Why does a child in a m kjet+xcj/w,8 qh3x7z l(:xowagon seem to fall backward when you give the wagon a sharp pull forht eqk3j:lczw87m/xxx+jo,(ward?

A box rests on the (friction+kj fz1s7yor73( scpv less) bed of a truck. The truck driver starts the truck and accelerates z7sj(1 sfcrk3 po+ y7vforward. The 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 an object is zero, are no forces acting on m:wpw3o)1d pqw6t ; mwit? Explain.

Only one force acts on ai.:kv6pwv 9czn object. Can the object have zero acceleration? Can it have zero velocity? E: 9zpvv6kwic. xplain.

When a golf ball is dropped to the pavementzw k+qve3 mxb*sg5 ) 8,adh-mk, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the forcev3bzk we +8sh- g*mmax5dq, )k?

If you walk along a log floating on a lake, why does the log move inv1tfy h jj0,cmd7hwdyb3b, 68eu;.gd the opposite di,,0ddhbu6 yhgt.dj7ce vjwfy31m ;b 8rection?

Why might your foot hurt if you kick a heavy driha:l( x+ 0iwesk or a wall?

  When you are running and want to stop quickly, you must decelerate -wr mvkjr5;nk,1; ce squickly. (a) What is the origin of the force that causes you to stop? s kc,ew-j;; mvn1 r5rk(b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceilinj 2ut8 hrz jjm(l;;sy4;ad v)ng, and a 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 t mn;vhur a(dsy4 jj2jt8) ;zl;hread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on* it70tc 5 txm2wqp wh /:vd;uh(j:kfu a 1-kg rock. Why then doesn’t vh0 d5f 2/p:wtcu( 7iht:j ku qmtwx*;the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if z 8hiey0;d ripe25.ca the scale had been calibrated (a) in pounds, or (b) p zi0hecr8; i.a5e d2yin kilograms?

You pull a box with a constant force l;hjj t8+pp7)m a0gslacross a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizonm lp thl0g+;7)pasj8j tal (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 influepl,f4w pr:unc,fh s/b ) v8j)ence of gravity there is a net force 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 :,fpjpe ,snf r8 )lucbh/4v w)Earth move?

Compare the effort (or force) needed to lift a 10-kg yw* nx. v2b/x5jgyu)t object when you are on the Moon with the force neededx./ ngt)y*uy 2vw5 xbj 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, each team in a tug of war (Fig. 4–37) pulls w+ pwr v,+ycdq/ith e+ cqrw/+d,p vyqual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag gg29*t-ioo yomt8 /oqof 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 what object it 29o/iq8go t oo-y *mtgis exerted.

When you stand still on the ground, how large a force does the ground exert j)j1k mr:qbh(on you?j 1(hq)m r:kjb Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident whenumakyp3vm ry(nn :64+ the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward a+ (y46vpmu rk:mynn3 in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trucks;1 *wv wujqz1 accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelev; wqz1*w uj1srate?

A block is given a push so that it slides up a ramp. After the blog f w5 ;viel(6(dsko.yck reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than ysiokl( 6;vwfge(5. don the ascent. Why?

What would your bathroom scale read if you weighed you6o9720xuo*l8ww gzv t6e yrkgrself on an inclined plane? Assume the mechanism fw l9z7w06o yogv86 tg2ex*rkuunctions properly, even at an angle.

  What force is needed to accelerate a child on a sl)v2reqpn ng (.gg ,h+hmvk t5z-q4h5 ped at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike anph(5dwk)fe8j8,n 5j4ma a swv x+aan6d rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is us x;9lujac2n p+ed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ow uwa, .r9l 040mrxhewf 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 8.0sz+jupuif:k,phtv4,j) * v :a s if the car is traveling at 95kpv)v *+:tja,j: 4pu,i zsfuh km/h? -  

  What average force is needed to accelerate a 7.00-gram p 1caehhjr.grcu-qxc +01 c6g6ellet from rest to 125m/s over a distance of 0.800 m along the barrelu0c6 hg-1h1cjrc e. r6qxg+ca of a rifle?   

