Why does a child in a wagon sgdepnjzw86 e ,np0o5pz p)zu(w7, th3eem to fall backward when you give the wagon a sharp pull forw0w(heepp,z8 3 n7pzj ndgp6,5 )uzwotard?

A box rests on the (frictionless) bed of a truck. The truck driver starts the t jyo4j d 2:6tuxjz8dmvfiri ) 4qdo3i0sg(-s8ruck 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) by Mary standing on the ground beside the truck and (b) by Chris wh3riog82j4vz o s iqis(:mj )f-uxyddd048 t 6jo is riding on the truck

If the acceleration of an object is zero, are no forces acting o3tz8;wzcw.6t w kdm/un it? Explain.

Only one force acts on an object. Can the object have zero ac-ae6;riyw hmj)i ppaho3 :9 i.(rbz t:celeration? Can it have zero velocity? Explaz93op6h ie-: ph)a yiw. ;mtirr(jb:ain.

When a golf ball is dlbxbrame zljx:29 +16v+dx9uropped to the pavement, it bounces back up. (a) Is a force needed to mr+bxl9x l1x2 abu e:+9j mdzv6ake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppou( komx2ug 1s4site directi1u(4u ogms2 xkon?

Why might your foot hurt if you kick a heavy desk or a wmhqo;8mialb1 6 +3gphall?

  When you are running and want to stop quickly, you must decelerab5)winkwz (6f x0q2qo te quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleratwonx wz(06fb5k 2q)iq ion 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 section of the same4l7 57yb*lj twtoyf -l 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 likel5yot4-wl t7*b flj7y ly 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 27yb f 1yh/5d0 fjqc5oc-kg rock is twice as great as that on a 1-kg rock. Why then doesn’15ybyj /o 5ff h7q0ccdt the heavier rock fall faster?

Would a spring scale carried to the Moon givsc k *;p)dsa l-/pwi9ce accurate results if the scale had been calibrated (a) in psccd; ap9wkp* /)-lsiounds, or (b) in kilograms?

You pull a box with a cgg( +h.r eyd*jonstant force across a frictionless table using an attached rope held horizontally. If you now pull t(hy dgg*r+j.ehe rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a ne-y*pg,1 ntgrzi3wu ( xt force mg exerte3 -n gptwg,1*zu(ixry d 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 10-kg object when you o17+r0d;8 5e inonnscw htvk* are on the Moon with the force needed to lift i1dn wk0son tren7v;oh5i8c*+t 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. zdl8o-a*cl)e bqjc a , 5y:vc.4–37) pulls with equal force on the other team. 5 vj:ocq,8 cya.l-cbel)zd a*What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries.b618ez - iwftk Describe the “reaction” force (Newton’s third law) by f8-e1 iz6tb wkstating (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 the ground exervb( dg*gra. kf0o kgz20seg g8-v91 ntt on you? Why doesn’t this force make you rise up into the ai(agv8d9gk2grb tgk.0 ego*- 1n zsvf0r?

Whiplash sometimes results from an automobile accident when the victim’81ypim 2y ietk:,xa)ys car is struck violently from the rear. Explain why thy myk8e,)1piyiax2t :e 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 tr x+ afoafp17/a7gt+ssuck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes+as ff/+a t7g1x o7pas the crate to accelerate?

A block is given a push so that it slides up a ramp. After the97ecg ib3 v0. kld7vqf block reaches its highest point, it slides back down but the magnitude kb37.v lqvd7ie9c0fgof its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read ifqw,d;jkh1y n vu(; ox6 you weighed yourself on an inclined plane? Assume the mechanism functionx;h,ydvkw(o1 ;6qjun s properly, even at an angle.

  What force is needed to ebp *el ; j+rg:frmefzao- 3fe p6;v4+accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ride ez z0(7*n;o:zum6s aeu fb5jrr at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wika rg3t;09sc fy 5 .7uqqjl;w -b.lenlthstand 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 o40k-bb2isv ke f 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 stos; dtbc762y lbp an 1100-kg car in 8.0 s if the car is traveling at 95bl2c ;7 6tbysdkm/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to mn1d8rd7g(pl9ikbb - 125m/s over a distance of 0.800 m along the barrd9gbpl7dkn r 1bim( 8-el of a rifle?   

