Why does a child in a wagon seem to falln, v)v*cigvu5mk(t( 9sv coj3 backward when you give the wagon a sharp pull forn *k,i ((tjcoum9cv3v sv)gv5 ward?

A box rests on the (frictionless) bed of a truck.k 2gc64 wzd4ekch -bs7 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 box, in 6-24 zcwg7dkhk sbec4terms 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 actingu o( p61uv1s5qbqas d/ on it? Explain.

Only one force acts on an object. Can the object have zero accelerauxq;3pqjvr /+tion? Can it have zero velocity? uvr; jxq/p3+qExplain.

When a golf ball is dropped to the pavemenj 4*tnfd18 0r r(1ut2h weahrnt, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, whartw u n a0n8(htr*4r1h2e1dj ft exerts the force?

If you walk along a lohlr,qaj4 +1 ncu *ht8a9uxo-d g floating on a lake, why does the log move in the opposite directiondr4qu- +9joanh8*l, ch a t1ux?

Why might your foot iyq7t3(x+u eg z z1ztco9/s.y hurt if you kick a heavy desk or a wall?

  When you are running and want to s 1xfb4a x +q*(u/dzjk )ieooo2top quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (uuz)/ o 1*kiqx+fd4b(2exoaoj sing 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 threadkmyy9jbn pf,x2h7 ;*k from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is t,kby p ;nhx9 j7*2fymkhe thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is t8y gz76c5zn5pk0sbu: cb yan +wice as great as that on a 1-kg rock. Why then doesn’t 0bcc 6as 8z 5yyzbk7n:5upg+nthe heavier rock fall faster?

Would a spring scale carriedhlqi1xen 3l;o26w 5nh to the Moon give accurate results if the scale had been calibrated (a)nxn; l 53wl21eh6qioh in pounds, or (b) in kilograms?

You pull a box with a constant force across fc a4hi8b8d /(dpqd1yzm+ fg 6a frictionless table using an attached84c6b yz hmf gi+pda/1fd8q(d 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) decrease? Explain.

When an object falls freely under the influence,u,p7h3a,mm d;mbym o of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite forcepoma,7;ud,mm yb,mh3 on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on ,lfld, om(3v xthe Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given, 3lo(,lvmxdf speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–3 0mlliez6uua6 p. 5zl87) pulls with equal force on the other team. What, then, determines wh8.ipuze0 lm 5ll6z6auich team will win?

A person exerts an upward force of 40 Ne(p dkhxr4ky l+)kef 90k lz49 to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) rkx 9l0+k (yee)hd9p4lzk 4fkits direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does t.jah8wm s ;-z8e (dmufhe ground exert on you? Why;8.ezw8f s-d(hmm aju doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when thn b2 m5ulnrbdm8. *vo/e victim’s car is struck violently from the rear. Explain bm2rnvn 5*./modlu8bwhy the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck admv3od zar +2yxs9qe0 90raocv ,n 51xccelerates, the crate remains where it is on the truck, ,sr+avac13m5n0 oxzd0yerx92q v o 9dso it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachggl4h+ k .hu2e:55w2fs zq wrzes its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on tzh5+hus 2lgq z:gw42rwef .5khe ascent. Why?

What would your bathroom scale read if you weighed yourself on an ina0()n pkpzn(*gl -:,bv/ wcz lonp*goclined plane? Assume the mechanism functions properly, even at an az:0(o)g- nncpk v z ap*,bn w*p/ll(gongle.

  What force is needed to accelerate a child on w:z 9 gl7plba 66;pn ihl m4ixr:xh5+za sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rideln pgon7k3ij,* ugop839b93 m- qkyo er 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 i -ru33 y:f0ky ucmtaj5 ;fw.got is used 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 /pfhyk3y(( ft j.gbq gt2(j, ya $76-\mathrm{kg}$ 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 fatjb0(;z -6,uocr6jwd(e4ttj;cogin 8.0 s if the car is traveling at 95km/h? --f6bajgo w c ,06 u((c trjez;4tdtoj;  

  What average force is needed to accelerate a 7.00-gram pel6 v or)e5lu0z ul;sap:let from rest to 125m/s over a distance of 0.800 m along the barrel of a rspv:a;5l 0zuo)lr6ue ifle?   

