Why does a child in a wagon seem to fall backwardga -ai54l/e8r 3qfmy3biul g6 when you give the wagon a sharp pull3i86m bglqyg43/efaru l-i5 a forward?

A box rests on the (frictionless)-h- 46 gppgvub bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the boxb4uv--h6 pggp , 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 it? Explt daw/ho:mk(/ 3k q(xiain.

Only one force acts on an object. Can the object have zero accelergzjrm, )j/6 hcation? Can it have zero vel r,g)mjj6/z chocity? Explain.

When a golf ball is dropped to the pavement, it bounces backc+jsc5r /1ui x8 :hhzg up. (a) Is a force needed to make it bounce back up? (b) If:j hcg 1zs8hc5ix/+ ru so, what exerts the force?

If you walk along a log frsl9 jmf7h- knqx103z loating on a lake, why does the log move in the opposite d37ms-zj xk 90q rhnf1lirection?

Why might your foot hur,inqqjk,s24ocg ) u( kz+sj3 u;1ahlst if you kick a heavy desk or a wall?

  When you are running and want to stop a cptl9a:a.,q8w3sjwck s4 9s quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (3qs.wp , 9ckt84 :jasw 9cslaab) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of thej:eh2, c-qn nt same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling tehnc-qjt2 n:, hread, 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 ro 7uuao tywj rmf*1f2.:ck is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fas: 7 1frfut .awmuy*2ojter?

Would a spring scale carried to the Moon give accurate results io5,k whz5-z c-pn0ael f the scale had bee--awpocz ,nhlk05 z5e n calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acry:jjo*mymoe*.qvbk7o0 h+ . jwqx+ b( oss a frictionless table using an attached rope held horizontally. 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) decrvobq..qxkjhm* o0(mwojb : eyj*+7 +yease? Explain.

When an object falls freely under the influence of gravity there is a n71 qjk)bs j0zm l7pc+iet force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. W7jcsz)j 1bq7m+0p ki lhy doesn’t the Earth move?

Compare the effort (or force) neededk6 jiw,4vjn2ovw) 1uw to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare wv)i o6 v,2ww1jku4 njthe force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pullsf ( xrenu,)3pk with equal force on the other team. What, then, determines fxu kp,e()rn3which team will win?

A person exerts an upward force of 40 N to hold a bag of ziri bz 26frk3y (55kxr vqe43groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnr53q53 z6i42(xkrz ybev f kriitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on :sc5 3gog tc6cthe ground, how large a force does the ground exert on you? Why doesn’t tco 6c3:g5 gctshis force make you rise up into the air?

Whiplash sometimes results from an automobile acci*xier fg(/ sxqy+ ur7 faxjo390 s8xu*dent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems ex *xx9qyg7 u( u+08fjo3r i*ax/rs sfto be thrown backward in this situation. Is it really?

A heavy crate rests on the bed xvq -zso*d.dqb),:f 3tdups 3q./wj aof a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, f.*-q3d:,owd.jspb )x vdz3su qqat/too, accelerates. What force causes the crate to accelerate?

A block is given a pus5f c4l/bdctgh0 6j((ds7 uoblh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than odjc(/0l f ctb4657ogludh(s bn the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incld 0qpg)w( 1bglvm)*p eined plane? Assume the mechanism functions pr*v1pe)wm0(d b pgg )lqoperly, even at an angle.

  What force is needed to v1 wf huyo2x.j5k a;9vaccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates ad-euyb1pu-z(6sr :7zg hh sb4 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 1gioc(3 ,3vkvi6q ebpused 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 av7jgs*5z6 ka r $76-\mathrm{kg}$ 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 inudek4 mrq.s,8xw* iy2 8.0 s if the car is traveling at d 4esuxy8q.wi,kr2*m95km/h? -  