A fisherman yanks a fish vertically out of the water with ani ih57g(y j b3ods1q6 (uzmk-d acceleration of 2.5i1qgib yo(s6(5jm du-7dkz3h $\mathrm{~m} / \mathrm{s}^{2}$ 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 ca0n o;)lk o-hhan cover a quarter-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 t*inxn n7y .rzys8aq ltu1o33 mn0:h2) is to be designed so that the maximum acceleration is 0.0680 g . What are u2aolx3:r qt.3 nh10ys* 7nniyn 8mzt the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale 3oy18f8:osi n- :yshru8vsa psq1, fdin a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regul 1d f188o:nisou -p3 sray,vsfqyh :s8ar weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg el;7vt fxs+ rf0wevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? +;f7x wr0vsft   ( two decimal places)

  (a) What is the acceleration of g1ai15a g3n ahc pvy3*jy vfq ck77o5,two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth y* g ci,v 3op57fc5h j1a7nvyg 3kq1aaof their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground b 7h6al959qe gann +plgeloa9gng9 +ep 7lqahl56nw, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests ern5q4mb yx1)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 box if the weight hangn b4)eqy51rmx ing 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 bas(j2bmemnk 0351lp zs-z da9m;o 9fv grketball 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 baseball (a) at the moment it is hit by the3p:feefn8y / kdowl /t*gv01mxz:iy - bat, and again (b) after it has left the bat and is flyin/:ziofy3 n 0xel*kw-dpye8 1m /:gtvf g toward the outfield.

A 650-N force acts in ww (js/ 7 2o8yd vtc:gsd84sfpa northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector ddp48 fs2d s:gw(cvsw/ 87tyjoiagram.

  Arlene is to walk across a "high wire" strung horizontally)89xz(*g jux)drgz r,qe4l nh between two buildings 10.0 m apart. The sag in the rope when she is (xh )dlrg )*z gej4 u9rxqz,8nat 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 massl)32yk,cugvm( en+i ;;zanf i ness 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 14tn6/me /f :7h4rl9.vzqm uek g.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 upli z1 f))7aia new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcesi)7)azu 1ilp f $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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, Figb)mq- kwyfp:d.61ty j. 4-47 . Determine the ratio of the tension in the coupling b : ytyw.qpjdkm1b6-f)etween 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 th e2 ctvvsz76 09zogwn,e bucket-pulley apparatus shown in Fig. 4-48. (a) How hao,zw6 t en svvg0z27c9rd 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 irikti) 5km .7began, 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 btuxoj/.3zda 0p i*q4iglkk)9lock (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 horizoncf 5c2mx)mpr0zzq50u wmqd3(tal surface are in contact with each other, as shown in Fig. 4-w 0qz5fm 2 mq5zpcrmud(0cx3)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. 4-53v3wk)g ldj1u2 are each initially 1.80 m above the ground, and the massless frictionless pullldukg 3jw3v) 1ey is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy )( 0d.e v otqls;tiu(k4)pjufcord of mass 1.0 kg . Calculate the accelev js4t)fkt) eq.l(;ou0 p(uidration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction be d/,2l trr9mrd2 ;mi7lljcae a5):qlxtween 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 reqha2g2wmn0u* x uired 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 acc)kf+p,b 8 1wee5mzf gzelerating at 0.20g. What minimum coefficient of static friction must exist betwefz1eb) gfmk ,e8p wz+5en your feet and the floor if you are not to slide?   

  What is the maximum acceleration zh xc8 z7(i4bza car can undergo if the coefficient of static friction between the tires 7h 4b 8zczx(ziand the ground is 0.80?   

  The coefficient of static friction between hard rubber and bkds0152sv inp mz;zn48k*2hcy: erznormal street pavement is about 0.8. On how steep a hill (maxi bzyvkpd;0:zc es2 r41hnm sn 2*k58izmum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4w( v z+togk16j.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 r9az i8nt rd:k0ough 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 very high cp:0f0ckm :eaxfx6nx i5 3t3iqoefficient of static fr ina06xxfq:k ce0m:5ixtf33p iction.

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 kinea du9dwr 7 zbf3(wn04mli t8m)tic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Examp3u/smz kny i8 i-(rguji+- r.sle 4-20) how large a mass would box A have to have to prevent any motion from occurring? Ass. 8iiirzkug/rn-usy3m+ s j(- ume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will exl*,+ v,buu mz +um+:zql uc(it go, given that the coefficient of kinetic friction is 0.20 and the b u+vm*:q uxelczu (,l,z+m +upush 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 o;h6 5bcln2y7 yv6jhei n a horizontal surface (Figvyh bh7i2c6yne6j;5 l. 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. u wf(v lq32kt,The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?kuwtf (q l3v2,   

