Why does a child in a76 d5afis y+uo wagon seem to fall backward when you give the wagon a sharp pula fysi7u +6o5dl forward?

A box rests on the (frictionless) bed of a truck. The truck driver startb4 k7u/1;ajy9o ft+d3itzeius the truck anyo+u e7au3ztjb 4i1d/ ti9k;f d accelerates forward. 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 ,n:)b.wk)y aqv+bb ad object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have ze ;a7jtz +u/nvxro acceleration? Can it have zero velocit;xj+7/ avuz tny? Explain.

When a golf ball is dropped to the pawgf1v 1s-us;tvement, it bounces back up. (a) Is a force need- ;g1su1stfwv ed to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the+-ls) /7ktk bsib 9 3ma3ctbyl log move in the oppositeb+ta7ctsb m3lk b ys3i9k/)l - direction?

Why might your foot hurt if you kick a heavy desxm bmo4icfubpq/ 09ym 8t70 cj/e; j)ak or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) /ct ;jr:lv qi jerdn l.6)3y psag:t+v90mn8cWhat is the origin of thlt9l+gn.d0v c3:m8stenjavr:iy)qp; j6/ rce force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and4zhtlo.rp r4i l6(r+ y a section of the same thread dangles fro hrltyzr o64.l+ir4p( m the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as qmyes1y:dgm+4 2 : f;byu(cgs great as that on a 1-kg rock. Why the; uq2ggsyyes +:d1 b(:f 4ycmmn doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resulka3tiqdr 0sqmj m;-fz653 sjoy9s c2:ts if the scale had been calibrated (a) in pc6i 2s3mrk qa djsj 50;yfq sz-t3:9moounds, or (b) in kilograms?

You pull a box with a constant force ai nhwp).6n6, -klwn vccross a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the.l6wn-)nvh w p6k,nci box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence 2gbbnh8af 7*fh3ffm *of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object ef*f ab*3m82h g7h fnbfxerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed .u4z ae6a.tsb(qqe x8to lift a 10-kg object when you are on the Moon with the force needed to lift qz su.qe. x4aa(eb6t8it 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) pullsv s*inm/y57olc0m0fl with equal force on the other team. What, then, determines which team will winy vci0n0 7*slom/m5f l?

A person exerts an upward for f)meca4pw1 s+py) c-1b i*viw+ttt1rce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what ovt+w-tws1c1a*p4)p 1mf bi)t+ec riybject it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, h1nabh oy g. v:5ay8+o )e2holgow large a force does the ground exert on you? Why doesn’t this force make you rise up into tebg vy2a1.: 8yl)goo5aon+hhhe air?

Whiplash sometimes results from an automobile accident when t f 97ex8uh6vrrhe victim’s car is struck violently from the rear. Explain why the head of the vict fx798e uv6hrrim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the xsf1. lsbltaf8jke* 6k ;i.5etruck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crax*lf1fse jsa6 tki.ke5l 8;b. te to accelerate?

A block is given a push so that it slides up a ramp. After the block reau ws88e6f xnwlor 3r22ches its highest point, it slides back down but the magnitude of its acceleration is less on t68w2o srxnw2e 3lf u8rhe descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an iu; eoficj,s73nclined plane? Assume the mechani,ej;f osu 7i3csm functions properly, even at an angle.

