Why does a child in a wagon seem to fall backward when you give the wagon x*qu8n(6 k jxea sharp pull fo(unxej6q x* k8rward?

A box rests on the (frictionless) bed of a truck. The truck driver c )+dzg p,q)u 4nphhl2starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss )l+ hz)uc npph4d2 q,gthe 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:4b7n4d9 vge yhfpl b3 no forces acting on it? Explain.

Only one force acts on an object. Can the object hq6 lxc4cm-z:3og fpvw)6i fm.ave zero acceleration? Can it have zero velo)gf:pm v.z 34 fw6o-il6cx cmqcity? Explain.

When a golf ball is dropped to the pavement, it bounces back upuw9 3wny d1 (wfhj-qk8. (a) Is a force needed to make it bounce back up? (b)3(un19f jkw hq8w -wyd If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposi+j)umu6t(u5emku f5o 4p1 / leh/hzdate directlu65+ aomueeud/f1z jh/hp45km u)t ( ion?

Why might your foot hurtwcbalat(9bo( nm0w 3wr(r 4n4 if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceleraexp0 (nc5d r;xns 6mr(te quickly. (a) What is the origin of the force that causes you to stop? (b) Estr;5sx(cdx0rp(n nm6e imate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thp-jno ou/f0,b read 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? Ex,oj -f0unpb o/plain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.(wi ndu+:rby ox5*is 2 Why then doesn’t the heavier rock bn:+wry 2*uisx io(5 dfall faster?

Would a spring scale carried to the Moon givet*;: z+mxy(vag7hfqg accurate results if the scale had been calibrated (a) in pounds, or (b) in ki7:mz;h gf(y*v xg+taqlograms?

You pull a box with a constant force across a frict (bmqh51zl+4u ow d:fmionless table using an attached rope held horizontally. If you now pull thb5q1zf(wm :ud m4+olhe 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 nqwvx 4ha./i y d,3:geoet force mg exer/,hy xe:wiodv3gq a4. ted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needeza ee(.; d ruznh0o4,wd to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object ho reuwae0z(h,. 4onzd; rizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of n ; rfgr)z+00j3yzdsawar (Fig. 4–37) pulls with equal force on the other team. What, then, determine)0n+ 0a ;grjydfszrz3 s which team will win?

A person exerts an upward force of 402 -won2yv--r 0bcos mu N to hold a bag of groceries. Describe the “reaction” forcem2rwoo-u0 cs -2b-vny (Newton’s third law) by stating (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 on th 5ytpf1; b(bpycvdm m.q /e87te ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the apv cy. (mt5b1fq/debmy7t8;pir?

Whiplash sometimes results from an a:n mm4x5atei /tj;l6q0)zofi utomobile 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 m iqe54);l/60tt:oznaf xmij really?

A heavy crate rests on the bed of asjp7bl (6r : sl+xuom: flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate6rspbo+x (:j7ul ms :l to accelerate?

A block is given a push so that it slides up a ramp. b(p12-n kp3k xpbka,zAfter the block reaches its highest point, it slides back down but the magnitude of its accekkpnz(2 abkpb x-3 p,1leration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined k*;lqv ;r4uux9qn jd9 x5mai) plane? Assume the mechanism functions properly,kjr4uni;xl 9uq; d )5xv9*qam even at an angle.

  What force is needed to a5. a+gzf+euec2oc8 qzc8a g d0ccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N s2k z9gvs8-x-. uxxnfaccelerates 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 is used to accelerate svvy k f +;dqs1de:48dfkk4;ta 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of au)13kg nc9ed+ qmrzn) $76-\mathrm{kg}$ 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 require e( sfyncz/ 78.m( ja7xife+tkd to stop an 1100-kg car in 8.0 s if the car is travelin((nfxzeta sc.y + i78/7jfkmeg at 95km/h? -  

