Why does a child in a wagon seem tq*g nu7 av*6uto fall backward when you give the wagon a sharp*au tq g6*u7nv pull forward?

A box rests on the (frictionless) bed of jn9ozg ;p gfjlngczej;e0c 0a9 -h*1. a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, inhg;90n0 c cjgj*zgz1- l. eof je;pa9n 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 oo /o ius5wgqh *qnx-3+plcc,+f an object is zero, are no forces acting on it? Explain.

Only one force acts on +bw*yj6.jyu c6 hosqy(y u 7a)an object. Can the object have zero acceleration? Can it hava6+yy67 yyb* ou.)sjhu cwj(qe zero velocity? Explain.

When a golf ball is dropped to the pavement, v (2mnglg+o4g5l/td mit bounces back up. (a) Is a force needed to make it bounce back up? (n/ g2l5mo 4m+ggv(dltb) If so, what exerts the force?

If you walk along a log floating on a lake, ww(0 mv*gl0eln) 5hl r 5ydkjw.hy does the log move in the opposite directiongvkwmh y0 e5n* 5w jd(rlll0.)?

Why might your foot hurt ifd7,bip+ t7c um you kick a heavy desk or a wall?

  When you are running and want to stop quicklk1a-/rzwg* p;w;p eqly, you must decelerate 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 of a person running at top speed to comra /;wzlk -;geppw1 *qe to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sa23g vgjfjh+9a0y:lo gme thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, wheo a:g0 v jg29+3jfhlygre 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 that5zq t1ex /qm*l on a 1-kg rock. Why 1z m/te*q5lqx then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moo,xkr7 /(*w tj (84yc phvd-zugx2ovfan give accurate results if the scale had been calib 4(xo,78xwvg (t ch p yu-rj2kf/zv*adrated (a) in pounds, or (b) in kilograms?

You pull a box with a c6 ep5wd : fiz(ryh(qd57 gyt3nonstant force across a frictionless table using an attached rope held ho57 z 5why: eg (q(pdr3fy6ntdirizontally. 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 fqqs( be dd7ad15 d0;lj+stxy 3orce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth md d(sq+tqaysb1j d3xe5 dl;70 ove?

Compare the effort (or force) needed to lift a 10-kg object when you are on oj5p)y0d aytq p8u)h re(o6)rthe Moon with 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 o65hu0oyr8( )tapd )y por )jeqn Earth.

According to Newton’ x- fn f1ret,ulu/dy(.s third law, each team in a tug of war (Fig. 4–37) pulls with equal force on th.x/y ut1lu( rf, def-ne other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descu3 2icqvpk*34j mb s tc175rsa1 2vtxqribe 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 what oxjtp3c 1vsm uc qk72vb45t3rq2a s1i*bject it is exerted.

When you stand still on the ground, 9vq9to)/ x, z9xzlxethow large a force does the ground exert on you? Why doesn’t thiszz,99)lxe xx vqt9o /t force make you rise up into the air?

Whiplash sometimes results from an automobile anw 8exb/ h9lw0l gbu zt)t0-e)ccident when the victim’s car is struck violent)- 0bn0exz t tb)wg98lhe/wully 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 thwjq9 ,kfav(rw6 f;:8, d nhfrle truck accelerates, the crate remains where it is on the truck, so it, too, accele rf,v r6jwk(n:d89fwlaf;,qh rates. What force causes the crate to accelerate?

A block is given a push so that it slides s v;toovju fbf a (9bhu*+c/82up 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 on the ascentcuohu2bb; (f +*v9sa 8ftojv /. Why?

What would your bathroom scale read if you weighed yourse:5fo v0ru 6by7ij jo-mlf on an inclined plane? Assume the mechanism functions properly, even at an anglemob r6o7ju :y05v-ifj.

  What force is needed to accelerate a child on a sled at2clro/2v8 wd r 1.25m/s$^2$?   

