Why does a child in a wagon seem to fall b5 ll8yn+zzi bvpiv+5 1ackward when you give the wagon a sharp pull fvz bpli yi5n+81 z+5lvorward?

A box rests on the (frictionless) bed of j ay tyw8/, sv8olj18:*y1 feobs s)dba truck. The truck driver starts the truck and accelerates forward. Theeyb l8s/v8a,j wd*)f11:s ob8t ysj oy box immediately 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 +l )hs/o;zexqs2a gou h.o qr(y7m x/gq*9ud5an object is zero, are no forces acting on it? Explain.

Only one force acts on an op7ia kkr-n*o /( xlozlmj57; mbject. Can the object have zero acceleration? Can it have zen mar/il ;opj7 kkxoml-5(z*7ro velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a ivbj17 gngo yl ln /jx4)(p13f6 he.7cyw:pwuforce needed to make it bou1jpny)y/ eoj1h47wi.gbl v 3l:unpfxc 6(wg7nce back up? (b) If so, what exerts the force?

If you walk along a lkd4ok llna782l h9:zhog floating on a lake, why does the log move in the opposite directio7a:8h lhl9ldnzk 24k on?

Why might your foot hurt if you kick a heavy desk or a wall? tt*b tr4g7:r 2h jqo4qgdbk1i2mtf 2/

  When you are running a6b)n-k et.v k rnr*:rqnd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own r )vrtkqbk-r:*6n . neexperience) 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*j95n 6;c/mvveq muy ny/fva section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely /ymq5u. e6nv9;van cvf/*jy mto 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 tqid3is9-zw 3r hat on a 1-kg rock. Why then doesn’t the heavier3rd 3qiz -iws9 rock fall faster?

Would a spring scale cjqv1woy /ma xkti *58+arried to the Moon give accurate results if the scale had been calibrated (a) in pounds, ot m/vwox+ij 8*a51yqkr (b) in kilograms?

You pull a box with a constant force across a frictionless tab:;9mx5injoh2 3*qmf g ncd8enkz fr;3le using an attached rope held horizontally. If you now pull the rope with the same force at an c3jf9ghqimk xn85e2 ;:r ; nomf3z*nd 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 u3tzo;q w 8wsx+; dkt.inder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s th 3. +distzqtk; x8wo;wird law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (oriau;6o7c*puwh0 uhs o5.;asl force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed tup 6;hocul h;aws.ou* s7a0i 5o throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug oz ys5ow:gv-h 4oi azg0 r6i)4nf war (Fig. 4–37) pulls with equal force on the other teamzo-r iys6:ag)gv4h4n 0 o5 ziw. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold9x1d6(xoxy6t j:zm mu a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a)t u z(9mj6o 1:y6xxdxm 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 lark:10vw gya8-s g huk3oge a force does the ground exert on you? Why doesn’t this fogk031wk gy-oav 8s: hurce make you rise up into the air?

Whiplash sometimes results from an automobaocxm hwca2/l2. 7/uy ile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward inm. w2ha/o c/xa y2l7uc this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accele0c6z88gh7f si01rwelsc8v qo rates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crat8ch8lr o s1cwgev6zq8 0is07fe to accelerate?

A block is given a push so thatz+r-9 jpf6 lptq6j8yf 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 des6yj-9qtf6zrp 8jfl+pcent than on the ascent. Why?

What would your bathroom scale mrnzy /ps5ra5, w +5qnread if you weighed yourself on an inclined plane? Assume the mechanism functions /ayqn,z+r 5 5n5rmwpsproperly, even at an angle.

  What force is needed to accelerate a6;dckgl on/4md9l y3 v child on a sled at 1.25m/s$^2$?   

  A net force of 265 N afiykx)bq-g0 .ccelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it b/-v k4chhevxeeor6 0(b0nla4.tlc 3is 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 g: p:hms1x.:zm4oul c 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 ist9cj6xz/lp)t5n j mp/ traveling j)x /9pn5tp 6 jtczml/at 95km/h? -  