  What average force is nen0czy(n z 2 7dwa4ti2teded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 itc7w2(4zd0 nznyta 2 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ofnp3c, qez 6oq0 2.5 co3p 0 zqnq,e6$\mathrm{~m} / \mathrm{s}^{2}$ 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 cm;5t k vk)v;qlan cover 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 maximum acceleration z/. wpd v6iu) yk0ov5y+ dg2xpis 0.0680 g . What are the maximum and m ypuio). kwg 05vd+y2zv6pxd/inimum 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 m(qrh.y+ nh )u1 epk6 eil1d6wa 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 acceleration.lk + wrqyh11edu6.( phmen6i )     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,1ad gd6qq9p )v750 N. What maximum upward acceleration can it give the elevator wi 9ag1d vq)qd6pthout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (m2s5k t igk7si4ass 132 kg including parachus i5 47kgtik2ste) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m1s sv ki00l:fw gcp0x/ high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If 00wk:0ilsp1x v /fc sgthe 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 tivz/ryhjr6mh5u/ 2t b 6t.eim,ed 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 o 2e5r zm6 ht,uj6hyrmib/vt. /ther side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram fojo;q. 0; kwql kcmj7fsu1:u 2xr 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 of a baseballgi;l -: wl+wut (a) at the moment it is hit by the bat, and again (b) after it has left thel-:ilwt;gw u+ bat and is flying toward the outfield.

A 650-N force acts in a norapsjw wdsm lh 5+ m)lr;2a+ft97 vj6*hthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points wes)wvjs;m tdhs +2*la7 hp695rf+j lmwatward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between t8-qqf6(,pvj3h cm drmwo buildings 10.0 m apart. The sag in the rope when she is at the midpvrqd8-,phfmm6qc3j (oint 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 buckeimz.x1z 1le +qt is hanging by 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 1aosmlhux d1 xan89-hc8 +l5 qx2 62yea4.0$-\mathrm{kg}$ 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, Antarcfivl 9t7+ym, 4zjrwi2frh s; 3h.i4awtica, as shown in Fig. 4-46. The sum of tah.; i vy2i7s r+t , r3mfj4lwfhwiz49he 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 the same mass behind it e4v frtc (;h+4(hmpem, Fig. 4-47 . Determine the ratio ofr eme4mv4f(hp+ h ct;( 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 herself uy2.ruq+m -mcfpward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mum -y2cufq+m.rst 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(9fz2hq ; npn j d-c58nj4b:ru oh.:zzjhxym-, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block+ :ifcishc. d +xc6s0eh0las r*5bvf4 (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each oe k6kj*w 3ppi0ther, as shown in Fig. 4-5kjp*i60 e3pwk 1. 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 qw;nq :iq:pa/1h8den in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m :eap/h;w8 1nndq i:qq 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 frictmrzf;be );b py nu)(,yionless table 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, uyfb; )z;b(, er)mypn using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frictior6e s0 edak3l4n 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 ax;estr+-a mg 8rfa;o6 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 acceleratinh;+- :vss(qd8cdz1ck c1nl mwg at 0.20g. What minimum coefficient o;nl-8c s(k wdc:s +h1vmz1dqcf static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can under7u)tzvhj8(iuw3 p iq3 go if the coefficient of static friction between the tires and the ground is 0.80? w73(zt3 qpuvh)ui8i j   

