Why does a child in a wagon s;,cztd za. 4xdr3f3 joeem to fall backward when you give the wagon a shardczx4f;z,j . ad3o3 rtp pull forward?

A box rests on the (frictionless) bed of a truck. The truck drii2rs x5ii os1r-rra2+.vd3 txg* /xvover starts the truck and accelerates forward. The box immediately starts to slide toward the rear of thritvvor *.3asxx-s1r/5d i2x2r +goie 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 ze,je ex fvb86u1ro, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratl l:y a2kdvlqs:8+ cl8ubd3w m18puj-ion? Can it have zero vkqvbps-:j1cl8+dd3 y 8wmul u 2a:8ll elocity? Explain.

When a golf ball is dropped th+-v :* zl9a;mp0si-d cfqnao )e p3swo the pavement, it bounces back up. (a) Is a force needed to make its*f3 ;+hw)ocmqe0d9z:i vl p- a -sapn 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 opyb n9y1 b3r *7iewn;ziposite dinn*;y w 7bz 93iy1birerection?

Why might your foot hurt if yx) gd+g bn*9dkou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you m1*zxq c 6l+xi:dk/ hz:e xx.zhf+)rsoust decelerate quickly. (a) What is the origin of the force that causes riz+q)1 eh k::x zc/lxhox 6 sz.+*dfxyou to stop? (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 section ofv tzd-:w/hvoi4xq:+l the same thread dangles from the bottomtd -oiwl/ :x4: hvqvz+ of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a w:/0 l ;acfdoo1-kg rock. Why then doesn’t the heavier rockfacd :wl/ ;oo0 fall faster?

Would a spring scale carried to the Moon give accurate results i*hv5 otv mxw07azix 92jn26njf the scale had been calibrated (a) in pounds, or (b) ijxa 60vv2t 95 hw*mo2jnxzin7n kilograms?

You pull a box with a constant forcc..i)rdood2 me across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the accelmdio2cr..d )o eration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls f9 * dn)us9 pe+fqs.-op,hueemreely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Ne) d,h*+nm -p.us9uofeq s p9eewton’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 objecsky.q+ 2e u.mut when you are on the Moon with the force needed to lift it ek .y2qu.+s muon Earth. 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 tlqb3*vj1c4q d+i3bucoh0d ( in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, thenj q+ bu4c(3* 3oh clq10tddibv, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thhtada4nx9 eeon5 * ixt *yda)dh9s (19e “reaction” force (Newton’s nodh(xtxy4 15)de*9 ha*di 9 9aeasn tthird law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert 8:0nc bkic rk-4fne m(on you? Why doesn’t this force make you rise up into the mk :c ricnfe nbk0(8-4air?

Whiplash sometimes results from an automobile accident when the victim’s car is-sxtc61ydcu )g n 5pz +zvod4fgg 91g9 struzu5+9c 96xd1fctsy -1gpd z)ogg gnv4ck violently 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 flatbe9hgqotm/2 aobbek/,osh)6/ln-)w mld truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the m/bo/h)o) lb2at9/ sgn hk6qm ole,-w crate to accelerate?

A block is given a push so that it slides up a ramp. After the block rex; tov4:+- jl+jm zrhdaches its highest point, oxj:-+;md l+z4 jtrhvit 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 yourj f7+4zt.8u ubd3gl ryself on an inclined plane? Assume the mechanism functions properly, even at .d7j8t +fbul 3zgyu 4ran angle.