  What average force is needed to accelerate a 7.00-- (owyztq.oh lw . 8)v8 y )b(c1(ifw8hzerkpigram pellet from rest to 125m/s over a distance -lcbiwz v y toi( )hkowz(.8(8hrf)qp8eyw .1of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration01admbye56p2 3xpifg wr*qs3 * oie+w of 2.5 f0i ix raw*gy6*+osdw53b3e21pe mq 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-.yq h 0w)tmah;mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be desi/nz8csn x : :-ka3pvmv58vtgh gned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motogv8av/hs3zptm x5n -n8kv: :cr 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 bathr..:8v,u gwq. 3 z vxg33 do;ibqi/swj)adpzeroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acce; q ii,bpz33sw:q. 3zea.)xwd.o8rvjg udv/g leration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 21dl2 qj);5u1v v rnh2tk25-kg elevator has a maximum strength of 21,750 N. What maximum r2dvh5;uvnt lk2jq) 1 upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallinl2ce8;+s (eb;rkstq ng sky divers (mass 132 kg including parachute) when the upward force of air tksnqr2+ ;se8;bl(c e resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. mt4f za jm3yrhzd rrt,.3g 3.0otgf7 :When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluag :d0 7,t3zz3m3rf4rortyf hjgm.. tding 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 ve q99qwdvwpghlb3p t skz19, *5rtically upward over a pulley and a w vwp31w*thl9bq p s9z,9qkgd 5eight 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 pla4lq 0a;fgl :dpd3t9h fyer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment il ;m89*mrl i3seg)k cjt is hit by the bat, and again (b));l9jr* m3c 8klmeigs after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650- 8w 4ytj4)iszmN force must be exerted in what direction so that the resultant of the two forces points westwardwitjyz44 )s 8m? Illustrate your answer with a vector diagram.

  Arlene is to walk acros:k2nlp 3 4sq0mu b.hdbs a "high wire" strung horizontally between two buildings 10hp 43bnk 0mdlubs.2: q.0 m apart. 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 from anothef(txr (1n0f e/)tksvb/+ m c5fiftp7jr 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 1 n7isx utcvqdbj 8cep 5zl99b6.) i/n54.0$-\mathrm{kg}$ 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 housi: 1.1cc/ zoyx 9w xeoxtszd6m4ng unit to a new location at McMurdo Base, Antarctica, as show96ye .oom:1xw4zz1 td /c csxxn in Fig. 4-46. 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 do/t apmc27zy5t8wi(o.- v cubehind it, Fig. 4-47 . Determine the ratio of the tensiaw8 vp./czoy57- ( iocttdu2m on in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward+h odx; +mwv8jggxo;x; a44nh using the bucket-pulley apparatus shown in Fig. 4-48. (a) Hahm+gh4 ;+nj4 ogd 8;owxxvx; ow 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 /)wawqg 0n1k. z ;zgrvbegan, 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 (nx 4bas1; pr4nmass $ 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 horizontal surface are in contact with each othe, xbfg2t s24a1)c mwpar, as shown ia4cx1w2t2a ) mpbgs f,n 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-y *ah0 iy-s;rlikaj6.80 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 acceleration of the lighter mass and then its velocity at the moment the he-ry* h; yaia is06-ljkavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes onst 8wiu1tyabg;a/6ypuc)i03 a frictionless table are connected 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 fr0i3;6sygti1cybp )a/t8uw a uee-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a 0jh3 oe6q/ kq+wbs.b n 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*-j4tlpg*bue w6haa 5-iqc*xquired 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 accelerating at 0.20g. What minimum co (l.ker )ooa/tefficient of static friction must exist between your feet and theoeolt (a/ .)kr floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient):3uonawz b1fb00v kp of static friction between the tu :0fonab0bv)w 31k pzires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and norma hum0ihoi), 3-iz,eqjl street pavement is about 0.8. On how steep a hill (maximum ahq i i-ij,3zhm,e0 o)ungle) 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 -4.80zk5;: 5dhwryc 7pjii0x2a- sn $\mathrm{~m} / \mathrm{s}^{2}$ 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 )7kmcc a7oil)30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a vbb6l-t-;vg4f 1snu d7 ,dw vlfery high coefficient of static fricttdfbwf6-,vlnvs 4u-d1 7 gl;bion.

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 fjsj6(gqafr./y)g t skt( f7x/ or 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 Fi4)/*(vv nora mzer1y, uj4v0ia s+ lxhg. 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion f(svu4+lr mianz h,ovva*yj0x1r/ e4 )rom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the flu d:8*8rcwnndf0u5f8 vt2s b,m.dhskoor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4 d820tkvuud sm:n f, d 58w.rns8bc*fh.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and scm. pz6/m qde0lkg6,110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 620 /ksz, e6.l6gqpd mmc0$-\mathrm{N}$ 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 fri n11p itvtvi,2ction betwet11ipn,vtv2i en 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 the crate slide against the cab of the truck?   

