Why does a child in a wagon seem to fall back 9xfwdm n31xz-mguemk+k 6n) +ward when you give the wagon a sharp pull forwaxk+d 1enf u+ gk)-w3mzxm6mn9rd?

A box rests on the (frictionless) b dv8ro p., iwdi1ldj*.ed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear 1rijp.d8od, lw .v*di of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? E5lgdwmb 9i4nh1ov6 x,xplain.

Only one force acts on an object.c swm(q mghni1y6 m,1 /p pv iys7-f11rq7qyd8 Can the object have zero acceleration? Can it have zero vef ygw (r1q7is16inqpy/d mpv1mq 8 c m,7-hsy1locity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force 2o1gu;sbb : u2:1wfktq (q2k4ktmx bsneeded to make it bounce back up? (b) If so, what ex1wgt4(bs 1umxf2 o2;qkq:bb uk :kt2s erts the force?

If you walk along a log floating on a lake, why does the log move in t8uejs 3n*um o,,o*mpmdid5t .he opposite directiomi odso8mj,**3mtudu epn 5,.n?

Why might your foot hurt if you kquuqfow;. 9 m7ick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec(bpb xg,b0v 2oelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration ofob,0pxb( g vb2 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 t2pghc-,dt6/f ua9n bekq/g 7w q3 us9ghe 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 stone or above it? What if the p- u/97ggunqw6h2 ,ag/ 3b deckpfts9qerson gives a slow and steady pull? Explain your answers.

The force of gravity oy9,ph:5mw kk wn a 2-kg rock is twice as great as that on a 1-kg rock. Why k:ky ,h9 wwpm5then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accuj h+*w0bih :fe te*7gjrate results if the scale had been calibrated (a) in pounds, or (bjf+h*giehte*: 7 bj 0w) in kilograms?

You pull a box with a constant force acros- )w9dv kfiz)8 ui)zs1v/qac(rz sq(s s a frictionless table using an attached rope he) 1qz (v i9s)dqkf8zr-uc ) v(awisz/sld 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 of gravity there is a net force ebtv(p wp.) -gmg exerted on it by the Earth. Yet by Newton’s thipv-pgew .b(t) rd 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 yo)vbo+w*antl h z7c0r;u are on the Moon with the force needed to lift it on Earth. Compare the force ne 7)w0v;nzr ao+h*tlcbeded to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third lao -ndjc7fw v0)w, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which ten0wfcd-oj7v )am will win?

A person exerts an upward force of 40 N to hold a bag of groceries. D 6t :tkn jbo.g c2fr )x;kk:av4ckq09mescribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, an vg; 4x0.: bcf 9km)r6k2ktt:ajockqnd (d) by what object it is exerted.

When you stand still on the ground, how large a force d(yemsqj. p0.u oes the ground exert on you? Why dy(.. msju0 peqoesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the ej4)l-r.vn,ch uy *bcvictim’s car is struck vieb*u,.c cyr4-l )hvnjolently from the rear. Explain why 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 pzo woku q.:p:..wa(i the truck accelerates, the crate remains :wpp(.izoaoq. uk.:wwhere it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afum; nn9g8au9 rter the block reaches its highest point, it slides back d9m aun g9nu;r8own but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weykmqir2sihjp0: 82no 1+lfo)ighed yourself on an inclined plane? Assui2his ko2+fqom nyp0: lr8j1) me the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 11o5ln tb-nnri twz59 ,.25m/s$^2$?   

  A net force of 265 N accelerajr c3+im2z3pytes a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to acceleratea0 d+o01ww5v yfofwa: a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a hdis 4) 2 6u xl:rikqhxb+smrj;f a39/ $76-\mathrm{kg}$ 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 is76y:2tx:c txq br ts6f required to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? -txycb t7 2xqf6:s6tr :  