  What force is needed to acz;vk/ lz5 kso:celerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and riderbfsa hn0a ,c 2i778q rilyb646lc3yx v at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 96ee0a,l c qx-, x3+h07pdklpbh0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o()6idrgnkl (b )e4zo jjl/ry2f a $76-\mathrm{kg}$ 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 in 8.0 s if the car i q2n-igy(s iauxv8y1/ s traveling at 95km/h/- xn(agq2syiv1i yu8? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125mnnjpmji) vfv5- ,:y1c/s pmniyn,j vc )vjf:15-over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the watqj.se;sn yyb6v*wu 7 k+pu)5zer with an acceleration of 2.5 ky7qy+)web jvn 5s6 s.;zuu*p $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track (px0x hf10 agv5 l3ewq(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 so7fz z:toc4-a r that the maximum acceleration is 0.06z7-rzao:fct 480 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevh(i j 1hgo( o-wgk*hb nvvg/ /)galz(9ator begins to move, the scale briefly reads only 0.75 of the person’s rn l h(hio( g- )vwga(*9gkhg/z vj1ob/egular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum )ns;5:lupf l o7hhhc 5: /bliostrength of 21,750 N. What maximum upward acceleration can it give the elev7l5hoocful n:;l: p5i b)/hshator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kqew0 zh+od ju: ur7+ vf*8h2fzfp;j4h+1tpwzg including parachute) when the upward force of air resistance is equ12fuw u +0vw*h+7 o hfz+hp :frez4p8jqtd;z jal 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 high. When he strikes thed of ;n2 1j;bk9q7vlxrc 9jts0 ground below, he bends his knees so ts r2 0 997cj; l1;nofxvjbtkqdhat his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs verticalhlo;x5b4 3fkl ly upward over lx34o 5klhf;b a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playerz0aq8g z ,g:dei ,mw*b.d2wuq
(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 basebal5g1go;pb dm/tu cjm ;7l (a) at the moment it is hit by the bat, and again (b) after it has left pg1dtmj5; c/u;g7obmthe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second dew( ngz;5i9qmf(o. j ij:hm8650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with h ze. (fm;5noq di9 jj(8gi:wma vector diagram.

  Arlene is to walk across a "high wire" ;/n yr/r lt -g9lbqw3yjw54 jlstrung horizontally between two buildings 10.0 m aparb ljg/ q-r4/93;r tywy 5lwnjlt. 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 massless cord frofd2ba6 u stq4.yc*+s om 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 14a+ya ;x08 v:sfwa( u78dryjux.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, Antarctica,e; 3/bivoy)l3zc rq-s* lic4w as shown in Fig. 4-46.-oqcel b iz3r/l4 3yw*;)ci sv 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 of the same mass behind it, Fig. k 5gr g;ovp5d ax) ;0lo.x7pey 4-47 . Determine the ratio of the tension in the coupling between the locomotive and theo 7a5v;ke0rx5 xd .pg)y ;gopl 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)k8 1a1 91 0zycotxjotswme4h upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowc)a0hk18yetm1z t ow94js x1o ly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race beganfrdtl;g c65cc(so3e -rcd 4: z, 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 blv-lf7gmm1;zn3 nj 23lg )3vuqwpc 30 up laqq9ock (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 dg1xl6, rktodkf s2*. horizontal surface are in contact with each other, as shown inr,x k6d2lkg .stfd1*o 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 0 vvh yphbc b7 j8ta.ll0g7(c8ground, 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 the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" splg h 8yh7j.vv0 ac(7cbb8pt0 leed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connecte, 6 hwlmaqs4a.wdfw9u2, yw9 q bfu0+od by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body di fqsm,wd6abq9y9wl,w.o40h2fwu ua+agrams 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 fr,vdn8 nlgiv ;sk)bfp 7d)+-fg iction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required t ):bmnh*t1heb :1gik ko 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 l-1w ug01bb9w cx lk+3 tvp3kfstanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are notv cll+x 19-wb13k bgtwpu f0k3 to slide?   

  What is the maximum acceleration a car can undergo ifi w)f mqq-l+h. the coefficient of static friction between the tires and the grou +-.li fwqmh)qnd is 0.80?   

  The coefficient of static friction between hard rubber and normal st1o. cjwp/ sqq7reet pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?p.wsq7 o1c/jq   $^{/circ}$

  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 -4.85rrs4x0 3f p6dpgml a-0 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a y8 o+dm qtg1 ;6tkbf)jrough 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 conta )royokup*b,u1f5m(8 d.ea ecz/: f vqct with an asphalt surface have a very high coefficient of static fri,v/k8.zyru(q)1 fauem *ope d fo:bc5 ction.