  What force is needed to accelexxt02 -toqmr.28ucrdxq v6 y.rate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikeh87bn.bypjjopj1n o -:zqr3/ 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 withsvt+hthi58hp)iqe(jnv * hqp39* 1yh wtand 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 +e6cgaqr 4,n1x+ bilbkp)-ro 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 1100b;8c4t 8yaxr6so /qbz.ajd4 pl8 e*ec -kg car in 8.0 s if the car is trav/4;bljxcr8c zeaps * qyo46.8edb 8a teling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gr)o b(qjv; pcndz.ptry n6/0 ;lam pellet from rest to 125m/s ove;j0pq()ot pv 6/d; nzrybnc .lr a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accele-t*xeg ino19fration of 2.9i-1n* oe fgxt5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 y m.y- 0c)rks.qit8/f,4epxbb, m d pca 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 ) is to be designed so ;z3 b+ujtboq n2yhh1kya.w/2 that the maximum acceleration is 0.0680 g . tk.abu2n+w13qzhohy j/ b y2 ;What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bat -mv jfnj7(6 hd3tpi6hhroom 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 acceleration of the ep 7 n6itmj(6 jf-dhvh3levator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 4azsjiyi c s:3zytay;*g+ )u 82125-kg elevator has a maximum strength of 21,750 N. What 8ygczjti*)z;3yau sy +si:a 4maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accele 7c s9fv 69ju*gl1teeeration of two falling sky divers (mass 132 kg including parachute) when the upward force oft71c j*ge seef99lvu6 air 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 roofx2ika0+1 dz-u8wsawm1yls ;b of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an appb-s lm uzsaa1y+; d i2w8wx10kroximate 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. Aq7 z lht)d+fmlmr c1e )d-fi.) 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 b 71.hm+-lt dq))eldczriffm) ox 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 bai, qh :j*h.kmr9 .exh,e3u 6p.plu mdisketball 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 mot,3eklh i.qm6 ment it is hit by the bat, and again (b) after it has left the bat and is flying toward t 3mtel i,.qkh6he outfield.

A 650-N force acts in a northwesterly direction. A seco ojhp, ww )no.83lzmsbs71l)snd 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate y8jlh1lmb ow)3 wossn7 zs),p.our answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwer xb2y9 pwmcbh;/ls78en two buildings 10.0 m apart. The sag in the rb/cb y92p swm8x;r7hlope 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 anotho+zsyrkx(8f0v/ u .qm er 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.ux1f ka. wk6o40$-\mathrm{kg}$ 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 McMuryx3qlg rnx0g(jl4+ 8rdo Base, Antarctica, as shown in Fig. 4-46. The sum of tlgr04(xq 3l y nx8+grjhe forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. -bw0 iwbw 3z *v-7zija 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fwazbi-- jb*0w7iw z3virst 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 upwa kax.89m o-zaom2,stc rd using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cozasc2 t,xmoao 9m 8.k-nstant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a8iuo2 ;e7zdn+9mzdh v 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 blbcauaz+z; * yj6-v,laock (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 frictionlessw((3kidd. sk i horizontal surface are in contact with each other, as shoi3d. wik( skd(wn in 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 initi :wobl wnl-4t 5*wgki;ally 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 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.]ltin:k-5 bw *w;4log w   

Suppose two boxes on a frictionw:hbgrps4 8dgm( 2v bo c4344afy:phyless 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 fbsh4gf:w :4 4mgr (3o4ychy2p8vpa bdree-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 betweekx6du++vu*w2 tgo 0c kn a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start ym)wdg6.hmz: 1+lv v ua 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 y*s.l vj-st+4 wz;r ppat 0.20g. What minimum coefficiel+rpspty-v*; w .j s4znt of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum act+xro3n z)w-t celeration a car can undergo if the coefficient of static friction+t3-wz)nx otr between the tires and the ground is 0.80?   

