Why does a child in a wagon seem to fall baro yd:ocm6b b )bk5+x)ckward when you give the wagon a shar5bbymobd:+r6cok x) ) p pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the u+;(do6lfheknwkr7l3 sfz *7 truck and 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) bu76do fk*7kh(3+lnelw;f zrsy 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, 1tslai(k)cm nl y;tpl.8n6f0are no forces acting on it? Explain.

Only one force acts on an object. Can the objdv bn(fp3 7xey:b8j,iect have zero acceleration? Can it have zero vel8 pj d(,v3febbi:yx7nocity? Explain.

When a golf ball is dropped to the pavement, it bounces bq/8bnq-cgt4 ewi/3 auack up. (a) Is a force needed to make it bounce back up? (b) If so, what exe 8/3qca4 uw/tgqie-nbrts the force?

If you walk along a log floating on za:w(pb ilx,i9-e8 vf a lake, why does the log move in the opposite directila9 xzv:w8 b -ipef,(ion?

Why might your foot hurt if you kick a heavy de8,*h dtgxkjovgq..l1 sk or a wall?

  When you are running and want to stop quickly, you m7zvsycb* u(9ruuod.+ ust decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Est9+uovr7sbycuu z*.d ( imate (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, and a xe9 qfr9 g.0jgsection 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 to break: below the stone or above it? What if t 9f.eg j9xr0qghe 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 a- kr ss:gzc)y:x l l85bd*nfxmq.y* 2p 1-kg rock. Why then f:q -bdlsml*p 5 k8gc.y)yx*z x:2rs ndoesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accf f ;kpvgzw.sk6 kg9z-q.bo0:urate results if the scale had been calibrated (a) in pounds, or (b) iq;9 gk0fvgow : 6z.-kb sfk.pzn kilograms?

You pull a box with a (p0yk8yiid : sconstant force across 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 box (a) remain the same, (b) increase, or (c) decrease? Expla(: 0idk8yisp yin.

When an object falls fbdb-+ eb21ivmreely under the influence of gravity there is a net force mg exi1b2beb- dvm +erted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10d.+ k z6w26kqg r-ledk-kg object when you are on the Moon wit6g+.6ezq dlwk-2 krdk h the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law,z2w5bf tp k qy)f m)cywgn(,am:;g1k1 each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will;b:g cm2y1fg1 kn 5awy)fm( kq z,w)tp win?

A person exerts an upward force of 40 N to hold a bagj2ex2rij 1fgdus)c2 e a09: em of groceries. Describe the fmu:2d x1c g ri2ej920ej aes)“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 is exerted.

When you stand still on the ground, how large a force does iv6b4v v2;jpbthe ground exert on you?vv 64;i 2vpbbj Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from angn ij5:gxre.w1/kwn61 ol+ x n automobile accident when the victim’s car is sx1 :lj w o/6rxne+ .1k5ggniwntruck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truxc.v-8zzt4 qr *d:rjq ck accelerates, the crate remains where it is on the truck, so it, 4 c v rzq-j8r.dqt:x*ztoo, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches its;o3p7e -ipa, u: q3fbkj 2tt- isbj;fz highest point, it slides back down but the magnitude of its acceleration is less on the de f,-; bta -ppk 37:;jf qjsuitbei2z3oscent than on the ascent. Why?

What would your bathroom scale read if :rl., 4 u9eescdfrn91q) cxnh7vk6 ya you weighed yourself on an inclined plane? Assume the mechanism functions propqae9,lhd xc96v :y rrn.kefs)1 4n7cu erly, even at an angle.

  What force is needed to accelerat+nr ghf1 h2v,z.fvam rn+;u +rzr8i6be a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and oyigo ;yop-qk85-p,08dbav d 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 withstaaa(f2ys0l(tv 18 jvtznd 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 ofj5 h)6zxr.k bc 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 i 8aky5g,prxy* s required to stop an 1100-kg car in 8.0 s if the car is trayy,*5 gp8kax rveling at 95km/h? -  

