, you must decelerate quickly. (a) What:i4rj7v )hjh+pt .mp p is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a seci7 +,cnc9 j-zo cd-humtion 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 slow and steady pull?cnd, 9czhm-i-uc7 +jo Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that osa:tznk/ 76gyn a 1-kg rock. Why then doesn’t the heavier rock fall faste:tg7 yaz/snk6r?

Would a spring scale carried to the Moon give accurate renr t2n4h)w8 dxsults if the scale had been calibrated (a) in pounds, or (b) in kilogratw8d 2xr4n )hnms?

You pull a box with a constant force across ar 2w qo*a55q )w-pruoj frictionless table using an attached rope held horizontally.jq)5oww- puoa5*2qr r 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 under the inzmr(nya ; k)-rfluence 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 thy )am(r-nkrz;e Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lif,0vjtjwrz tr7b-0 8oued8 g8f t a 10-kg object when you are on the Moon with the force needf80t wv0br-j8 ortgj7u, 8z deed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war pktqmj8mr8wrj64( q6l(cz,c (Fig. 4–37) pulls with equal force on the othw( 68 qr ,c6mq 4lj(rczmp8tkjer team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holxy 9:g)besm6 o:wr (ecd a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magn(m xbr wee:s6og:9yc )itude, (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 d h:970rz h3m* zpp-f; lynqabforce does the ground exert on you? Why doesn’t this forcerfl;- 0b : hnqmy*hzz7d9a p3p make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victis6ops, kwtxw4 de(p/v3 +mmw8m’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is i 46w,vps(mo/e wpsxdmt+3 k8wt really?

A heavy crate rests muscgt5e )kz) 04 ba(won the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates.eba ) wcks0m t)4z5gu( What force causes the crate to accelerate?

A block is given a push so tha9 0.u0,ytl xanppc* kbqji;3kt it slides up a ramp. After the block reaches its highest point, it slides back downjk.q 0cx pit0 3nkpl; ,by*9au but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scalsccbjxdhir0 7 :7od95e read if you weighed yourself on an inclined plane? Assume the mechanism functions properly,7j9sh:d70xrc 5bcoi d even at an angle.

  What force is needed to accele3g:0rejol awxdm 5+, jrate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accel ji6wx 39ml+myerates 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 izny2*y+ 2rf; hfp3ysvs 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 of6xwf dnwk,;.(g i h4vc 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 requ0chxwo+y*z) uired to stop an 1100-kg car in 8.0 s if the car is travo+)h*0 wxcyzueling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pel)dg )d;kdv2 vwxt *fp.let from rest to 125m/s over a distance of 0.800 m along tk )pfd)v.wtv;2x d*gd he barrel of a rifle?   

A fisherman yanks a fish vertically out of balg02hq:zf k ua. en+ f34h*gihr.- ithe water with an acceleration of 2.5 ne ribkf+hg .q*ha4lgzaf23.-h 0 i:u$\mathrm{~m} / \mathrm{s}^{2}$ 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 coverq hd1ne+ g0v- tdt-;ud 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 8jx uxnft 30l9 8adtckz1av1;maximum acceleration is 0.0680 g . What are the maximum and t8 k1axu381v;ta fxnc9l 0jzd 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 motionl;v.+j/w,grfv -eg3g qh, nbq gess elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accele3qh;bwvrv.gnqg ,,+fg/ gj-e ration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strtg,qzo.t 9lu0j )ztx/ ength of 21,750 N. What maximum upward acceleration can it give thet . tl,oq zx09)ut/jzg elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fpm tq1affs6/s7rg v()alling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of t )1aqs(pv fmr6 /s7tgfheir 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. When he strikes the groualisq,cts9 .s 9u+ y6*iig:v ynd below, he bends his knees so that his tor9yl+v yu qat,i6i cs:9*is.sg so 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 tie3q7zou5arspn 3dq7z6d 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 the6q 7prq zudzna3 os375 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 f*)/ihuqnoajfo+t:c p,t+ n/zb 6e)e yor a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram ofs+ssc2 9c+ggb a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfiecgb+ s2cs+s9 gld.

A 650-N force acts in a northwesterly direction. A second 650-N force muxcpu2 )s+mzsmazh * qj lz/26:st be exerted in what direct l2qu*zs+ xzcamph 2zmsj 6):/ion so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bu2yv))q dvuf7t5 0e3d3ocem u iildings 10.0 m apart. The sag in the rope when she is at the 2)umy)ut5d73qeevd0co v3 fi 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 cos* lsq26m5cuzoc2k(x rd from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14;0u9uadp ) ov,uaga3e.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctit3s4wae(gmkih(0wb;h ye , t(ca, as shown in Fig. 4-46. The sum of thek (s( g3tt4(e0hwwb,a yi;ehm 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 t lndf-u,vu)qr.-q zi( he same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the vd,r -nlu) quzf(q.i- coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pull.zc+1:tr raplbr/v u1*d)c,n hx vov lw7fs0 :s herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to rais+,r u1v nwc0d)*lb :cral/:hzp xot1 v.vsr 7fe herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a .px4z(yb-l g,u u0 mxl 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 bl0:y/n ehuj650(gbnl px0c- reo 8 colbock (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 fric3xq)gv ,(yt cbg q58phtionless horizontal surface are in contact with each other, as shown in Fig. yq q t ,)8xph(bvggc534-51. 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 initiasknusw1 :vhi f.)v9mp pa+4:l;*voqhlly 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 velocity at the moment the heavier one hits the ground. Tvqmso:npk* +uh):p;vf94 vaw .il s 1hhis is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table arey7 (ng:kq ;nms connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. qmkgnsn(7;:y 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 kinetica 2wy+4.epy i9+sqo0 ;ojolh x 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 start a 5.04rf -x3hu8b0vz p*yie.v -t7y 2 2- atrwolshi$-\mathrm{kg}$ 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+gg b3hu z*6g+wae2ad train accelerating at 0.20g. What minimum coefficient of 6a 2wg+z+h* 3u adeggbstatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accelee 5s f1 ib8shsylas1j.ke(-4l m4+li wration a car can undergo if the coefficient of static friction between the tires and the h1wj4lk4liebsmesf5s. as i+-yl8 1(ground is 0.80?   

