Why does a child in a wagon seem to fall backward when yspa+ ktfw;z9v50euc8k +eyxr: k;i0s ou give the wagon a sharp pull forvwzcfak :ir+ ye; uspke8+90s5 kx;t0ward?

A box rests on the (frictionless) bed of a truck. The truck driver starts to7c +.rcs:8 q,b mqunvhe 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 g:.,+ v c buqqn8orc7msround beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero,d cv+i93 so3kg are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accel5g1 qs ioeu6;mpgs -5jeration? Can it have zero velocity? e5jsqgiou5 g- ;6ps1m Explain.

When a golf ball is dropped to the pavement, it bounces buwgva3n 3 /qn3 zg+y33eyr*osack up. (a) Is a force needeuo 3ny3g ys3 *ge+ rzqnvwa3/3d to make 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 otw lppempxlf 1)(od p1 1,4ns3ppositexpls13(,)p1pl dw n1t4fm ope direction?

Why might your foot hurt ifzq,3(f*hpv :sgt p )qp you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qagw 8:eicmto(pb:j:iexl j 5. i8cgq 9zq-l67uickly. (a) What is the origin of the force that causes you to stopmqj97iz5:li (p8 lwq.oec-tgc aiegj8: :x6b ? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a secti 0 hqml2yn19g -6e xqar2to7k;zpbiq.on of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the s71b 2yilqgtx0e p9ram- zq2nkh. ;q6otone 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 twice as great as that on a 1-kg rock. vnh9 (9swp d:1v7dlf gWhy then doesn’t the heavier rock fall fa9dnp7(vg wdsfvh: l91ster?

Would a spring scale carried to the Moon give accurate results if the scale had5d 7wma6iz 3,/rwf lxe been calibrateda em, xwr7l5 3/izf6wd (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table uo+fjozi (x,yk;6+ * ajtxg ki5sing an attached rope held horizontally. If you now pull the rope with the same force at an angle tkz*,x a6gfiioyjtx jo;k+ 5+(o 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 qg o.bjy+n7z4gravity there is a net force mg exerted on it by the o. n7 zq+b4jygEarth. 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) needed to lift a 10-kg object when you 1kv v* kt,4hlex/x4xbare on the Moon with the force needed to lift it on Ear4h4vt,v* k lb/xkex1 xth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug/v - tk44xuh)i i5fyaw of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whichkv-4fth /iy ai)4x5wu team will win?

A person exerts an upward forc :3p,js14dbtloo d)ushp/ 66t ph0gwie of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on whatsp0 wso6h:htp/)6 pgl 4b uoj,dt i1d3 object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force drqn v ./op(x/k)i6rd toes the ground exert on you? Why doesn’t this force make k/on )r6/tdxi v.p r(qyou rise up into the air?

Whiplash sometimes reln b;zpm3xaw69y wb*6sults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to ;3xpww6ab96 ymz*bn l be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When thlt , :c1tzhyh 72(cqbfe truck accelerates, the crate remains where it is on the truck, so it, too:cbz2 1,(hltcf yt7hq , accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides uvojb:)q6l 1 d9,kbi m-+cys vop a ramp. After the block reaches its highest point, d- vcq6 1)kvm9oby:,i+bolsjit slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yo . 0p4;b+ 4qrcxhsqfzzurself on an inclined plane? Assumf+0pqczb .hs4z; xq4re the mechanism functions properly, even at an angle.