On an icy day, you worry about parking your 5b*;/ru+hd p w4-myb 5bsoqfocar in your driveway, which has an incline db5m*fwo5pryhbq 4;o/- b +usof 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 w)c qj47r 1va-*sbthrtith 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 anbcrvp6 +c2-r6+/vr ladgsm2x gle $\theta=22.0^{\circ}$ 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 vipw, a c-if853.0 $\mathrm{~m} / \mathrm{s}$ 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 tjhp ui8n p:fe(94m0b7lac-tihtp *f4op of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough walzg(.d tqwcq7 g1w:wj b9:g z+hl by someone pushing on it with a force dirc.wgz gzq(t7+j w1dqbwg: h9:ected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roof/2xt 74a(ek5raagp i:-kv7sar jado 5s can become dangerous projectiles as they melt. Consider a chunk of snow at thd ag aap5a5j4o 77vta(2sx-/rri:keke 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 minim* )7q,daesoutu l6 r*num stopping distance for an automobile traveling at speed v is equal to u7o*, tlnda)*eu6 q sr$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 dashbo*tmzn;c-l ue+tl7 imzt u*; ,yard of a car slides forward on the dash when the driver dcemt*z ulm t *i7l;-t+;,nzu yecelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speep+-0.e 6 - 0kadm h:pld,uvz baidp-ttd $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from when+leaa*+ g-wre* jtf 4re 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 between a box and the belt is 0.60, what is the minimum transit aj+gtewrefn*+ -a*4 l 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 vd+3zvs / kz19qkv :bit32da rbetween $m_{1}$ 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) iys/dg;5 7qg acan 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 mode n865zhae 0t(vy91f sbxs rc8ol of a mammalian heart, at each pulse approximately 20 g of b 08vca1y6btzsos (85nhx ef9 rlood 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 ofe:m8-3da -r0y7*o)xqfw a j ynr8smnq surviving an automobile crash if the deceleration is no more than 30 " g 's."o-8x) nrfjq3m08-arw:ma7eyqs* d yn 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 earthqua))7s-d 5wabvm/ h psbgke is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static g7 -s)5svmpahwbd) b /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 invpqk+ipu-lun 1n v*5h ;olving two cars, measure 72-m-long skid marks of one of the cars, which nearly cq5vp pn- n uk+;uh1i*lame 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 d7w28r.o qnyl fown a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast isw7 8rn2 yfol.q 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 Leaning Tower of Pisa and faa3nffm;gb6z 30 ry rf-lls 55 m before reaching the ground with a speed of What was the avezfaf 0f6rn;yg r33m -brage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy3ev-0n8xnoj 3m z6hxz.rdlb - stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretc0eo vx.3h--dx brn3l6mj zzn8 h 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 red p(bct7rze28mesign of a hilly portion of a city. An important c8 7 ctmb(2zepronsideration 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 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, d -j+qqqi9se ,iangles her watch from a thin piece of string while the jetliner she - 9i +ejqqqis,is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a superwpv:mt) .z;1m(dou cwmarket, there are to be several ramps connecting different parts of theuzwp c.;:m(odv1)tw m 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 )6m7o2x,r,.ejuh l( e m ghldk is needed to lift the piano (mass M ) using the pulley apparatus sh(kmx2,6he ,rjdhgeml.7l o )uown in

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

  A jet aircraft is accelerating at 3.5(cohu05yl 0/ pig f1zaiag74r $\mathrm{~m} / \mathrm{s}^{2}$ 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-restral 9tib4uf s86cint chair, an engineer considers the followictl6 f984u bsing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train haj.y8d ep6vey8pyc, / us 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 sodk4yrvws 2 ;i 66ca2cafety 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 climb26dc64say 2i;v krco wer is more likely to be hurt?

A fisherman in a boaf p8j2.n5izsi v;mhf9t is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to59x 2 uve tczqy-ehn/6 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 ropg(krzox n aj9- r6w;w svcg62* ft27sqed together are ascending an ice field inclinxvwwg9otr( 7 raczk6; 2*6 sgfs nj-q2ed 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.