On an icy day, you worry about parking your car in your driveway, which ha ,8(gve6 .yysi7y,0dh yvzslns an iesv7z(y6 y igndlv,ysy h80.,ncline 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 with a 28)0( +wb5rws nepm8muu$^{\circ}$ 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 axa3 kmls)u8b2 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 initia bet nn )(okd:vi94hv rkn8bs/9.8ump l 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 steepest hill with a speed of 6.0 ;szl8ws1 axi)$ \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 plyx rhqtb,s0,q5 c or.5ace against a rough wall by someone pushing on it with a force directed upwardy rqr, qth0,.55xbocs at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles 6 zquv mg,9) cxh obre37gtc5pudrq:3xoj9 )+as they melt. Consider a chunk of snow at the ridge of a roof with a pit9o:xtp63ohg vczu uebx9+75jc d ,rq r3qm ))gch 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 stoppinzt6dq / eq7xu;g distance for an automobile traveling at speed v is equz6tuq 7qdx;e/al 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 dashbo2a pjhrp bs6ux4 d8l. zv1bwzj4;+tk8ard of a car slides forward on the dash when the driver deceleratelad jbs;4zt2 z8 8.+bu 416xhrvpkwjps 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 i cq fx:ga( .7psc(m8glnitial 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 belt from where they are filled to the packing s6cqd +ucsxdo 7): w0nhb*wc(r n7mh,rtation 11.0 m away. The belt is initially statiw*h7 )hno:q wr nrs m+dcxcb 0cd67u(,onary 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 / sg(c /gynm/ emwfng;yab*01of kinetic 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 kga3 v)q3on6 cmt (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 simplified model of a mammaz:q;nf.p gf 0qlian heart, at each pulse approximately 20 g of blood is accelerated from n gqzp0;:.q ff0.25 $\mathrm{~m} / \mathrm{s}$ 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 reasonc5wy+io z. g0gable chance of surviving an automobile crash if the deceleration is no more thw+0 o5igcgy. zan 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 59lvtt*t):u ,vbo d1. pgpf+or2 dvbpan object is going to "hold its place" on the do.ft gtl1vpd:o vb*)59r, btpvp2+uground, 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, iv )ts1dqgsbx*v*4d5examining the scene of an 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 about 0.80. Estimate thxs5 *g)ddb*v t1sq4vie initial speed of that car assuming a level road.   

  A car starts rolling down a 5-.yl dap,/ qcb*bpfqx x(r/z1-in-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 going when it reaches the bottom after traveling 55 m?b(/x-f/z.drp l*xqqc ba5y , p (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppb qco0. 2guw0zxk /h;-(uzwu sed from 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 airo z( u- 0w;uks u/bx2c.qwhz0g resistance?   

  A cyclist is coasting at a stea45telj4hy 66dvd *9kw joiw e9dy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the j6w9w i 6td4oe9d k*4l5evjyhcyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the r( o upgakm)sj)kuh 7l )kj.q99a 3u0hkedesign of a hilly portion of a city. An important consideration is how steep the roada sl0h3 k7(a)m9)j.k q uj9kgkuouhp)s 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, dangles her watch from a thin piecehrr ;c eeaww;2 n6q4g)btblbc 358uy, of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle ray6 43n8l2)ewwh b, ccb brq 5e;;tguof 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, *v u/o82m8qw l(qo1w1faqfbk there are to be several ramps connecting different parts l2o(ua q8*w/b11v8wfm oqfkq of the 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 is nee4zmw /:/cuxu:ncp xl0ded to lift the piano (mass M ) using the pulley apparatus sho:ucp/x 04l:m /uwxnc zwn 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 3.53v jrq2ly)eqv5o * bc- $\mathrm{~m} / \mathrm{s}^{2}$ 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 chil *:( faujka3h5xl7 eebd-restraint chair, an engineer considers the following set o3*(ef l :ajbhekx u5a7f 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 has a mass of 660 metric tons (660,lctn. 17-gijz/uic 7u 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. Karen'smyl*xl /v/smql 7. (1xf /moqe rope is more elastic, called a dynamic rop m lql/(1mv*x/ sey.x/fqlmo7 e 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 usin rux.4lxnkv45qg*+dq: 6 ncodg 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 to reach a maximu gg/ m:+j;d)w.6xxz vw- /tjrwbqh :oem 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 a4xp ,.+gdr1noihck* vre ascending an ice field inclined at +o x. ,vp*kc41 nidhrg21.0$^{\circ}$ 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.