  What average force is needed to accelerat m 1wd3ph5yc+gup9 l3oe a 7.00-gram pellet from rest to 125m/s ovem 5u9 cg3y3 ppdw1loh+r 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 alvp zh-t,h4+.+l tha ,hzv4-p5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quart z:2,j k+o/jt/kgvpst( mxbe:er-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum acfrdb .0 bk.lazx9)sx,celeration is 0.0680 g . What are thezrlb)ds9 b.x.,f0a kx 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 bathzd 1n6u r yg/no*0jd( 8xw23wh9cvd jbroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of w vrwnjd(xjz0o dc8 gn *9/13b26hyud the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whixh-z2pq h p1tu3 ye7os6n6l+at maximum upward acceleration can it give the elevator w e1 hop37znt+ ypxhq6uli26-sithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diver(+j+- li:gp1zbjrrxg s (mass 132 kg including parachute) when :jlpbj ir1 -zx(gg+r+the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m hil za2 okk8w2k2gh. When he strikes the ground below, he bends his knees so that his torso daolk2w kz 82k2ecelerates 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. A rope kyo;;qw 1b6 sctied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-4 qskcy6b1; wo;0). 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 pefyxf v* ttjgs7.(6(olayer
(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 hit by th1mvozx w;q 4wq 99g+qfvb i22ke bat, and again (b) after9gwv42fb9kqoxw1 2; q+ izmvq it has left the bat and is flying toward the outfield.

A 650-N force acts iie5oup.ief j1i7 -33vrp i.7pt,i sfkn a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate i .r p,3iikv-fe tui.1p3p f5iseo 7j7your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two building1tgfb.bdg7zp0 mt he7+6v:8xd wm; e gs 10.0 m apart. The sag in the rope when she is at the midpoint is 1bt8 ehp6 e+gwd10gx g7fz7 m;tmbdv:.0.0$^{\circ}$ 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 massless corx4k:uyvy y5p9bgqpqg4w,p ,sx i*t1;d 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.ga31/glv 70nol lbt4l0$-\mathrm{kg}$ 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, Av/s7,p 3j iaijdgr6 7rv4 go6f)ntmn 3ntarctica, as shown in Fig. 4-46. The sum of the forcev34 p,r v6rnfgost gmai7/jj)3 67 idns $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Figg2 x5(rd3qsx u. 4-47 . Determin53s 2rqu(xdxge the 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 tgr-pua0-p:8wq 9iy jxhe bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constqixrp89u g: -jyp0 wa-ant 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/f9n f;uha q: a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (d. gm1 bmy,g)bgh2) g+z shp(mmass $ 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 hozylc+nh+-l2/zd 1 qc zrizontal surface are in contact with each other, as shown znczlyhcd/1+- q2 z+lin 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 1.80 m above the grouh8f+7zuhiin ga /li; 55d i2j zd4tl2znd, 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: First determine t; +zfgi5i/zd8i7l 2zuh4ih a 5d2tljnhe 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 heataup)/czs cc gp4c/9 2r08rsivy cord of mass 1.0 kg . Calculate the4sric8 9ct/0scacpg)ur z2p/ 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 friction betwee 4om5np lzm)n7n a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.rnv+,qqa2b (cf,d w 1 5s+rebz0$-\mathrm{kg}$ 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 standbo97l2ao1x 0cy be9rf6q jo7 cing on a train accelerating at 0.20g. What minimum coefficient of static 9crbxqloye 7o9 7oca1 b2j0f6friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can828 5ogs)g6mu gngr js undergo if the coefficient of static friction between the tires and the ground igg2 8rjn gm gs85o6u)ss 0.80?   

  The coefficient of static friction between hard ru ,aetfq* 6z ;d+a (q-szptx;sebber and normal street pavement is about 0.8. On how steep a hil zz; q-; +*t,aep(qt 6edfxssal (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 7/l lwoxd)p6h0s i :nz.vkqoc 3hin0e+:z-ti-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 vmu:o8y64: p0pb-;l ofmdc 4gt h oqt: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 vg :kcgke5.j+y 4 5xkhmery high coefficient of static friction. h+k4kc55y.jg gxke:m