  What force is needed to acceler*li; ejvq4-aj f ;gc3fate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.3pec lt6g8f k)20$ \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 ueu fz2z 3 h9ramo44z8csed 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 a pv+9u h+ nk4rx $76-\mathrm{kg}$ 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-k3 xuyyzxr804qa/iu k (g car in 8.0 s if the car is travzr40 i8xu (3/ykqa xyueling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to +duoasgkw45 oi22xf pi0e,hw.0) jds125m/s w0 psxf,d 2h w2s 4+uk0.iij5g oadeo) over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.fss9w6( 9*8xbksn2cdk a1s5j kws7 n:be p, lh2dnjw,a*s6(s1eklbn:p5s8bf7 cs kx w9ks9h5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 -nqevm)hb h8c h2zj u6 32ru+kojp:1scover 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 t:; ufq;ao9bxpo be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max = ;o: ufbp qax9;   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. When the elevat ai3jju( isw,mt3/9otp (dul9or begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevalu pt(m/ud3ai99oj,3w j t(sitor, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximf77wxfvv.nk)fd5 b9:3 avmszum strength of 21,750 N. What maximum upwar m:fn97b a 3fv kvds7zvfx)5w.d acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 37kn.6g ladm r132 kg including parachute) when the upward fol .n 7akmdgr63rce 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 v9e)bf: afst/h z+br,3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 mfvsrb:,)h/fza +9 b te. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A ropzpm;.*3 qd.x nmst(a.an my2 te tied to the box runs vertically upward over a n*( m;z.2dasqa.m.px m tn3typulley 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 weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball plat tp)u uyj:xssr2qdl ;497x4ryer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the wt5p h( kgo:76xxwc, imoment it is hit by the bat, and again (b) after it has left the bat and is flying tow7i k(:hgwcp5 ,x6 twoxard the outfield.

A 650-N force acts in a northwesterly ds.)aww cq* s;v:pe; gwl4o 2zzirection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector dizl2eww;sz qos4*c p :v .;a)gwagram.

  Arlene is to walk acro3t)+/ l6 l9kabqonyzmss a "high wire" strung horizontally between two buildings 10no3t/6b) l m9 klzqa+y.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massley js7r vhdzouid6tc.0;5sb+e-n 9m o;ss 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 14n;;32mn hrive cj tr*:.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, Anehxq l--skhu6e rtj9x)/z 3k .zks4r.tarctica, as shown in Fig. 4-k/q.6h9 xr 3-luhxkkst)ee- zs4 .jzr 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 cars 9o 71lirap ve2of the same mass behind it, Fig. 4-47 . Determine th iao v7rpl91e2e 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 herself upward using the bucket-pulley appar;( o3o; deoae95 , kmtia p0mfits2ew6atus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constatot2s6 ;m kmo9fo5p3 (iad ;aeiew0 e,nt 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 dva21;qlwr3 z19 urxc65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a bl(oes+dsa-l6 a ock (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 frict6vm)qc o 85lyaionless horizontal surface are in contact with each other, as showol5m8a cy 6vq)n 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 initiallypq:9x6bp mcp-vb/;xq b;zfi * 1.80 m above the ground, and the massless frictionless pulley x; f -/: 9bq6xpmb*pvczibqp;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 connected by a heavy cord ofv sc1f;wxfi*3rc :m4p mass 1.0 kg . Calculatepfm 4 cf :v3*isx;1wcr the acceleration of each box and 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 f79f pwpxz yg.)riction 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 requi6atr:nt aa9/m.:cru pred to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train aoj+t* 2wws2l gccelerating at 0.20g. What minimum coefficient of static friction must exist betw2w2lgjo+ *wt seen your feet and the floor if you are not to slide?   

  What is the maximum ato (ljotq6a84 h0n mq6cceleration a car can undergo if the coefficient of static friction between the tires and the grou( nja6qqt6toh0o 84lm nd is 0.80?   

  The coefficient of static 8u9ere ag9kf.friction between hard rubber and normal street pavement is about 0.8. On how steep a hiufae k.g 89re9ll (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 wv g8cjf 0,q0g3cudk,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 reskg,m(8 zpyw)b t on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a ve,amhp13 l o8mdry high coefficient of static frictih,o3ma8d1ml pon.