  The coefficient of statib;/y)ecietdc5gimh: zh4.a8sz .n- qc friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum anglm48yz5ghe-/ze;iq in )cshcd: b ta..e) 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 -4jt hg k0e-2.upe8 :jcr.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 rouhh2*ne* e5o; dnu+ amifvsadla7r;n1x0 .4g fgh 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 surfac,e/+gd ajli(c e have a very high coefficient of stade /ci+ (ljag,tic 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 kineticm-m5j+oep:-hy-k5 g * )wkfsd.rg o a4jh m/hd 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 (Example 4-20) how larg8.fvfnx(4,u((d;3 f+ps ligtidh lwie a mass would box A have to have to prevent any motion from occut(sdvp;.ifn 3x g((fiu,w l 8hf4d+ilrring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so thadpe ),d-j/wgzt it slides across the floor. How far will it go, given, ejwdp-z gd)/ that 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 75 kg and 110 kg , are in contact and at rest on55fk5nl*g u xl pxzq6) a horizontal surfac 5x ugn 5q6)kpllzf*x5e (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 dz +yf* 8daqag+(iav*coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum ratevdgada*qa +f +zi*y8 ( 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 car in your driveway, which has an itmkx5y)pa 6y5qwi )9vzlt, y) nclinta)ipy,kx wqzl5)ty 6m 5v9y)e 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 slidem4 m7wlo+9oz .xl cn+e with 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 fzrg m8g0. js6rs:w c: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 initp.7p mvs1j b db.dm94tial 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 spebw hts8)c/sm (ed 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 wall by sbrwa+ 3(bkc .0 btz4qxomeone pushing on it with a force tw(0kq+4 xc.zr3 ab bbdirected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectileg0a0+fmk v5q p/u 8)ucrk4:mm w n:uvus as they melt. Consider a chunk of sn c5f mqm vv+0p:umgk8/)w:u4rk0uu anow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automob89g1gog7d v s/f 1gufl i8qq:mile traveling at speed v is eq i1ds :gl88qf79v umgq/1 gfgoual 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 dashboard of a car slides forward on the dash when the d s 0gt(brpcv (wb*i87sv62bly river decelesysr gbw26cvl7p b v(b i*0t8(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 is givnc-94h g) cglxen 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 belt from where they are fiu 1c2)398 .sylextb7,ae dfv*zc ybd clled to the packing station 11.0 m away. The bellxbu8,y vy17 at*df9)sd3 2.bz cceect 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 friction bgrf/m o;mzhf7 u2vu0dvdi:5,etween $m_{1}$ 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 kk l 9cqzo;g9 /c:.qcvwg (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 ofhqw1ah/h8 l(t a mammalian heart, at each pulse approximately 20 g of blood is acce(q1whtl ah/ 8hlerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the de tv 1zwd j;xtb/5-3dzdceleration is no more ztdwb1d t5-xj3/v; dz than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an;ml /nptr7fmi:de8 e 7 earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient oflmep 7;trm/i8 dn7:ef 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 c(u zr29yf jf (pt2/anof 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 fricticuyr9(2/(ztnfpa 2f jon between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means th crfyasoyd*2 ho1fj xa w6as -56bnm8 t./;zj(at for each 4 m traveled along the road, the elevatixza ;mosj1-rfft * 5.6cw6ds2 /yh (8aaobjny on change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leanuk9rv 8 c+t8fvmbls 1r9flu- -ing Tower of Pisa and falls 55 m before reaching the g9fu + m9c 8t8-1vkfulr-lsvb rround with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/) h* 9d+)omd2 rg,nxoj:rhhyc s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge frro*hng:d) r+)j2oym x dch9,hom the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hib gc-g n3 fyk4z7*j2qvlly portion of a city. An important consideration *c37gyzjqn-b2v4k g f 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 be(c*s( xv fv j/zjv)vybsy:vh x)ypq5/b1:: physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58).c :bsqfvj( 5:vpjy*/ / ys) vv:1vxh()yexbbz 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 ar5 -1n/gtfo*pvl1 qbt6m mug.he to be several ramps connecting different parts of thel-5gpg nvm/ 1qhotbtfm*.u 61 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 needed to lift the piano+ b1ic qd fdbzr9t;*5eqrv d1, (mass M ) using the pulley apparqi1qdrd+b;,9b zrvc d1 te5*f atus 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 accj h)r maknl;33ebg)js us0 43eelerating 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 chai0:r.e wfw f0ekr, an engineer considers the following set of cow rkfef:.e0w0nditions:
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 (/huibn5 al7 m*660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar length. Ka4xgaceq 4i(gm6z,c :yren'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 li,xg c64myq4:c eaz g(arge 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 qx vfsmb*:ec6czo0 *gw 1 8(7rb vexl:k4iia1 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 alt dbz) jju,x;)iw,-r ud w8mq9lowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped toges5,v:ou;j k hpther are ascending an ice field inclin; j:ohvpsk 5,ued 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.