A fisherman yanks a fish vertically out of the water with an accelerati1*v ;r xt -x9v;xiib,et/tlyxon of 2.;y tt -1vxv9*exir x l,bxti/;5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-m n7: b*w-j9dqazkihd+ile 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 accelerationv jq3z g3 zuajrn8 /3lqmw6cmq1q0v10m .p(ma is 0.0680 g . What are the maximum and 1wmqz(gpcvvm 8r1ju.0q 3z3a mq3ml/q 0naj6minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator.qdqnzt igxl- (v0u( 6( When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the0dzlti-v( guq(nqx( 6 elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maxid5bhjltd -/ 3xk (t9ljmum strength of 21,750 N. What maximum upward a ddt9kl(/5lx-jht3 bjcceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (ma3my d kr;,yvo1ss 132 kg including parachute) when the upward force of air resistance is eq;vd1 y,ky3 ormual 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 r/srv 8rol8 i-5bl 5jfyoof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate ir 8so-5lbylrf v85j/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. A rope tied to the box runs verticu at h*un2tr*8ally upward over a pulley and a weight is hung from tu8 n*uht*r 2tahe 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 diagrqr9 +rzyx- a59bk4g4 ow 4mkfsam for 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 baseball (a) at the moment it is s9sa86 a0 fogz iji3j9hit by the bat, and again (bfss8z 30iaa9g oj9ij6 ) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northeisqbzry z.9s-0lzsao 1 +cy3 ,lkmo - *.bd3lwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwarqm*za so+,zz 0l9lo-skl3rs13yd e. b.- i bcyd? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two b /lstdq 9.vgck a3(,rpk po(c*uildings 10.0 m apart. The sag in the rope when she is at the ,3(9 /ak*ogcl kcdstv.prq (pmidpoint 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 masb3 oi0tq1i 2iwsless 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.i-pnxm )y) ydvj3kz zf6;l7m; 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 housig;gdfjq1 ;q.-p++pzmr e 1dq bng unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces e-;gdrm+p d.bgz f;p11j+q qq $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 behinddgda** 7u/pgy it, Fig. 4-47 . Determine the ratio of the tenpdgg uy7*a/*d sion 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 upw50sl q9y+yq(pg +olmpard using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spgs9+yyp+l (q 0qplom 5eed?   
(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 )niee77zl2 xb 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 b-zi55 b 3k:kopz ih7jglock (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 hor+ r 4)bata1klpizontal surface are in contact with each other, as shown in Fikt4 alr+)ap1b g. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abovehj87wjx54c(nfb 4 switx;q2 f the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lightsf5;x7q4 inj2jbhw48c( wftxer 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 fr+d5oy3x hs h(s,9mjn qictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension ah+ym (qn dos5 ,39xhjst 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 meoh 3)5 i x.c50w gkbq6xim0mbetween 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 requireduug5 0ii1w991y ffny w 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 sta;ul .)py7itci+zwv 8 snding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist betp8i.ziyvu+t cs 7;l)w ween your feet and the floor if you are not to slide?   

  What is the maximum accele yyi3+)g2b *of 7qsbmkration a car can undergo if the coefficient of static friction betwee7o 2yy)i*kgb sf qmb3+n the tires and the ground is 0.80?   