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 fricti:ipl ko1uv p6;z 6:jbson08fson for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A ha1(mick +w l k,6s-la8bwygbl 7ve to have to prevent any motion from occurring?b 6+w7,g li8 lksm(a-wylc1k b Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor*ndgg/dnm)nfv8giw - k vz-2 .. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impawmv*)-ndzn 8 2 v/i- g.kngdgfrts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass k epozt7x 2.m:zm.52xu;d a ph75 kg and 110 kg , are in contact and at rest on a horizontal surfd5;hx.zapup zm. 2 to 27:xkemace (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 frictip ,bmbh3vq;kv,b 3:t con between the crate and the bed of the truck is 0.75. What is thv;hq3 pcbb ,k,t3: mvbe 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 parkinl0/o 2hhw9-gb5 o9u xlohte+*o/ l, gp5awerag your car in your driveway, which has an incline oua9/ptglb/9oew re *h oo0ogl,+5-h2hl5wax f 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 28w;q k,u1wpi ajy/0mf bf e--,c$^{\circ}$ 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 onu8e /5ifmefr7x5 m82 nttbaf 9jb7v1m 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 initial speed of 3.c1; ll 0r+rukqa wmju7 *09q w(;dimnh0 $\mathrm{~m} / \mathrm{s}$ 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 3u3wl a;0-mzjus)x1 lo m2qdwhill 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 agai;gb ) fzy6t:axrgt s. r+8bs) oinf5u1nst a rough wall by someone pushing on it with a fot i.f5ns ;8bur1tfs6x:oag by+)zgr )rce 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 as they meltr3h+m 7a l)jz begzzzw*+l2-t. Consider a chunk of snow at the ridge of a roof wzhzea+wzmt+7zg 3 *) -jl rbl2ith 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 autoo b-q*ycb,)im2z,wzg 8 gaa2gmobile traveling at speed v is equal gwobma g,yg2zq,*28)- abci zto $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the dfh680fk(r vr9fvkt-h river deceleratefkff60(9ht r8- vvhr ks 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 3xzvnp(i: fks*z/8f a n avj:3an initial 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 dhwyboy9:h+ oy fn(r8 4rbggo 54up3 :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 betwee4:g8yr ghbu wr:n3p y y+ 9o4(ofoh5bdn a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betweo5dhhfxs +i :-en $m_{1}$ 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 theiyhs:ya 3 w )zhh63bm( 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 hee-b v2 gsqj3537jtdoa art, at each pulse approximately 20 g of bloob jj53q27 vs doe-tga3d 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 reason5j9xmx8 wg; g8fvc7ysable chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calcgwvjmg yx589 ;f 7sx8culate 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 earthquake ihb:p,rcrp h(yjw4uq i(vc/c8p; 6 u3es a , and if an object is go4hepy,:8 3 /(q6 chb ;ivjucp (urcpwring to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an*-dy5 dwsf o;4 (erixk6p7qcf accident involving two cars, measure 72-m-long skid marks of one of the cars6yfdiko7d x s-; (*w5fpre qc4, 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-in-4 hill (1-cywtma2d7a c0* 4e ,(xioy* lmd8tw +vin-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom afddwtvi48 mcw(c aloe702*yat +, my*xter 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 and f6c8ol ks ky5f5y2vs :oalls 55 m before reaching the ground with a speed of What was the average force of air resistanccy2 v5ky:f6skos85ole?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy t8,x, ,0p41wyloqbi) obrou jiv)q.r stretch where the effective coefficient of friction is 0.6p0oi1,vl yjrtr ) qxu4b8, )wb.oq i,o0. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a7 7y/*tss w 2t6gdboo)wh4rgx city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular smallts *d g2so64ghbry/tx7)7wwo 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,fw +zlmok65sf sj/ /f- dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that/swz+s/6jk f-f omfl5 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 supermah1hz9 uvkch( pvv. ,o2rket, there are to be several ramps connecting different parts of the stor2 v,k h9u1cov(vzh.ph e.
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 ) usin7phug6x pn k15 ;yjed.8,tok1 kb2vcag the pulley ap1hybj.kac v7tk2ppuke; x1o68d n,g5 paratus shown in

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

  A jet aircraft is accelo8c s(z;ie3- b -a q( 7ylsgirrcwi5 -mh)im3werating 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-restrfh2. u7tzhl 2)ubw*zn5p td +o ctjo5-aint chair, an engineer considers the following set of con ocj-75l5b+hzpt2 ftd )no*.uuzh2wtditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (66d9 r izxikia,l5;n*)7 ljmaw10,000 $\mathrm{~kg}$) . 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, Bi8 fzjdi+fg8 u,ll 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 his weight will the rope pull on him? Which climber is f+fj,gzudi88 more likely to be hurt?

A fisherman in a boat is using a " 10-1 -c28m ;ng 8h6pbp hc9gi1c roe$\mathrm{~b}$ 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 to reach a maximum speed of ,cd.z-b1oic agwge 253.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field inc fr-a)j5ovprhu j79w77j cna.lined at hucnj7j ao.r) j797a5 vp-frw21.0$^{\circ}$ 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.