Why does a child in a wago vgcqq9iib:4 eqh5 l+/n seem to fall backward when you give the wagon a sharp p/ +i gb5vi4 qeqcqlh9:ull forward?

A box rests on the (frictionless) bed of a truck. The truck driverrbooqe- )j*2 z starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who i)jo2-r eq *zobs riding on the truck

If the acceleration of an object is zero, are no fov2)fswqh -.(c k o0bzhrces acting on it? Explain.

Only one force acts on an object. Can the object have zero acbr.,6*65ih4 ymdjkl5uoxjzwmrh:jwxo/2. oceleration? Can it have zero velocity? Explazjxdol5:j.u5x6i/ hmwo* h,yrow 2m.k4br 6 jin.

When a golf ball is dropped to the 2glx , hi6tqg9)fvr:aup*9do pavement, it bounces back up. (a) Is a force needed to make 9 :fgah2t6gr l,po9 ix*duvq )it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the op2o;;r fy;evzgposite dirro y;;2;zf gevection?

Why might your foot hurt if dl56 d:dc*3x0zne5v1vozc nawo e*b 5 you kick a heavy desk or a wall?

  When you are running and want to stop quicklt blbly5sj6 2h e7gy;m26 jrz6r-h8jcy, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximumej 72j-yl6r5bhl z t2bj6;sry cgh68m 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 f (.b7a 0y55jmjc wnjothe same thread dangles from the bottom of the stone (Fig. 4–36). .5cyaj5f( 0 j 7wjnmobIf a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twici5y32 q5dtfrxyf70t m e as great as that on a 1-kg rock. Why then doesn’t the heavier rockf dq505t 3 ymt2xfy7ir fall faster?

Would a spring scale carried to the Moon give accurate d;uz0os,c*;ew ur3dq z 1jv /lresults if the scale had been cali;zd r3uvc;lodsq /1e,* 0uwjz brated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a f.m mldfk r+ip*b-w7w w5au-m9rictionless table using an attached rope held horizontally. If you now pull the rope adup*lwm-wbmr .5+ki7 m w 9-fwith 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 ttn5h-7 jhcr o loce47 m ij90-lk7+ovehe influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third m-7 + vholoo9 jhjln-i740ccrt 7eek5law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or ds2vme 6 s;bf5force) needed to lift a 10-kg object when you are on the Moon with the force nebf m2ss v5;de6eded 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, eac;cgu2ukv9x s4frq05 * xfw/r,2gbprih team in a tug of war (Fig. 4–37) pulls with equx *wp2qffbx,/4u r 59 gk 20rcisvg;rual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. 77)o wmsum d/7tobz g(Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (dwotmg(/ mz77sob) 7d u) by what object it is exerted.

When you stand still on the ground, how large a force does the gg kg(els:* n*sround exert on you? Why doesn’t this force make you rise up in*g*(slgn e s:kto the air?

Whiplash sometimes results from an automobile accident when the victim’+ ltw*k 4-ez .tcqjq8u.nlr wvdu ).;js car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. q*48rw+ qktdu.n..-c ewujzv;)tljlIs it really?

A heavy crate rests on txt.bvq5:sm6ri g(1 f ghe bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate tbgft (siq.x5r1mg:6 v o accelerate?

A block is given a push so that it slides uvlr cz(p-:w) jzh0 myp .t 1e*b9:hjrfp a ramp. After the block reaches its highest point, it slides back down but the mz hrv) z(l t9 r:h ppey-m*j:w1bf.0cjagnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scgr;04h2 wjyd hale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an ang; whdy02j gr4hle.