  The coefficient of static friction between hard rubm3-,9aiut 6 byjijvw8ber and normal street pavement is about 0.8. On how steep a hill (maximum anim wb-jyuv i3a68tj,9 gle) 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+y: cabk-rz6e,dm(ln.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 re4z mk6g 3ulxf,rh/ dh8st 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 c;mdrf/ tdy6y;h .q3t aoefficient of stty da qt;h;y/fmr63.datic friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic fr0l73afgqbey+ iction 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/c:eynmb :t+w box A have to have to preecyn+/w:mb : tvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a pusz5f uji12 a bkxi,.l3th so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4b3 ikj5,.i2z uf 1atxl.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contgos05. f8-wx.uir meract and at rest on a horizontal surface (Fig. 4-54). A 62.ir mow5-rsxeuf . 08g0$-\mathrm{N}$ 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 coeffioa8y *(70ep ttc5ip:cc+pclncient of static friction between the crate and 0pcny cc l p+:8*7(tpo5ecitathe 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 truck?   

On an icy day, you worry about parking gyzfyvw3 q1k5 oy8 +jts7xrhr,i o07tc5 a,* ayour car in your driveway, which has an incline of 1y8tshfrx 5wy 7ot5g7vq1 yjzc3,a*k+ r, i o0a2$^{\circ}$ . 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 slitg3-m i7zx( uf4d /yvude 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 ,ot-4z)vpb ti-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial frb sg 77:,pvespeed 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 of 6.x8hlv7 l-g1n q0$ \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 pushing on it witf / a( /vze*k0rw0cm/mei(om yh a force directed upward at eofycvw k/a 0ze /*r(m/mm(i0 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 0. f:aprji ws/dangerous projectiles as they melt. Consider a chunk oj:/ripws .af0 f 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 travelingzw -wqk .iw6gfr/;z6e at speed v re6/- kqiz fgwz.ww6;is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the d yi7g7ge+vl/friveg li7gfye7v/+ r decelerates 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 initiaexmo : ypv:c ) ;cge0gi.aj;b-l speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to the packingv:je,q.)so7bc3qhin a c + fq4 station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is qce)vibfa hj34s,ncqq+. o7:0.60, 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 kih 5omu ub ogm1a))4p9pnetic 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 (including the bicycqb-.;xuxb 7as le) 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 each pulse approxima)bor-dstx ts9 hko5)+tely 20 g of bloo-xkhr+t)dss5otb9) o d is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile cras + wvc 0o6czeb6syb5-qh if the deceleratic6+ b0oqye w-bz6 s5vcon is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration p5 sp- 4)zi/gaqeiy6p vroduced by an earthquake is a , and if an object is going to "hold its plac4)zavs p 5e6i -gq/ipye" 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 0ir4r5* oa iajscene 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 kin0iaao4 jr5*ir etic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-i+32xaup *.ny-sns,lvul rl s2 n-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after travelinln n.al-ss*ru+yp2vusx3 l,2 g 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppeb,*/c:zap q2n*r2hy1uh8b+ gihe fmn+: u yikd from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground witz+n c,g/buhq i12u:yn*epmh+k r*y8:b2h i afh a speed of What was the average force of air resistance?   

  A cyclist is coasting at a sta5a0 cp0i4n nl3srs 3keady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If rl cs05na 0nsa 334pkiso, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of 6j+d5-t(os xeltxb/wa city. An important consideration is how steep the roads can be so that even low-powered cars cao- btwx +de js/x5lt6(n get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles h+c-j+ tudegl ffy j .:vo)tq8,er watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of yceftgd.qulj v+)-f 8tj , o+: 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 seveii;j tg0zq9nnlg: * p-+f wwsu8ni4 x3ral ramps connecting different partsi-zwwtg+q gn8n:n0s 9up fxjii;43l* 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 p,auvws(0 kj*ikw5q) M ) using the pulley apparatus*5s (pw j0iu,)aqvkwk 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 acceleratzrbm3w/.wvp t:aqe 2;ry.e2x h5mi ;ging 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 engineer considers t qx.xk;zy7cb; ynvy-p+yoo 32he following n yk.vyz+x 2;ypc o 37bqyo-x;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,s*3gzes *o+yq ws4 vio3yr9)v 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)p-j1ir)/ai gp bq(wm 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, hogpi1abr ip(jw q/-m))w large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a evzf54c. j e7jcr ri5j /w+x3z" 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 bbbd/dalz v1 bd8 03 rth6g gr*8xq0f6dv v5;yruilding 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 an ice field ino9hvck et;l-h+ft(c3 kb(v w(clined at 21( fc(lo9h kb; ( wctvt+khe-3v.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.