Why does a child in a wagon seem to fall backward when you give the wagugos g+ aj36( vlj/0jlon a sharp pull forjgg0su6jo/+(al jl3 v ward?

A box rests on the (frictionless) bed of a truc;o:)nzvr1e;ny bv j(vk. The truck driver starts the truck and accelerates forward. The box immo1e(nzv;vvny ;j)br :ediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object irf 8ujg q ak5/54bwhz2s zero, are no forces acting on it? Explain.

Only one force acts on an object. Can t/fk 8*xupuijpf,-dtk m g.tvu wv2)(b,y8lv(he object have zero acceleration? Can it have z., u-j2( ()*i bdguvmkf/ ,uw 8ty8flxpv ptkvero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a cw a.sa 89+ dvwf3/qfkforce needed ts/w+ a8 .wkdaffc3qv9 o make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log movad6e*az bqi87aw 76 bge in the oppositaaadb w6bi g*7zq e768e direction?

Why might your foot hurt if you 6mkm mn)*cv+ikick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec8brdrv7wg rc a:p(59 felerate quickly. (a) What is the 5brrf(dv wa9c 87:gpr origin of the force that causes you 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 thezy r-( 7a yx:xcln 8 t55(3adge(xvkhe ceiling, and a section of the same thread d xkc((t: e7n-ydlg evxz(5y8a3xr5 haangles 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 person gives a slow and steady pull? Explain your answers.

The force of gravity on z www0v:(r;9e.pggvka 2-kg rock is twice as great as that on a 1-kg rock. Why then re;pzvg .9 (gvw:wwk0 doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resuy zho:/ elyx0gpxod3*mj0)t 2lts if the scale had t0 xz/md*o3e g :l 2ypoy0)jhxbeen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionlej 9s1c6szi3t4m wj, q w*8edvmss 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 acceler3 js6qs*cw ,j4w98 i mtm1zevdation of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there i 8c4m 6+jgjcf yzys7/hs a net force mg exerted on it by the Earth8yhg 6yjz 7cfcsj4/ +m. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object wh di2k7hh+q:r sw4c0 nhen you are on the Moon w i:sdh+cnkqh4 7hr02with the force needed to lift it on 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,g7yl79rs t*b)k yn bm3 each team in a tug of war (Fig. 4–37) pulls wit y)m7snbg*lbr7 9t3 ykh equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N tbbdf /l stpfbx,ud,0pbf )k(v426z:do hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what2 pxb bbl, ,ffbk /f:6(vz)dups0d4td object it is exerted.

When you stand still on the ground, how large a force does the grounbcoft j9;qx7l v.(d44kw/ tv ihc-u; od exert on you? Why d-x;7k otf biuh9v4d l.o(cw;v4qt/ jc oesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident wheiy4 jv8 + dk vsnm0-+yw5jfkl5n the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it res5vj5vinm+ dl-0 fk8 k j+w4yyally?

A heavy crate rests on the bedd-cb7qhf- iy* of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelera7b*id-yf-c h qtes. What force causes the crate to accelerate?

A block is given a pui 7mrixq5 v ly4un-v++sh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than lxi vn-4+7 m5iyq+vruon the ascent. Why?

What would your bathroom scale read if you weighed yourrdy zagv5 w+: -hs4k1j/ehnp (self on an inclined planeghn5ra+hps4zy e1-wv /(j kd :? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelg.l * 4( jsybgi1x2l/jzz*ebdlr- fm -erate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider a)b16d az0lp uot 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 itt)ppx-cn6ll 7.yf* gf 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;m do0wrf ikif (w+68d 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 943uvo j*(1gdmeelg cj-j , 2 lop,jkyis traveling at 95km/h? -49 ogj*e3eljjjl cdpm vyo(gk 1u,,2-  