  What force is needed to accelerate a child oib 4j1f)r, lttn a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider aux+8sc:mu*a pt 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used mt2 x/f,1slh7sqbx56 loqxt; z; tqm*qvqz-9 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 ajvjq)kba ;i4. $76-\mathrm{kg}$ 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 requ479m rtavrr d9ired to stop an 1100-kg car in 8.0 s if the car is traverrt4m d a979vrling at 95km/h? -  

  What average force is needed to acdd)h4 ks io3z+ha.cz.celerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.803 z)sh c.d4zdk.h+ iao0 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the e2-g :tsp6pz9 mii (oywater with an acceleration of 2.56ey 2s-g m zpt9i(o:ip $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile trio1jo y:z +km(ack (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 desiph imy*. wpt.k)*b2c bgned so that the maximum acceleration is 0.0680 g . What are the my*p2kh*imt).bb c .wpaximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. Whe z9pg)oss64:uu 33yzo hlj:lsn the elevator begjo 4olz sy u: s33g6suh9:z)lpins 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 acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum svv 2ntl;) u*7,xtrp dex6ql5 htrength of 21,750 N. What maximum ul5t;ndqxh xe,t6lu*rv7p )v2 pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including pt/a9tij2 wv4 warachute) when the upward force of air resistance is equal to /w2atwjti9 v4 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 strikes tk0k16po dkq h6:w.srm he ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass do h.qk0ks: w p6rkm16of 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 rcca+y+,e*fr oj 8j5 abp 23xidests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hu5, rbo 2a3ipyc*+dex+acjj8 fng from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketb-n k/krbd-or8u- m1 3 gza7r)zo hpaj6all player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body ) n y(tz75 vibgk4uuzi:qmp0/diagram of 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 outfield. y5in:t(4b gv zi) m/0qk7uzup

A 650-N force acts in a northwesterlypa 4qp(2) -;e nbmvmqa direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustra-; aapqenv qm2p 4)mb(te your answer with a vector diagram.

  Arlene is to walk acr , jh* )5anv+ed;reeyc6lbo lwov3+z+ oss a "high wire" strung horizontally between two buildings 10.0 m apart. The sag 5v )obh+ +;ez j6law*d le+enc3yrvo,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 bktu uk zid 8p,,n0:fa*y a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1u)8x *y(j; unboq)fle4.0$-\mathrm{kg}$ 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 locati)c.e8m, kt p8x ktny a3zgd:e1on at McMurdo Base, Antarctica, as shpan) cdzgxm8k,: 1 3e.y tek8town in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two carvlw4r m..w58bj e8hu as of the same mass behind it, Fig. 4-47 . Determine th um4w5h leb jw88a.r.ve ratio of the tension 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 heremmdlqwk(( 1v h 5ar-,self upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How,vml(5 k1 md(eqh-ar w hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a ksgc60bql2k5b 5g yn765$-\mathrm{kg}$ 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 nxf .gws1 :q(kcx3c :iblock (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 fr2aghmchmos+2 7 ;s .onictionless horizontal surface are in contact with each other, as shown.m2g ;os2 7ch samohn+ 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 in Fig. 4-52 are each ic3lsgppjtk3: -x l a0/nitially 1.80 m above the ground, and the massless fs3-: xakg/ppt0 l3c jlrictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are conne*v9 y*.d n mjqd+m.,3h-b xti:ix8jad k cy-qpcted 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. 4-53. Ass 3d+k*qji:8 cdxptd9-* jbm.aqyiv,x my.h n-ume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a che lu 2gr 371fqkph/6 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 sed59eh /mkz,k+ k8y* - uxjry0dz-lxd tart 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 okpysfmr f6-+f 3mw + n*-qw7iln a train accelerating at 0.20g. What minimum coefficient of static friction must exis+ s m*l-w6fyp+3 nwfm -k7irfqt between your feet and the floor if you are not to slide?   

  What is the maximum acekfcuklu2w::ja)k9up8 8 5vww10 nkxceleration a car can undergo if the coefficient of static friction between the tires and the ground isw:)5aufwk8e up120kxj wvkl 9:u k8cn 0.80?   