  What average force i ,3zq h. y0vlhs.ophvep76kwq 342fjd (wzu6ds needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alonujo4 3yzvps,6vh k2 ql 7ez.(3wwdh.fhd p6 q0g the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerationu(9y1 i:mg erx3k,tkc of 2.etr3 ygu :1,xk(kc 9im5 $\mathrm{~m} / \mathrm{s}^{2}$ 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(z q ee8.q9 2topvn4lz-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 4850wegszhb w: .m g71y:e0 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forw s.heby1:em7w g gz0:ces 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 +-hn6 -ok1y;00ysyqhpvgax bgfhv 1+ bathroom 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 theyohhbyan vx 600 ;1fs v-p1yg h-g+qk+ acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a ma- vl+pu fgwhx4) tutc,/1x zy9ximum strength of 21,750 N. What maximum upward acceleration can it give the elevator with4-w+ucxf gl uxy9 1pth/tv),zout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers ms0-kdf -m- f*k 5l3ve* ntv1c8nejmq (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of the1nfm8vc k- m* lqv te0es n3-5-dm*kjfir 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 h 1vxta 4hsu3f:igh. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of xs3at14 uvhf: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 ofc 5m djb-xrc+ x955ltn 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 forcejc5mx5xd5tlr-b f 9 +c 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 6/f0o fx 0gtkx3 wyg4ls3e p0nfor a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momen-5 f4epk 0kwnas+4y wst it is hit by the bat, and again (b) after it has left the b sf5keyp0 n+s4 w-k4waat and is flying toward the outfield.

A 650-N force acts in a nwz.id wa q(+l4w8 afp)orthwesterly direction. A second 650-N force must be exerte(wp.+ afl a4wdqzw i)8d in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" sx6t 2wc // smlds1hsu2vuy(1qtrung horizontally between two buildings 10.0 m apart. The sag in the rope whenwv2smql21h/ utxy us(c61 d/ s 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 buckai*su66 v)m cju)wx1yet is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.qnd/.0., ba n g9ealws9s wgt.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarct)3 2qf5dni)yg mrwt- qica, as siq2 gt yfmnq)3 r5-d)whown 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 behind it, Fig. 4-47 pr yo m q0k82pbd:.s/9myj ,hi. Determine the ratdbm pk:8ihj,/rq2. sm ypoy09io of the tension 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 hersec-vhc87 ita ,m( nvt6tlf upward using the bucket-pulley apparatus shown in Fig. 4-48. (atcmct7- a,v8(hn i6 vt) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 0jqujtad /z l m*.q5z865$-\mathrm{kg}$ 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 bl (fp398xrr nneock (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 horizontal surface are in /i(de)a-1y2ygrn phd 4ku8z xcontact with each other, as shhd 2a1ru-kinx)p4ze yd/gy8( own 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 aa haycy 1d5l(.re each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum yacdlhy1( a.5height 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 cord 2gf4v*vci*9ht3 x rfqof mass 1.0 kg . Calcv*xrqich* tf2 fv94g3ulate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetzi y -ahu 2gy7f 8+he7w5irtd(ic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is rea7n: nmv7kuzk e+ :6pcquired 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 0.20kaa,ezk p 6)xfwo:/(z:gm+p ug. What minimum coeu+ ) a:,emkox/6 k a(zwfppzg:fficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accelesf..1fy/df cl ration a car can undergo if the coefficient of static friction between the tires and the ground f .sd1ffylc /.is 0.80?   

  The coefficient of static friction bejxb6h)tcfhfrp 302b 7tween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum ahb) ffxc p3rt 0j62hb7ngle) 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 -4.806o05( + 8op okmlwhify $\mathrm{~m} / \mathrm{s}^{2}$ 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 5ys4zpmn 8t5 .ljnmzdf7p 0-ra rough 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 h/+ba,s-., fa 1 g;etjiwb;xczm1y9n ggbo9dmave a very high coefficient ,fins g;,o+agmegbt y 91cd1 /wm-. jab 9zx;bof static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction forj3e( vv hnyn4. 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+g 8iql..k(9izge qv7mk5ulh 4-20) how large a mass would box A have to have+ kg.5e8ilz9lig vqh7m q(u k. to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. H-ao smo8 qbpge7 5va46ow far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an i mo8a6abqp7 v-4gos5e nitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are ici :9x2 mfj5lfa(. llfn contact and at rest on a horizontal surface (Fig. 4(xfcl lf jmf295i:.a l-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 carryi9 k8ly7t4gco xng a heavy crate. 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 havin cgkty8x794o lg the crate slide against the cab of the truck?   

