Why does a child in a wagon seem to fall back)mueg/7mag1o jl-:s uf3pv. q b ke86fward when you give the wagon a sharp pu:s-j /oa.e 73)mu1vbupm8flegfg6 k qll forward?

A box rests on the (frictionless) bed of a truck.pfe i65lob4 e2z2x 4ub The truck driver starts the truck and accelerates forward. The box immediately sta5x o2 i l4e64fbu2zbperts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on y(zv sfeb6zrro.)8rk/d/gv 6eyib3 . it? Explain.

Only one force acts on an object. Can the obje .( bfs10c)msagnt.bict have zero acceleration? Can it ss(0mbt 1c nab..) fgihave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bo1uf2dapb 12 bkunces back up. (a) Is a force needef1 d2ukba 2bp1d to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating o +qunt81zxz3,t7gav)mt jiv /n a lake, why does the log move in the opposite d 1m 8zua)v t7qngv/jix t3t+z,irection?

Why might your foot hurt if you kick a ka8+s4m7 k jr5 omq/ncheavy desk or a wall?

  When you are running and want to stop quickly, you musfypkf* nd:gq0 ;:j vom.ly0 0st decelerate quickly. (a) What 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 sped f pljokfvqmn; 0.:y00:gs*y ed to come to rest.    m/s$^2$

A stone hangs by a fine thre4 th9l6q-lw:vg/p gjs gowgc1 d:t9 a;ad from the ceiling, 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 slow and steady pull? Explain your a lq;ww 9a9-l6gjgvt 4g::dos1h / tpgcnswers.

The force of gravity on a 2-ko7ylz(6n no9kv/ iqu3uwq +e8y5u9ymsil 8v .g rock is twice as great as that on a 1-kg rock. Why ulq(vylyun895./q+3 8ke m n9zo7s wy iu6ovithen doesn’t the heavier rock fall faster?

Would a spring scale carrif4e,3kpvq8+g( 8c uzits-q mged to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogramsk ,-t8m8(+3v gfzeg cq pus4qi?

You pull a box with a constant r*m926 m.* zccnrh y(kti :immforce across a frictionless table using an attached rope held hc.(*mn mm:2y *iizh9k tcm6rrorizontally. 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 influence of gravity there is a nc/0jel6*vy0lf3zujmrw i /1 met force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equaczu y*3 wf/elimv6l jj1/rm0 0l 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 ykiur(hz31p3 zk6 d9lthe Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed o6l1 hz k(rzkd3upyi9 3n the Moon and on Earth.

According to Newton’s- a,4p.z;35bzdv)x8 c4 ,d nf1khzb cwlbxq dn third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team.4)-4 hk . zc d8zxqdnd vfzb,wac35pblbn,x;1 What, then, determines which team will win?

A person exerts an upward force of 4; we7)xp raw1e0 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by sta1wrxwp ;ea )e7ting (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still,ug q,dk7 s, w8wdjl5t;wb9zr on the ground, how large a force does the ground exert on you? Why doesn’t this force make you wd z 9,5udwrq,k8l,sgbw;tj 7 rise up into the air?

Whiplash sometimes results f,g8t hks8jq5prom an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?8sh8g5 j,k tpq

A heavy crate rests on the bed of a flatbed truc 01qn8xx( )o5yuiond 8ljj5 vjk. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate tojn)x xyoo5id1lj5u( 80qv8jn accelerate?

A block is given a push so that it slides up a ramp. After the block reaches it;qak) o 9n2)zmoxkr c/s highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the aszm cr2) n9ox;o/akk)q cent. Why?

What would your bathroom scale read d u;5,q fb o52oh1fadoif you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at;q f,oodud55a1h2ob f an angle.