  What average force is needed to accelerate a 7.00-gram pellet frn0v7evf 0kd; oom rest to 125m/s over a distance of vn7 k0;d0vfeo 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelee(6g n69 gi/h dv-nlo;mo+ rdaration of 2.rd nioodv-h6g( m/g6e; aln9 +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-mi( +mpju9r a bsq*qbe/47toq-rle 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 def d4m obku g,*et,livdn)hpn k6*87w6 signed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on ghw, tioupn68bv dkdf )k,l*4e* m76 nthe 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 motiolk 5 mf m72r7au-z 9k)8qddcj;kpuc:rnless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelerat9 r 2z;dapck:mru md)cfquk577-ljk8 ion of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 21c10cw sfa7 eiv(c)h.v 25-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it giv v1whc vsc7.fi0)(eca e the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling s6ijsl4t4m.c2s: o 8iop2py-yz w(u a kky divers (mass 132 kg including parachute) when the upward force of air resistance i2u.:42(p y -mikz6oilc aw jptyos4s8s 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.mc) u j8;q+unx9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an a;8u xcn+ )ujmqpproximate 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 rests5z w9w,pas.kv* n azw, on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the zww,np*s,ava9 wz .k5box 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 i iz pohi6od.+w)h 4lh3p46niaca(:xa 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 .t f;d6u 5 5tncn hr;jasda:g7baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is fl5t7n;u:hsnj;c rtd ga 5d6f a.ying toward the outfield.

A 650-N force acts in a northwesterly direction. h qaoba *3 j)*6jiabtri/*5x o*e-mne A second 650-N force must be exerted in what direction so that the resultant of tho- ber*a* 6x*ea/amji)h*qn53jtiobe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw))lsjme6 il v7cx-e y(een two buildings 10.0 m apart. The sag in the rope wh(le 6 ixy)-)mjv 7cselen 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)vf4svy c5l 9 lae:tdok;(br, is hanging by a massless 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 1ht0k6v gq dljx 0)82m lvu5st*4.0$-\mathrm{kg}$ 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,r :nwwmuu 90(f;*) wi0zci6pkrh n zq new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fp:9nnm06fw hi*wwzr k0rz(u)uqc; i, orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 iswm2 0fnxw:ya 4 pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension infm: 0w4axw2yn the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pull eiyvk1o--n /7u y9gupey apparatus shown in Fig. 4-oynu gu -i 7kye/1-pv948. (a) How hard must she pull downward to raise herself slowly 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 began, a inelrgv1bj3 ;z ; .xj. 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 bwde whu) po684o;uw wua0:9dtlock (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 hr b swgx;gr.yg,n2r44ob4bt6orizontal surface are in contact with each other, as shown in Fig. 4-51. A forceb 4g6 ,sgb4 x4.tr rwrob2ng;y $\overrightarrow{\mathbf{F}}$ 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 shownwe;l ;3by gt4nd;jn3cb5;zzl in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object r e;;wlbt 33;cb j5znyg4 z;lndeach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table arecz;v6a +w-mt(v*xnn bz6 x/ ig connected by a heavy cord of mass 1.0 kg . Cal-xn v g+a;tnizcmx* /zbw6 v6(culate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of k:v 6sqcgc+ce,qam ps * ta-a+)inetic friction 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 req16rv h hjqd9o s-ll37iuired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train aui,5zkzq(. k t 4tpp*iccelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you a45itk * i.pq(zk tz,pure not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of static zeck3x43d p,wwhl1)h9yc g+ahds ;)e ,cdbq9friction between the tires ah ,zcc+3ewc p hxg 3 )lw;hya)qbke1ddds9 94,nd the ground is 0.80?   

  The coefficient of static friction between hard rubbxeveed l2u7* x 3z(wl5er and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parke35lw uzdee*x v2(xel 7d?   $^{/circ}$