  What average force is needed to accelerate a5h6*p v :bj,zjl b4mhl 7.00-gram pellet from rest to 125m/s over a distance ofb zbvh4ph*mlj5 l,:6j 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of c(.v e.me* foethe water with an acceleration of 2.5eoc(m. * efve. $\mathrm{~m} / \mathrm{s}^{2}$ 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 coverppfp; k8- 1brh 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 toxl69cyi:g/. ix hzxh4 be designed so that the maximum acceleration is 0.0680 glxcx/i.ghzy96 :x ih4 . What are the maximum 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 motionl 0dmc9128 qe3ys/4wz ybxh thtess 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 at c91s/4qh3y b8t0x2 zey dwhmcceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has am+(hq5bsnhy0j:8 .e oi3qgu f krgt u.s1s, 6h maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator witho5 +m u y6,b..8siqu1( shof: q gkhnhrtjes03gut breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including -rz -2vkw9huvouc*qj/c/h e, parachute) when the upward force of air resistance is equal to one-fourth z-/cr juh k2-cvu*h, e/9 vowqof 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 strik (6xz( r*fmidqz .)u v4iid(yles the ground below, he bends his knees so that his to 6ril*qdmy zi f) x(dvizu((4.rso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table.waa,r na6(e 8pu ,pqyt; (fqpr3.l2gs 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 the pulley weigga, pa(pt qr.e32ufsw(l 6,8 n;qp aryhs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbnr uf2qb4(xe/all 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 basebal+t- wpzp4(g,s i;6 prv1qz*kxoo*mg il (a) at the moment it is hit by the bat, and again (b) after it has left the bpp4m*w+zs 6ot*g pivq; 1xor,-zi gk (at and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A sexu, jkvik4zgro 9br4-d hw:,0cond 650-N force must be exerted in what direction so that the resultant of the two forces uxb-94w4vr:o ,gd r0 zjh,kik points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "higfb0w 5o 0sg3sty p/(yyh wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is ytoyw5/0bfygs(s 0p 3 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 mt0b pmos,.h 8;wl- hncassless 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 14.0ae(wdc8- dh vn:24d yk$-\mathrm{kg}$ 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, Antarcc638-pgveki yli9a mle,*m ;jtica, as shown in Fig. 4-46. pja ,vicik3em8y g6lml; *-e9The 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 iwkp 2 ,0wqcrghm 0r47cs pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betk q2r wm4prh00,gwcc7ween 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 usinj1c s2c8 s x3fnuwyt tt)2s w:h,vfk84g the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant uj2ntw)2y:3sfcv t c 1wxs8 ,hfstk8 4speed?   
(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 65 bmdbs28y5 yb 1dc..et8zpo 2n$-\mathrm{kg}$ 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 blockm,i6:)rhwd jh8r7dr y (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 fr4t y*h1 omscr/ictionless horizontal surface are in contact with each other, as shown y41/sc*h tr omin 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 j987ue2bk3sgofu y9q 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: Firstu3ufb2 ks7 ye9g9jq8o 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 tabe5mw8:brogt 3k(h 3e hle are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box ank8eo(bwh3her 53:tmgd the tension at each end of the cord, 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 friction between a 3y(plf7tw+t bdw758 5ppa iu0mi sg+8r5$-\mathrm{kg}$ 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 requiwu/1df 9(,xtfsfh .klxu + bx-red 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 stl7uz2ss o s8)zanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your s8zos 2)z7 slufeet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coef6n;5o9 2 cwkdjra6ke sficient of static friction between the tires and the grounracjskk6n; 5o w de629d is 0.80?   