  What force is needed to accelerate a child on a sled at pjjnau: 2 lu)( hy,pu21.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.3v0ueow -p-y5/f ofe(g 0$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelp e2(t0zo i v2lblev8)erate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of0vqd se.7x 9i1mzv6fy 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 car in 8.0 s if the car izt 2x-z1m0iuxxyws*-,6 pp qp s traveling pxpm wi - zq,x02p-16s*zytuxat 95km/h? -  

  What average force is needed to accelerate a 7.00-gr74)jqd l ejb3wam pellet from rest to 125m/s j7qdwl4b) j 3e over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water withq n)fcsy3lung :g,:yh 12(wka an acceleration of 2.5 h)3 12n yq,fu a(gwn:glskc :y$\mathrm{~m} / \mathrm{s}^{2}$ 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 czallvgjc .u5;ybn g6us(dn/.:. rv1vover 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 v4u(5fvl skk )opl6d eo0c; h*) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on td0h leo fkv; 4oc*vsk()56 ulphe 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 ba7z +mdu5qw +gzthroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of ac7+w gz5dz+umq celeration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stq;pdd. fmk- v0rength of 21,750 N. What maximum upward acceleration can it give the0vpkf;.dq -md elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fptihq8m 6g 4.xyr3 c,halling sky divers (mass 132 kg including parachute) when the upward force otxr6 .48q iy3gmhpc,hf 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 house 3.9-m high. When he strini) f7vs0qzz :juet..m-hk:ekes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs.hveqz: :z7kt-mufj e.n) 0 si) 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 Nnl2xa; nvp4 la gq3.qh1gb c)- rests on a 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 table exerts on the box if the weight hanging on the other side of thxn;gqq-h3 b l)2pc.a 14l agvne pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbal) ,e3ypg8k dz- f)mqytl player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by theu-x+g:t+j2 vst/tdwls-w od 9z gm04t:ad go( bat, and again (b) after it has left the bat and is fltg+g:wjm(ts+z4sd -do l tg09 o2-/atuw :vxdying toward the outfield.

A 650-N force acts in a northwesterlpc5q-k-*w etw icp5,oy direction. A second 650-N force must be exerted in what direction so that the resultant of e5ok5*-q ,it cwcwpp- the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" st-f4 :*ma m i+mg8latt4+ qcpdmclk*g 7rung horizontally between two buildings 10lc47 qaa+-+:m t md8*4pkcti*glgfmm.0 m apart. The sag in the 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 corxsv - 3(abz0z8 ni-ovld 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 148tm4uzd;c 1(0e ynhd 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 housing wv-;4q3yzkjttp*0u nb,e(.liuf*h uunit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forb*h t,v u(w lkzf.4-qu*eitpj; n 3u0yces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behi-crg1 - .pksn:fokz-q nd it, Fig. 4-47 . Determine the ratio of the te:pcnsok-zgq r -.k- 1fnsion in the 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 pulls herself upward using the bucket-pullerx rp(2 ll,v a+qz/u-j9k9xjiy apparatus shown in Fig. 4-48. (a) How hard must she pull a9ip vx9-,/kjrj xlr+zl u(2qdownward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began,4g3 yvvp nny)g fw-yp+8wo+0h 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 bl.qptql4v7o ;k(*x qwsock (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 inxl0q 9o: 73 krxi+ktoy contact with each other, as shown 0q+t l ix:xk3 yo7kr9oin 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 absxf *0yr+-g uaove 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 moment0 yf-u*s+a grx the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tablec.n(d3iny ,4p ,oc:poijb rv 2pnq:1s are 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 sho1 nj4i 3 ,:2o,ry.(s:pcdqbpcvio pnnwn 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 o tf fgz6tpzb 1t.9h9-rf kinetic 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 ,7: w);xpng9 (v k,f ozboynfjrequired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0ld9 ef dtfyow;3z,q);.20g. What minimum coefficient of static friction must exist between your feet and the floor ifledtdo;qf f y;9 3z),w you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient ofa3 e05ifnl *cb static friction between the tires and the groundeic l 35nfa*b0 is 0.80?   

  The coefficient of static friction between hard rubber 98as + ithj7id vo,2mgand normal street pavement is about 0.8. On how steep a hill28 ad+vst,g 9ioi7 hmj (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 at o+n 47qbboy9l -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 res54ahdfe+66hcum k931m zoh jat 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 asphal(tfjia/3 ux f:t surface have a very high coefficient of static frxtjf(u a:f3i/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 friction z-2ffaolx2/v 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 boz/nd7 ia5. afrx A have to have to preard5n.i zaf/7 vent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far cixnu1fbd81h w ,9 )tvwill it go, given that the coefficient of w9cn,h x b id1ft)uv18kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizonta.ahvaj/ gyf2-ty9e 5nl surface (Fig. 4-54). A/j52n -e vta9gyayhf. 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 uj/jl 96ifj,v obn;cf6ib,y2; or9i xcrate. The coefficient of static friction between y ,o;jr 69o u2b96ni;flc jb, xfiijv/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 truck?   