  A net force of 265 N acceleratesm,gec 8lu r)(xrf+,z ; f-vlom 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 wn +brgutl;q (/n/:o/ f;b wt8ir1 aarxithstand if it 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 a (0,f 3m36nus cvyjuo*f5a l0ufxu8 jb $76-\mathrm{kg}$ 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 110+x;ws :,ft lk drj*(po0-kg car in 8.0 s if the car is traveling at 95osr(t:d fx+*;p,lkj wkm/h? -  

  What average force is needed 1rbx 0aiur n*p:0yb2ef823ztbzz up7 to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along thin*0zbpzu 2b xb3zau2 t er 8y7:10prfe barrel of a rifle?   

A fisherman yanks a fish vertically out of the water withwvxea3 u;i:c * an acceleration of 2.53 ;iv*cewu :xa $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile4*v mlew+pf:i; ezhk. 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 4850s; nvb p h4dmz6069gsz kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the 6 9p db0v4z6nsshm;zg 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 elevatb05 g ty)boxp,or begins to move, the scale briefly reads only 0.7pbo0) xbtg 5,y5 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator ha,hus tbj,b jb8:g (4pes a maximum strength of 21,750 N. Whath(ube4 , stg,8jbpjb: maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f5ee7qx t 8;htjalling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth oetejx78tqh ;5 f 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 3r3uv d2a-kie5 .9-m high. When he strikes the ground below, he bends his knees so that his torso decelera e25urakvi -d3tes 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 dq- qgy/u c2h5dz 5w,xruns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts onu/d,- qy gdc2xqw 5hz5 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 playerg 44 6akw/lub:n9o yuh
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagra o( z2u7uj uibzov,/,em of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the out7ji u (ezozu,/bo,v2 ufield.

A 650-N force acts in a northwesterly direction. A second 650-N force ;q svxcylh+gol x 0x )(zf0+7qmust be exerted in what direction so that the resultant of the two forces pv)+qy lhxol+zg;sx 0(xqcf0 7 oints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wir35m vd7kn)7rpjm :0- vkic +slzwxw 6ne" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 1mw zx0jr7 6k+v7m 5nnswk-cl )iv3pd: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 cord from an;b;7i r i4f)xelpz0i hother 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 14.0 xp.ckfhb.p1 /t3v:om$-\mathrm{kg}$ 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 df) j 1sqngjb3*k7i6p Base, Antarctica, as shown in Fig. 4-46. The sum of the forces 13)7qdpkjng i6bj *fs $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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. z)uaje e,7, so4-47 . Determine the ratio of the teja, s7e ozeu),nsion 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 pullsf kd+ inl64emb jk7h+e1j6wb5 herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard himlbw+d6nbjk574 1+ efjk6emust 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 bf;y; luq9. f e;v/ci yiow/yd,egan, 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 (m hy;b q:(e,a6qbbzqn/(go0 c 7wstym7ass $ 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 frictionlsgcu( -6atm jy5j0r 0wess horizontal surface are in contact with each other, as shown in Fig. 4-0 jmw0 jurs t5ac(y6g-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 (cg95u wy; svlare 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 reach after the system is released? [Hint: First determine the 9cv u( wy5;slgacceleration 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 byztpap6kl0gu1fc*s0zvk-5t 3 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 diagrams shown in Fig. 4-53. Assumelz vta u*pkg0kctf-z350p16s $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 bet11r55aebznq ;tuti4 dween 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 re,chegx)n1d k y+s)x4equired 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 acceleratinv/ kbou3k /nf1g at 0.20g. What minimum coefficient of statibv / ku/3fk1noc friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can und uim)eq b0s+1we)9j. d of:hirergo if the coefficient of static friction between the tir+mqdjeeh r ow0ifb.9i us )1:)es and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street p 5p9pjngg n.ranbg*86avement is about 0.8. On how steep a hill (maximum anggg5nann8*jpp6r .9 bg le) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80(wa*tg g8 yx04m( ynve $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough 30r2cx, hnr3y k)$^{\circ}$ 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 very high coefficienmq84 8h us/y ;3jqeecgt of stat s quejg3eymh;48q c8/ic 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 fopwn)g,tajooo/-hc pe ,)i g0:r 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 jzz)jcr+bh+hsw 4d,-mass would box A have to have to prevj 4srj )h++dzwhbz,- cent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that*8r wkac j7t)0ljqa (v it slides across the floor. How far will it go, given tha rlv*j at7(8 k)cwqa0jt the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7rgcov(tkq hj csg a22-ypw49 dy*l3 pib7o7715 kg and 110 kg , are in contact and at rest on a horizontal surface jir*l q3 7 pap b7(c71kdgyg2942ohos-w y tcv(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 sta,n/u5jw h a35 /fnxss2 deqt/atic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having tha,e5qjn5n fd/swut s 3ha2x//e crate slide against the cab of the truck?   