  The coefficient of static friction4gtwn4g )6fs*znl5ul between hard rubber and normal street pavement is about 0.8. On how steep a hill (maxig)f4u45t 6wlnng *zslmum 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+9:dt -.gp/ogxdntw n at -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 340/8kdi czx u1srw :px8yumx753(v n qa* goui0$^{\circ}$ 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 con4od)b6po1i b ll )l8gftact with an asphalt surface have a very high coefficient ob g)8f 6ldl)pil1oo4b f static 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 dcw0 h gqtzkh3)7v42 fy+ia7z friction 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 w d21s4uq/kodw ould box A have to have to prevent any motion1 2kd /so4wuqd from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrossb a-heohn *pmb18 :8rs the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initialnr :mpo ba8 b81sehh-* speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 vzzf z) onts.,x .af*zt8me)7kg and 110 kg , are in contact and at rest on a horizontal surface (o8f )z z.tft.se),z z 7mvxn*aFig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient o9hlk u f(ql 44bskz2 bns*l7z2:yv 3ocf static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the dr4znofsk93(ql lvbu*yk lsbc: 7 2h42ziver 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 anasgtx(wstx:mle 0-;sbe);6 z inclexse)gl zb(- s:axtw; 6st0;mine of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 2dhl* 2tfp(h .o8$^{\circ}$ 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 bps k*8qadyv 2 hkm*3v72 za)da plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spe9p.,wljxhd333fe a7 vte /tx eed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with1bj 7 stz.tu9n 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 wi+c(ntv79rwvqfk v69c c +4holth a force dirvh v o+crktv9 (lcf496+qn7w cected 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 become 3z9 c xfmzxapb )pg)enu24szf9i9o3 5dangerous projectiles as they melt. Consider a chunk of snow at za9 53bp3zxensgf z)mc p u4f9x 2)9iothe ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automo 1 d6llv49lckzbile traveling at speed v is eq1lc9vzl 46dklual 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 ;dul9uqmvcn+ u1q: n /car slides forward on the dash when the driver decelerates from 4 ;qd+u:v u /9nqcm1unl5 $\mathrm{~km} / \mathrm{h}$ 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 initisxo90h5ybf n,e)* 2mag h(uegal 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 befotub pxcjhib*6) dc340t ao4 :ql)7ylt from where they are filled to the packing station 11.0 m away. The pfatjoh6dtcl4xbbq*73 )4:uy o0)icbelt 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 each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction beqa/h s cb585j)vr k*iotween $m_{1}$ 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 (inclu *h q b2xmubn49(ssuk9ding 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, atfg: dz +bza(yzje7v8 1 each pulse approximately 20 g of blood is acceleratebvf7dz1 ejg (+ 8az:zyd 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 dec 5,lni+nyr2p js2cn9releration is no more than 30 " g 's." Calculate lr,n 5j92cp2riyns+n 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 earthquak nj p*8j asin)l1n;/hye is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must b h*j8npn/li;1a )yjns e 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 om)j:ts8y iy ir 42zub nbfl *9f16hd.gf an accident involving two cars, measure 72-m-long s.9b* zdbnyr4i u8ilmgjsft2y:h ) 6f1kid 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 1ty+iwf; 6idn:-in-4 hill (1-in-4 means that for each 4 m traveled along the road, dytni f ;w:6+ithe 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 dronjxexu- 8e+/,,y topgl,9s 0jlv1h rz pped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resist rl0x-jh / ougstel,z, +px91vjn8e, yance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mudj 5xm,vw; *v)hfmq* dm rp7/axdy stretch where the effective coefficient 5 vvjm7 *hf) ;xwmraxpm q/*,dof friction is 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 th.kd e) d*gkh9pbq9r7 nrz(;zpe redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that eg 99*dphren k).7;kpbzr qd z(ven 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, ( kmb1tv43lk 0ssxe 9sdangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makeskve(t1 bm 3xl ss4s09k 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 a7u3wb lc vszu:39eg3 cre to be several ramps connecting different parts of the gv3ce ubwu: l 9cs733zstore.
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 lifoqu(. c skv74x i;u(plt the piano (mass M ) using the pulley apparatus showni;ckuqv7ux( o(p s4.l in

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

  A jet aircraft is accelerating at 39 p2skt -)rx smynxkp4sk*;c3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 fo. c4 fn-y:lvwhp-1 pjap tf6v8r a child-restraint chair, an engineer considers the following set of cond-np :vyt6fah4 8v.c1p -jplfw itions:
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 (660,00r vq:3s,:lc1 ma7crg a0 $\mathrm{~kg}$) . 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, q.t+ )eq6- vnzuv5tiwuse safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Billvq unt5 ize-qt) .6v+w 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 her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 0i ls6tes.* elr6/wgn $\mathrm{~b}$ 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 buildino;)qrvf b2q z-s s78ckg is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together gqt-- kpbidl dr 3h,)i22jfh6are ascending an ice field inclined at 2dilb-r q-)p3 g 6f2hhijktd, 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.