On an icy day, you worry about parking ykiq xap7fk* 7/dpts3g8 7 ,ey:m-qvi vour car in your driveway, which has an incline of 7 i8y7qt 3d /evp-sp7f :ak vkxmqg*,i12$^{\circ}$ . 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 . 9mq(y(rp zzsslide 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 at an and ; 1c*l9a(hfk c .axajaegr;0gle $\theta=22.0^{\circ}$ 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 an6nj .uvgn )he-xr iw:( initial 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 horrjjqim 8 de e/25r.+ill 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 pvm+a ehq5+,0y5dakn q lace against a rough wall by someone pushing on it with a +dmhqky5ne+,va a 5q0force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become danps,pba --df vk 21e,pqydau,q9 3 ysk2gerous projectiles as they melt. Conf-,uaskpyqbqypdksd e2 p ,,9a3-v1 2 sider a chunk of snow 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 db c)86.waq .rddf*mgg istance for an automobile traveling at speed v im).6rd*g8cq fg b.awds equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slidej ,esyzsb/s.qlv9: y7s forward on the dash when the driver decelerates from 45se / v.:s zy,q9jybsl7 $\mathrm{~km} / \mathrm{h}$ 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 b1vlq4t- acjn0lif f1l8/qm5is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a con-ris q2 -wx1 aliq14a+hwcp.eveyor belt from where they are filled to the packing station 11.0 m away. The belt iiw-12 war q-l xsc1ihp +.aqe4s 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 bzh-nz3v c6:* md tv1jpetween $m_{1}$ 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 (incgtghqzlw4 b 5fr9e52.luding 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 mammalian hearzzlr(2 8w-+ fjzs.k j lml7/djt, at each pulse approximately 20 g of blood is accelerated from 2dl(.-wj zrmzs/jzkl j l78 f+ 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 decegljk0s d;) ,bxleration is no more than 30 " g 's." Calculate the force on a 7;k,x)bgjl s0d 0$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an ob,ai)pc wgdt21fc ab-)3dn 4 pkject is going to "hold its place" on the ground, show that the coefficient of static friction with the grok)c,3-tnfp4 1)wd ab c2pgadiund 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 inv/p( ;yseela )y1h nt7oolving two cars, measure 72-m-long skid ;yyae tle7ops)(1h/ nmarks 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 the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4+,fs/ygk9p au,0 rzf(n5ly wp m traveled along the road, the elevation change is 1 m). How fast is it rps ,p nkzla5 0f(,wyyfg+9/u 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 fallfj 5i 6.simr.rup3 -ybad40wi s 55 m before reaching the ground with a speed of What was the average force of air rw5pr .jdba3 ri6.im sf4 u-0yiesistance?   

  A cyclist is coasting at a steady siu08abrognhx, qnx*c*6m x2 (peed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upoxbgxxr i ua nh**nc(8 mq06,o2n emerging?   

  A city planner is worki8ckkiq q9 6x o*ocn*+wng on the redesign of a hilly portion of a city. An important consideration is how steep the road 6koqi9x*cwq*o8 +cnk 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 piece o :k6o mgyk/-zmg 6cs)a4 )vmpzf string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices th))-kgmzpa6s vycm omg/ k4z 6:at the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are,)eae ttubl83 to be several ramps connecting different part)beeuta ,38l ts 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 needed to jz q7jcf 4bw2.lift the piano (mass M ) using the pulj f72cz.qbjw 4ley apparatus 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 accelerating at 7.ko1d hjpu 5j 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 fogl b e*539a .msnjks:fr a child-restraint chair, an engineer considers the following set of conditions:ess a9mkn:j5lgb 3.*f
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 trek e.2d,k k/6o)sx bmgain has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill ala0 mmc9 i8s7ynd Karen, use safety 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 dis09 ymi c8alsm7tance 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 yj*sp*, u,oa l )-cqtdz:cy w)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 buk)**blb w4 hicilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped togj2r/sb*cqgxok38e , eether are ascending an ice field inclined at 2qs3,cb*g rx / 8jkoee 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.