On an icy day, you worry a rhti yfjm,-21bout parking your car in your driveway, which has an inclinh,jfy1 r m-t2ie 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 wltb7.f 5 eqo2m,:xtuu35e *ya2 ylevdith 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 azl9za:-b5kyeu 0k 8vu 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 inithcm2pfin2p n7h l-6c- ial 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 the top of the steepz gh / l,*ugbyc;jvph0g:* *pfubie);est 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 mpjqm nc7wshw84,fz,*m,y , ragainst a rough wall by someone pushing on it with a force directed upward at 4yc7qmp ,mfjs,m * hww,,z 8nr28$^{\circ}$ 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 trjsh 0qy6o8 z92r jg5vhey melt. Consider a chunk of snow at the ridge of a roof with0ghz98 y oqr5rs6jjv 2 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 automoyea+ jf,- 6qk8jmw:pz bile traveling at speed v is equal to :jefqk,j-p8 mya 6zw +$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 io,mb*ctm)lv3 kl)5 v d*r xn*slides forward on the dash when the driver decelervxinkd o)t*35*mcl b)v,ml*rates 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 dv w 1 zr;gvs+mz :ieg4496ueg is given 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 btfxyim,qn 5c u 9j+s(.vt0yg9kwd:u u9c hy74elt from where they are filled to the packing station 11.0 m away,t: h( m.j7wu k4vcunqf+ictu 9yx09sgy5 y9d. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box 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 kaf+8t .n)m oyfriction 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 65inj c4y 2m(f2c kg (including 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 simpli: -oq5lt3jjvn4ym i (gfied model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from -:5v3(onyjqlg tj 4 im 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 surv) g0ynq+b- npniving an automobile crash if the deceleration is no more than 30 " g 's." 0qy- pn+nbng)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 accelerat8je 2u8.he9 eih4ugv kion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show9.8ueeh2vje8i gkh u 4 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 accident involving twoqttl 4bqqx0tjd: k)+0 cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic frictq d:bqq t0t+ 0jl4)ktxion 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- (o5k7 wt.tyj5; xhn-7 znfjqmin-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it goinjk5 7jyo -;5.7xm nqhf(ztwtng 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 fror-/x3b w/vtk pm the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resx/-wv / rbtpk3istance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mz qp-2/ajpad4y/mbu d;5)je muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedaq2uba/m p y5;)dpjmd e4 z-j/al if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign oohhvkx/ 0 6a alo0sce4xgz-xemw.4 36f a hilly portion 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 partxcxw03.o ehaxak 6/me-gz0 vhs46 o4l icular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her fg 8ez fs9 vbycjb 0oj4v5.+8,pj n5;tfqt2bx watch from a thin piece of string while the jetliner she is in takes off from J5 jsfqv e.bx2z40c ,nf 8yg5t+8ob9 f;p jbjvtFK 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 v4ly4;lvvtsb ts0 hj 50ix6x7be several ramps connecting different parts of the stortjx lstv vis07;vybhx 404l65e.
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 the puv o5op/zdiy 8z* r07gnlley apparatus/57onvdz 80gziro p y* 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 acceleratq.ylgh3 y ;be 84yew9ying at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair,7xic7wq1 .so p an engineer considers the following set of co.c7oxw7s q ip1nditions:
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 ofl 8mh1eln9z6 x 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 7z-y) 7: g ssefp+kiieof similar length. Karen's rope is more elastic, calle :7yefi ssgi+7ke)z-pd 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 more likely to be hurt?

A fisherman in a boat is using a " 10-1vz *+v- zdb0e,)i vz15u6ozaxf t-qcfdo- i9h $\mathrm{~b}$ 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 tod- dfoy /g)gh( reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending ano,0 yfwd 26oy o9pyq.p ice field inclined at 2fo 0.9 yp wpoq2yd6o,y1.0$^{\circ}$ 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.