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 frc ocj-3(7ie6qcoaeb7 w9 ew/w(* n2en aa+woxiction 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 (Exeidyvo v)3e9a7s3e5x z l35te9 :dq igample 4-20) how large a mass would box A have to have to prevent any motion from occd9):s teyxi593oezde7v3ge va qil53urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slp z.gn s .wm,dt7fba0gw2:n,u8c1mwxides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an pmbgawwfcxn .z,mws g,u. :72t8dn0 1 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 ay /.:,wkv ovz( ahrfs- horizontal surface (Fig. 4-54). A osr ,h. -zw:(kyfav/v 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 of static frictiom4; .nlyh nyk-fas4) 7icx)con between the crate and the bed of the truck is)4yx.no4lyfik 7a; s)mc-cnh 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 ,0cbtxvk:2gb11- 2) tvj qy3 bz;wvip ogep t3an incl gvc0p3)t e1vgy bbq2w,pztk :;2tbvxi o j31-ine 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 2fj p3a3hkea-, 8$^{\circ}$ 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 ondmfz+ilxv+(ea)jy.6 1 mz,d v 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 initi5jx. 9iqyq urx*;v)nwal 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 reachut 9yb42::c acm x;xrres the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held i f.ika3m-k*r ;eq.fgs n place against a rough wall by someone pushing on it with a; gekram ksq-.3*.if f 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 become dangerous projectiles )9t j7 1jk ,hsro9jbxaas they melt. Consider a chunk of snow at the ridge of a roof wib9a rs k71 )joj9xjh,tth 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 stoppirtzqd yb ,y 0x; )zhr,-*ecf:jng distance for an automobile traveling at speed0, ,j;yr f*t-q: bdcxehzr)zy v 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 dashy 2iccvpds-d)7bju 70 board of a car slides forward on the dash when the driver decelerates fpvs cub2- yd)0ic7d 7jrom 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 spe(gdq:1mg ay aqkpu;giz 3w:7 6ed $ 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 aovm8t*lu/s07w lqouij kq,c2u +r :9 belt from where they are filled to the 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 anm 2:u/ls u,8i+jao9vr l*k7 0oqctquwd 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 coefficie3ei9ak6 yv5z9f z g*spnt 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 bicyx(r9v9 m do.u y-*mckqcle) 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 approximatellw 2pot*,t1 rtj2+qiiy tj,2+p* iwqlr ti2 ot120 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the dec4 5 oqqujxd8 q;wqi8v4-:j gebeleration is no more than 30 " g 's." Calculate the force on a q84e dqb:qg84qjjix5o w- vu ;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 earthquake is a , am y9x7reu (zj/h i7a-yj /dlstb73tv:nd if an object is going to "hold its place" on the ground, show that the coefficie(i73jmet/ys/ uyra x77bzj- vdt9l:h nt 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 sc9flw .*vru+ d j swn)n.q:dx.xene of an accident involving two cars, measure 72-m-long skid marks of one f+n v l:x jrw.ud .s.w*9x)qdnof 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 w0/6o:4me/s+ju2i ejbcb ;x1b gizmha 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the el+c4ue zm60b/xmobgs2je b;h : i i/w1jevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped fro r:a. :-tx5bphjwr grq,h*q4mdcq2a7m the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forcet-q7hdhqjqx ::brrg.* 4 ,5r 2apwc ma of air resistance?   

  A cyclist is coasting at a srwh3:xgz )o (rteady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the mudr w3hr(o: z)xgdy 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 portion of a chujd dw(lc( gdz:(ttf 1.,c c/ity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills withou: df w(.t(jct1uc(dlgdh/,c zt 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 d:5d;/n 0,7d7keyn g dgi brtqexperiments, dangles her watch from a thin piece of string while the jetliner she is in takes e;nr7nd qgg di td/:dbky07,5off from JFK Airport (Fig. 4-58). She notices that 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 severq2 rn)7qm:zu yn,;d74iqhe:xjnb7 y cal ramps connecting different parts of c x4db n7,yhqnnj)qu::zm7;y qr2i7e 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 t1z3ld3e gs : o;s)ldfche piano (mass M ) using the pulley apparatus sl :og d) l3zc3d1fses;hown 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 accelerav87lkou1 x0zjob 3 x7fting at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint n4nl pom8va 8.chair, an engineer considers the following set of condi.n nalpo84 v8mtions:
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 p)* v5nlq-+jch .f y-uehbn g.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, Billgd;e+ ahnp1*l 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, 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 g paeh;n l*d+1his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-syn0md0c8ji b4hrv 04 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 talik;lb d-7j;3 ta6ksh4blj 64bq/emy d l building is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an 8vr 2 gdq qsr2v ;d)ty/p-z*cxice field inclined at 21.0 -s*q2cz2dqp8g/tv) rdx ry;v$^{\circ}$ 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.