On an icy day, you worrbw0( ajqp.-ut10a u5 7ahtja uy about parking your car in your driveway, which has an incline a7 t1wbu- atuq u0a0jap .(hj5of 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 ismi 97:oy +ifd)l 0jda slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plwuaut+/q h) l5ane 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 if qt0tfl;ui3pz+r)+k g.lax * nitial 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 wf+jva)w)u) qtop of the steepest 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 som ix:o6x/q jis6eone pushing on it with a force directed up 6: xqjx/ios6iward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as thed2;d8i-p lzd gy melt. Consider a chunk of snow at the ridge of a roof with addlgd28p;iz - 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 trave)kg vfy-+qe b-/du 1yyling at speed v is equg-k edf yq -+yvbuy)1/al 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 kdvw76 j,j8 owon the dash when the driver decel6jdj ,kw7 8vwoerates 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 initjvw8luy t-.b.t(uu: pj )atq8ial 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 fr3q8t;dawi* m; biv 2fo8y dq1jom where they are filled to the packing station 11.0 m away. The belt is initially stationary and mubamot ii;d jd ;yqv38fw821 *qst 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 fkk v48-dp/qun ,51v9r mx futrriction 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 bicycle) can cbioz r1n n4m(;x3.kojc +ge: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 mamm3- z(ruq s lf;zdfalgm(p/m o/fb)i:* alian heart, at each pulse approximately 20 g of blood d mgq(:oi )m-3*las;//b(zrfuf f lzpis 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 crash if the deonnog8)k m)x4k y7 xc.celeration is no more than )n.k4cgxm8 okno) x7y30 " 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 b 8 ggvk:m53vwly an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of sta :glv5vkm38w gtic 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 accid(yxb: 6l0tu1*j rxroj i i)q)cent involving two cars, measure 72-m-long skid marks of one orjy q)txx)(i lr1c6 :bjuo0*if the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for eachsr0nb .vppzgt0*8k ,5/gdwik 4 m traveled along the road, thtpvw r0kzb/*8sgnigp,5k0 .de elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning T3tboa8x b4)ulq9ocik 8hh3k-ower of Pisa and falls 55 m before reaching the ground with a speed of What was the ht8k -k)9q b3ihlob uacox 834average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but,nal urkx5-8 tyu/a rzo9y(rzn3 m3 *e enters a muddy stretch where the effective coefficient of friction 39loauau r(kr,r*/nx38e5tyy z m -nzis 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on thzlnqeod.mx3k,.szh9 t 8 jq-v83 r6 uve redesign of a hilly portion of a city. An important consideration is how steep the roadsovvqhzs ,8 k38dlj3m 6nex-qutz r.9. 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 to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch p 2zu:ri5*ufmx3j ,t wfrom 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 x*j2iwtzuu3,fp : rm525$^{\circ}$ 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 rampiwj.z)64g( uu;gk1 tw2dtsi*crek d af 9wg02s connecting different pad0a g*.tke9wuc2zi(dw2ti)w gs4 1;6rj ug fkrts 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 (mlh7p 8yh9i-jfiq5h2 z ass M ) using the pulley apparatus shoq9p52hif z hh7iy8lj-wn 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 4n)f+ic5j oka 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 the fz2he+enwr-+ dg 6f z8kollowing set of conditions:g dnek+62fz + zr-8whe
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 Italian6 tnp/dnvvj a2:a5x+) fs jsc3 train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, .6n9mgpdwd0 l8lvmg,rz5o i4*bf: zu 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,gi 8ub6mlp f .wm r:9nz540ld,*odgzv how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is uitb kf3hsau), pvj5vfa2x/ d;a4xz0,sing 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 s,-mrr0q; j2 m nq;7jlchrxaq: peed 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 fih9b g: chh)vifv(ey5:eld incline5:v hfv b(cgy:i)9 hhed 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.