  The coefficient of static friction between hard ruwdu9tc,g;k 5d9z2pe/xm)hmzcm4 9vrbber and normal street pavement im tw9;rx5p d e9g29,zv/m4k uhcmz)cds about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate a 1 6bg-xfl+ r8kwhubuife(* :ut -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 yf0in s;,d;nu hlq5n0 e1ju l7rough 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 wit+nhxn0z:53.)pfs3gnen pg fh2h w d9rh an asphalt surface have a very high coefficient of staticn3pfgh +2wfhd3 9nrpz nx: h.5n )0egs 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 friction0 ftl*3)aoltas,k ) p b.tpxlsad: v* iv)2vk+ 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 lar/2 dliaxx)la 9ge a mass would box A have to have to prevent any motion froml 9i 2xdax)a/l occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesl2rgksn* (m xulx6 .y) across the floor. How far will it go, given that the coefficient of kinetic frictionru k2*ysn6)xlxgl m. ( 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 horitk6stk;:1qk izontal surface (Fig. 4-54). A ti 6;1kskq t:k 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 hpo4 sy6sdud9j8- q25wze3:uof ou8a peavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the dri8e s wspa qo:jfyu3 u do62-948o5dupzver 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 hix(ha bhf),rt10 mrp6as an incline o6a tpx(m0brhh), 1rf if 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a v:n:wz4ms,og yay)bxfi4 knw;(( *qg 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at anlh9 *d ajb5i(yze93 vf 0fzib1 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 initi*;e0.19g0yugb h uzp1pwbs psal speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of phituep (t:j9 j1-2pc 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 with(znr;xd 9hjo: :j(xd;n9ho zra force directed 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 beconq(*r0m,d smgt ytl bj qo,v:w55.c4w me dangerous projectiles as they melt. Consider a chunk of snow at the ridge 0lyqr4vgtb ocwsm.wn,, j*5 q5:(d tmof 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 stopp-r+zsyb9 o)poni3 ao6rbu; k;ing distance for an automobile traveling at speed v up6 o o9a skorrz+bny)bi 3;-; 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 driveiak ,lgmhh4go -2o*0cn )l:xlr decelerates froohxh l0l-m,lo g)gac *i4 :k2nm 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speee +tn;e6q)xs;s:mt xg d $ 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 ts (w)zcl w2m9r,9stbc he packing 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 0.60, what is the minimum transit time for),wc 2s9l wmrbtzs 9c( 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 kinetq4y. mh8;ao adic 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 br*zbd k zsg/) 5+uyi -u)a4dic8r1qrkg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse apprvhlyf3b e/ )po-3lxl185 khis oximately 20 g of blood is acceleratik/phhv1olfs-3l5l y 8bex3)ed 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 t5 -4-llrf2i0 90sqwthqaq:v( y simb automobile crash if the deceleration is no more thanbsfqh9- ilyvl-t(tm0arwqs :504 2 iq 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 accvq a2,+o puw9ikh 53roi zu30neleration produced by an earthquake is a , and if an object isuropwiov3u0 h+ i3 a,k5nq9 z2 going to "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 tp25 ,vz notqkhf1;( lrhe scene of an accident involving two cars, measure 72-m-long 2k lvo(pfzn51;q,tr h skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1- jwbbn 6(o*(vein-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 traveling 55 m? (a) Ignore frictionnb w((v*eb6 jo.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top eh 6060phb 8,w(mv7*ywfqwxx,s3y jqjt o7aa of the Leaning Tower of Pisa and falls 55 m be q wwyaxa w,oh bqt7jx*my,v6pf(he37js006 8 fore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting ae :l)zt4 tg7v(w) uualt a steady 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 11wlt) tg7lu :eva(u )4z m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a h afzh n;6mc 5+i)opas-illy portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particulah pa+;omcan65s )f-zir 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 likesjqfifp3-4; yir/. w rc physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices thay3r c jwqfpi/r;4- if.t the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be severa5 7at,neay;w0lobnp o*5d2cz l ramps connecting different5t;l7n by *wco,ae5zo20pdn a 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 qa e n:fr79:dbF is needed to lift the piano (mass M ) using the pulley apparfrd97 : anbqe:atus 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 accelere jn7/ xseg0yy+ 0e-vwating 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-restraixw:kj4l3 11d(cy lc kgnt chair, an engineer considers the following set of condidw 1:(4k 3gyklccl1j xtions:
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 (660,00 9;bqb 6nkqua40 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's r5ke8 uc. u5h/ 2qhlxdjope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of hqkh5jx/uu85e.lc d 2 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 avd 6lwt k776pr " 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 *bv b7dk9 )otgis 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 ingrr3, v3qv; e; *qxqfeclined a rfvex; veq;rq gq,*33t 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.