  The coefficient of static friction betjir+v:vnpwmq4 4 y8fiei:w12cg +j 5uween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a cj gj +i:ce: y8 r4f2+unwvi5w41vim qpar 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 ap iqolvg0*u ;*s.adcpf g48j7t -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 rest on a rough f99v. iwydbg2b;7s1q qp 9.*zf ecpy r 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 surfacekn -w 9 6qljsq6cltr44 have a very high coefficient of static fr cq4q6nj6lkw4lrts 9-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 +z *kglz :rm48sguyi5d)j v3h ;;uavffriction 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 (Ex)4a.t u4//oy seycnk xample 4-20) how large a mass would box A have to have to prevent any motion from occurrin/u nat/4y4k. sx)coeyg? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fl t/a 4nu07fascw1k;qc oor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiala1usc40 kq/ ncwft7;a speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 r,/tjz2p:cr vkg , are in contact and at rest on a horizontal surface (F/vr2z cjrp,: tig. 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 carrh gzv0 7w 7+lyo8j8,get;wld1 ry0oovying a heavy crate. The coefficient of static friction between the crate and t01jt0y88o,wy;vgl7 r glov 7h d+ozewhe 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 your car in your driveway, which has :f:q1an.su4 jw;p3uhhu/ui uan incline sp:.h na 1u;uquw3 h/4ifu:j uof 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*,aubtkc) gz8 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 7d g:31dik+yhpt lal2lies 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 inyu rs ckr:1p3j ;chd5*itial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top ofweruqto9w(:+,.mnkje.:i fs 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 someone pushing on it ;c9xk dwl0kwd0 c-- xdwith a force directed ;d0-lkc-xxd0 9ck dww upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can becol.odf6* rn b)zme dangerous projectiles as they melt. Consider fl roz6n.) db*a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stop-vcoh5 /htfvl0 nswu)c /r ,n0ping distance for an automobile traveling at speed v is equwf 50l)on vt/h -sc/r0hn,vcual 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 zt l:14brf57k q: ojipthe dash when the driver d17t:: 4klrbqiof 5jpz ecelerates 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 ieulo. *p g *rwcy8uv0+s given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they ar8;x:(pknd) v hae/tb we filled to the packing station 11.0 m away. The belt is initially stationad8bwv hx akenpt;):(/ ry 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 coefficienvk t2jyil7vh0z 2sk5 f yf8.*m5tuno;t of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicyclme)nfha fzi5e z q3c:kit260/e) 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 simplifie,m4k5x o4khuz. trvx n:a4mi ,d model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fv. 44i:t 5ha,r xmuz4onxkmk,rom 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 7ezhd u :85asi2p*;ec wkjmy2deceleration is no more than 30 " g 's." Calculaea* 2ed8ymj2i kuwsh5z7:; pcte 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 earthquzt+f7i1.lsuj j u 8p; xf(q,eox:pdk/ake is a , and if an object is going topi, ujx.+(q1d7tz8 :pl/;uexsjff ko "hold its 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 scesko(mdm *nb5tg 35v4fhn1eb* ne of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about5shbn*m35*m(1 nd btk 4 vofeg 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hijk9u zg,hlqed7j8r5 + ll (1-in-4 means that for each 4 m traveled along the rgzqu8j9,rlhe+7k5 d joad, the 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 dropdh8u+ plv2o m5ped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the au5 m8+hld2op vverage force of air resistance?   

  A cyclist is coasting at a steady speed of 12fyykoij-mnuv ::/ )w cu*ws -2m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will :*/- )ufo2jvku iymwyn-c : wsthe cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly pby 0t.idq.u3oortion of a city. An important cb itu.. oyqd30onsideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest 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 watc)8;xab34y rn-x hrn; vl-pjpsh 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 mal;ps v bjn-84r)hx 3;xypr na-kes 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, ( biw/j ,*qjxa)cgo )gthere are to be several ramps connecting differentw aj*c/x)b ,) io(gqgj parts 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 (m;w umia;fgvcf; 5d: k+ass M ) using the pulley apparatus sho5g +fva;f u;i:d;ckmwwn 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 ac6vdrb 3bqzqd 6-i sp des298d/celerating 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 ol;-8xiv d;8w1t syrzfor a child-restraint chair, an engineer considers the follo8;z xod8rv; y- itwsl1wing 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 tg3)sue5up6e qsy ,6 barain 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, Billm 57it ncatxsa 21r/9b and 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, ass/t9 irca51bsx7m2a nt uming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using 6z3hs bnfvrqbm2-71h 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 build((p wub5x+ ed sfaavct;mudt38) l)u 9ing 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 rox/ 2buzol4wwmf5 y6k+ped together are ascending an ice field inclined at 6wu/5 mkxzf ywb4o2l+ 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.