  The coefficient of static frictio. . 8jivxt3lsx1hxvm -n between hard rubber and normal street pavement is about 0.8. On how steep x.xvjlh1 v t i.x8-s3ma 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 at -4.8lud a:g km9.1 v8xeq2i 9ywlj8jl2 8kz0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rea t x1m/g6gr55zusqc:b;m /fust 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 axaf(a+lrg*z tl ./; khsphalt surface have a very high coefficient of stati (kgzlhatxfl.+r /a *;c 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 friction fo ts6r5fc2d 9dor a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box Auch vi(*oyazm 0)7/6rbav ht9 have to have to prevent mi*6auoy h 097abz)th / vc(vrany motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it s0c l+q3fg5 yohlides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and tf0ohl c 53y+gqhe 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 horiz;xpcsa8w /(o gontal surfaceoagx;s8p /c( w (Fig. 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 of static friction 4cxz52 gj wf7rbetween the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid ha2x4 gwzj 57fcrving the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yourrev+)sekxea :4 c 0 3fx3l)ugu driveway, which has an incline ofge 4uc + u)fae30l:x) kr3vesx 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 slizh5/b3h z)si /+2dbkdosvy0 ,j l uh/ude with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an anglesxhdvy 5jj 1 a3(5dur/ $\theta=22.0^{\circ}$ 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 spee9:newru2 iwj;x b0tk:d 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 with a * :q) qvrisxz8g-nq1flu v7,q(teh *xspeed 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 ss1 a n1lonod0k9r x:3against a rough wall by someone pushing on it with a force dirk193loa1nrdss:x on0 ected 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 becisz c 7xo8 2hsyy/+rt,ome dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof wiy,zh8s y2i 7o +rtsc/xth 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 automobile traveling at spe5 ks7xwnk/ 2 )0tbch0a5ts:fg:a+qwh z;x a zfed v s00 sknt2fhh;gbx)xzcw:/:kza55wqf7a t+a 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 p p p a0tzx+3qepk7 ;8)fj;kglde 2xt8the driver de0p8kp;+ fdk 32q tpg jp7zl;ex8atx)ecelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an init55-p4ic 9fif0g o4 xsz9mjp ppial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to the pvasay- 9 k )c9imzny9;acking station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accoi9ns-c)99ka ym;v yaz mplished 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 frictiong q*fgqo* gy7/2grg3i8xkr y2 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 bicywns;j+o)foz7f u z5ds .k 7ea.cle) 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 mod d1upb 3+8ffgfwdhn 9 i)xw+z*el of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from8 u wf3wx)dhfif gbdp+91+nz * 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 autw 6te fd,m(1cnowc0w7t h 4zynq5m*9qomobile crash if the deceleration is no more than 30 " g 's." Calculaw qz1deq( hnom09nc4 tct*65 m,w7wy fte 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 e-bqei al8+f;ef9 o2p koh1m b3arthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fr1q3hoff8bapm+l ;b-oke 9i 2eiction 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 t,a1p keca8e*nk n)p3ghe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient ) n 8kekn gc,3aapp*1eof 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 dowk /qldbynh2+s g2bh.4n a 1-in-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 req2nsk .+ hbdlg2 y/4bhaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa v+ wor;cz2v- nand falls 55 m before reaching the ground with a speed of What+-nc;zwrv2 ov was the average force of air resistance?   

  A cyclist is coasting at a steadl5cw6o1j/q wx+gkha - y 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 fojc6gowwha 1 /k +x-ql5r 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 city. An imsm jcw( v dzlpo5.6:qi21riz 5portant consideration is how steep the roads ca:1.vljwm(cq srizd6255pzi o n be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch fln(9ys+5ppfi rom a thin piece of string while the jetliner she5 yfls(nip+p9 is in takes off 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 seve d(bsc9(82vk )umrt z1wj1co tral ramps connecting different parts( d8r9zw k1sb1c j uctov2mt() of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed 7ueus gub 54/oto lift the piano (mass M ) using the pulley apparatus shown 7/su ugu 45oebin

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 acce.adxnzw1)y)0v:spx s)khz6 eng ps- 3lerating 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-restrainti; +sf )/ w*2dvn9(cof *qv2e mrsqevs chair, an engineer considers the follooc*eqri /f)(d *fw2 +sq2v mev;vsn9swing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of pagool7fur: 2(;ruef 1 j /7hu660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use*li2f2qmi662zcutzux ( umu opd/. s; 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. (Expr/q2dml(i uof2z*sc 6ui upt ;m zxu.26ess 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+y/z c,n/b4f e+nlembsww4n/ a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is , zl-fr3 lpm4zpw( hf4allowed 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 ros56 uxr)+oapj 9hdptm .h uwfy +c /p6:x,p2osped together are ascending an ice field inclinedu+of9y ,p:wx ps)jocp +s/u 6hp. 625xh tardm at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.