  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 h5n wll0d-z w2-4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough4ombx5k1 g tcjn+ /q8k 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 uj8q (77-mpd wa4w2r6mr)z sq+yhi wpasphalt surface have a very high coefficient of static7+8m-(i 2sdwyu pz7jr 4wr qqpm)6 awh 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 for h3v+ )oka0 (tdfyed5u 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 (d i/ /9mjgb o37rh oq kt6:ooinwg(,l;Example 4-20) how large a mass would box A have to have t9mngboqi6,ht( w7 /i;3oj oldkrgo /:o prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesoz- 6z:elfc2xt w0voxt9v;zfs,* uu9 across the floor. How far will it go, given that the coefficient of k 2 tvx ,uwf;fovzx*z6z 9ctol:eus0-9 inetic friction is 0.20 and the 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 horib99lmc.kgw 29an/yy k zontal surface (Fig. 4-54). A 629cm yy2k /b 9nwl9g.ka0$-\mathrm{N}$ 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 ap, -ywj8,n*vjzgs ewte u 48.g heavy crate. The coefficient of static friction between the cratep gvwej8z-s8u 4t gey,j,n*.w and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about gm9,b rcdm u4)s)iyp5parking your car in your driveway, which has an incl5 gm9ridmsu) ,4 p)ycbine of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide w5 )c2xihyci*s ith 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 angledq2 *sy5sqbl / $\theta=22.0^{\circ}$ 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 au7g6cc;c jw; c4wab 6+d lh)dof 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 thew b.p25ky5 no72sja np 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 t,g sou sg0c:7c qi/3dxi;ts. against a rough wall by someone pushing on it with a.sci0s;uqi /7:tosg dxgc, t3 force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous po+ q;be r:)lbbrojectiles as they melt. Consider a chunk of snow at tbble+ r) oq:b;he 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 fofq lw92,(s;q uc yh(i3pnsvr) r an automobile traveling at speed ,fp(n9;)iqq s(hwc2 3rusyv l v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashbolj dkm n.- e*z):ffsyl (pl4(mard of a car slides forward on the dash when the driver decelerates from 45 (4sn d :fl)-yzmm*pe(.l j kfl$\mathrm{~km} / \mathrm{h}$ 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 givnqq o0j0ct +so6* ,oqlen an 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 b 9c0dggkth-k-elt 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 thegdtg9k0h- k c- 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 r :9d(ordw86w:xyl(h k 1(yu zj rfyl3kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6v g51x ce2 decfwq: 6js;ta0/r.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 mode /(tu vc yo7n(.byn;gdl of a mammalian heart, at each pulse approximately 20 g of blood o t;cn(y.dvynu b7g/( is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an ee n-:(i ppkig1 ;pw2tautomobile crash if the deceleration is no more ti2ep w1-;ppek(ing: than 30 " g 's." Calculate 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 is a , and if an objeb2cxb :.z-kq lmcz,.x5ah e2hct is going to "mc h z elbxk.x :qb2a-5.,z2chhold 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 yj.1z pn,7bq9cc,s jh1n l;psan 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 of kinetic friction between rubber and the pavement is ab7j9 lhy p;z1j.sc ,,scqnp1 nbout 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down qf ..il1lck,ntpa 6f5+q j6 gi8mdd 7va 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, livd7kmd6q8 icf.gtf jn 6 p,q. a51+lthe elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Lezy-vv7 j5sifm2d0 kw6aning Tower of Pisa and falls 55 m before reaching the gros725 6yvfvwd k mj-0ziund with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a a 5*w(lr x bd*v0 3ub;wbsz;zoe( z-rxsteady 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 for 11r d(;x*; *b zuoa vw wz(exs-rb3zbl50 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly port* c4ia8*j so/69)zzof *hp 9ohzwbkm sion of a 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 small car, with a mass of 1100 kg , can accelerate on a level road from 6zs9p h4jkozf9*8 m) h o*/*scbozwi arest 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 watcw 2g 8a(a)ekc h0d s5pipuie,2h from a thin piece of string while the jetliner she is in takes82(i)u5 sawa c h,eigp0dek2p 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 several ramps 1 f8g 8-xnz8 , ed(aatao:xsjvconnecting different parts of v:1nj-fo z( dx t ,sexgaaa888the 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 isyyuwh6s,m*3u8pr 3t4 k x ,ezc needed to lift the piano (mass M ) using the pulley apparatus shown inyz 384 y*epm,su uw3ch6t, xkr

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 acss29osax +ov 0celerating 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-resthy*,uv qfd 3lkx89 1pdraint chair, an engineer considers the following set of condi8hd lu, 19xfdv *y3qpktions:
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 tra:s v -etzc)/;um;a0soaa y 0xrin has 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 similar length. Ka y1 cj1ko nka+w7))w(zu p,djuren'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 ti7nowky( uj)k1 ,j)1pwdz+uc ames his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-r x-jk2vsiy /r74:frk1 $\mathrm{~b}$ 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 bh .8vx ) aukpb.2:u;n2tefufuuilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped togethe 5+zibln* oby k:o:vq*rado0:r are ascending an ice field inclindiklrn :bay*5o *zvb 0 o:+:oqed 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.