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 kcs0vw)m2 y+u m7d0i t c0fmpf1inetic 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 (Examvalk+.l imb(gg)w1-hvom 9lk2u - nk .ple 4-20) how large a mass would box A have to have to prevent any motion from occm1o vvl)u-h n-. mbgwgka (9lk.kl2i+urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will iths b5e8 h:5+-3ns0ul bgogfcy go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0-ush+l85fs gyhbnbo 5g: e 03c $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizo6z 9ze h2o :.rrdfdai-3:*fp.omzodd ntal surface (Fig. 4-54). A 6ezf.6id. pfd o h-9zd32dzrr:: oa *om20$-\mathrm{N}$ 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 coefficiex e 9w yhh9vy8kb5nmm 8pd5/q1nt of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can dece5xw m9hm9 deh y18nqp/y bk8v5lerate 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 dr8,b z 9oouwsz)r o/0tbiveway, which has an in/8,obtu z9)ozbrosw 0cline 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 sligc*f yjq4*f ;ykk g1ld-3/ scrde 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 onzpml)y5rvgk+ck- -lrryqk + ;d+ek - w,t5 .bq 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 initialmdt4wes6q3q7k1 + u7fdws a;p i1zgb .kq.d7p speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches theg1agqk qs oz0dus,kq )uz 1:;. thf1*f 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 in place against az+ qge3 vg,l y6 f5:yzvinb03h rough wall by someone pushing on it with a force directed upward at n560gygeb q :3ilyzvh3 + z,vf 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 slipperyf ).dz5e5pcxm roofs can become dangerous projectiles as they melt. Consider a chunk of sn.5 )dcfpxz5emow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance -ublubron+bh26 ;u(gyt8r- e for an automobile traveling at speed v is +t(u2u gey6lbr--;unhbo8 br 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 ozp :.ecjk 2o+zf a car slides forward on the dash when the driver decelerapzzok 2 +c.je:tes 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 initial speag+.,svpjr5l1yh a t hu34ij )ed $ 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 packing sfzj:cbt:xj86aq s5 z7,z iq( ktation 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 dista a6z:qs:z q7tfx i k(8czbjj,5nce, 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 kineticofu 3nky2*du ( 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 (incl:6pu ptkthio w f0.)y p*um:i0uding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse a;z1n 7ylu+jx9 59g6qsxuy f( yqn*ebqpproximately 20 g of blood is acc q5y*7 qjuxn9uyx9zq(e 6b;fny+ sg1lelerated 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 6b q+aa;zda1ridn/c; dvz/ dd7.m*ucchance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a v*bc /rd dz+7;i6.u1qac/ ma;d azdnd70$-\mathrm{kg}$ 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 i vi:-bqpqj;45ts2 kqk:g lb0cs a , and if an object is going to "hold its place" on the ground, shocbk p4gl2;-:j qqqst:b0 5vkiw that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene lp.2rqi(wpex 9vp,0 vof an accident involving two cars, measure 72-m-long skid marks 90pvwr 2exipq(,vpl. of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-indt-2ulf c5d zm+o*y2ez0 ihe )-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m)m z2 yodlz0eu25+ice *) -dtfh. 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 from the top of the Leanisb7a 4vb z9*c(hav5jyng Tower of Pisa and falls 55 m before reaching the ground with v5h4b bca7v (*9sayz ja speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wher 3ybjo iej+zv8c,5 4dpe the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be4e5,yo 3 b jj+cdipvz8 the speed upon emerging?   

  A city planner is working on the redesign of 7 eh,:fd4l x8by6yzp.kxrw6 wa hilly portion of a city. An important consideration ih:.7blfxdk84 we6 pzy wy6xr, s how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dalu .k6qy:fp0m ngles her watch from a thin piece of string while the lu 0:kqm.6 yfpjetliner she 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.a rgjyzs j; al1)o:l+ft9bd- , there are to be several ramps connecting different parts of the store.do)rjg l1f bla;s.:z- yt9j a+
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using tnopq1006 dys fhe pulley apparatus show yos f60dq10npn 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 3.5 lxgod 0z 8pc).4 wep*b$\mathrm{~m} / \mathrm{s}^{2}$ 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 chair, an jeog0fye3 xum (l4(4dengineer considers the fol4(0l4ox gf(medy3ej ulowing 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 hasfv bbh)x py/*7 a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similarmtz)mjf+ 4/gwh c/ ki/ length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in p)cj+gk/fmmt wh /4 z/iro 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 " y-aa(odu9)rvh-b/ uj 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 allowed thb*z 07bcq;/ bd+ nzfngbvp22jp */uro 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 ramck.3 m27sdt oped together are ascending an ice field inclined 2mc3dk7.amt s 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.