A fisherman yanks a fish vertically out of the wate1kfxz6k y1 rmh8ev 8+cr with an acceleration of 2. r11yk8mf68kceh+vxz 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track (40zezm,;ma )h** /lwvqpwv. s1m2 $\mathrm{~m}$) 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 y0.mnl 7*2+k g3v uadu rn(zljtwsd6,to be designed so that the maximum acceleration is 7l60nurukdm+(ta 3w ys2zlvn, *j.g d 0.0680 g . 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 bathroom scale in a motionless eln jx(b . w.ph6jb-7fnp3loa 8 ;c0xtadevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight.0of -pdjxtx7j;aa.( nwhcpb . b6l38n Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum st1), /x s ;hwzkrm5wvq+k i*eabrength of 21,750 N. What maxiwmw kvh, es;izb r*x/)5kq1+ amum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 17e(cbze89t*1plxwlov ukg + kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight+ez*u1pkv c 1o9bge 7(x8wllt?   
(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 3.9-4v00p bx66kmqx mn+qem high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate d pkbq4mv66n x0qx0+meistance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vet7a 7-;ymfh4qkra 5ua rtically upward over a pulleyk tu7y7qm a;-fhaar54 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 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 av3wzl 5ew 7;ka 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 moment it is hilu8l*h-.v sw: y kge*f gg5zx4t by the bat, and again (b) after it has left the bat .g5f *kv ex y:8szw- *ug4gllhand is flying toward the outfield.

A 650-N force acts in a northwesterly dir2niso3bn/ /h ct3rz+jrqe;n(ection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points west/zh i snen32+;/rctor3(j nbqward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high w0t o6wulf ,m3uire" strung horizontally between two buildings 10.0 m apart. The sag in the rope wutfow 063mul ,hen 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 tk ./ia bcp/d29kgyh -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 14j * 5sel3 4i mr1q;5lu0hvknic.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 atk7u+wu;g xuo+bas8 n5 McMurdo Base, Antarctica, as shown in Fig. 4-46. T +n5g7u8bawuk;s+ ox uhe 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 isx jfq xiq:2c kxk6:/z3 pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio ofqf:j263: x/xq xkc zki 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 herself upward using the bucket-pulley apparatvtl2cy 1;0xqn c:vj: h,m+t squs shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cocq10ncj:st :hyv x+q2l,m; vt 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 b,m ky1zm b iytj.8mc*+egan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a blockka-3tk 3bwv1m og0o4g*)jlpn (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 frictionlessc)ys(,a4r de0u q y2zk horizontal surface are in contact with each other, aaye0 y uq,)kds(r2 4czs shown 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 initd yxlre:8h9, zsgt,e(ially 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 9 (,8,lxertd ygs e:zhthe 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 3yt ,lmmf:-oi3fdwim )nh6 g;of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagmw -n 3ym,;g:d fhfi6)mo3lit rams 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 rh (n;ohoz.q(1 f lm.:4bddirkinetic 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 rgwu9i3by dm(2equired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum coeb374 /zbo7hhkir.kv i fficient of static friction must exist between your feet and the floor if you are not thbvz7b/h k.o7i 4ir3k o slide?   

  What is the maximum acceleration a car can undergo if the coeffici+wf4 fgwb8( ruzq2 )veent of static frictiof42egzw+)v8fur qwb(n between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal str4n kdi ef-9irl3(zr b3.stpo- eet pavement is about 0.8. On how steep a hill (maximum angle) can you learefkp3rs- i9(3bnzt i ld- 4o.ve 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 / k+v6chm ):ca8g;vbishwg 8l -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough 3007..f-bb yimzpkv4w t$^{\circ}$ 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 anhgc)n +h 5ao jvv+y vocwm41/, asphalt surface have a very high coefficient of svjwhhga/co,y4n) m v+cv+o15tatic 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 ki. 6hhjw y8i8yf/yqk6jnetic 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 large a mass would box A havg 2bcfza5 4l-9cws*mb e to have to pcb -2s9*b c 45zawglfmrevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so thaw))c-7-mr 3ea3p x vv5fce vixt it slides across the floor. How far will it go, given that the coefficient of kinetic friction is pex )wa3vi5fce 7x v3cvm-)r-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 on a fv;mfpqtzdd. us j;) .v3q/+xhorizontal surface (Fig. 4-54). A 6v+/qj f3v.zm;xq s; dudtp.f)20$-\mathrm{N}$ 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 carryincxzspc8 a-0 4q2 ;mpjbg a heavy crate. The coefficient of static friction between the crate and the bed of the truck - 4azpjq;bs8p2c0 cxm is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has an (75i-hr mpjf zincline oj(f-ihzmr57 p f 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 2haj)n5diq rz( 8xcg*cd8 q79ulsd9 a( 8$^{\circ}$ 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 angle b;jh7k4b npf;j 3e/ry $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial s +jm9n/ok bqm(peed 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 om/ 4e0 nv3uovmf the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing mikki,r8o89u-mmlnx k+6k8 don it with a force directed lu88ki mi m +kk-8x6m nod9rk,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 becodo-): u bv9e:vmlw8is me dangerous projectiles as they melt. Consider us9i ::d )mebv-w8vloa 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 distance for an automobile t+ tb)4mh ;5mf;lp8(3ds hnfnhxz2rqg raveling at speed v mhr4h 2( xmqptb8) ;lzfdgh5nsfn 3+;is 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 slides forward on the dash when ksnb 67u 6e 5s74onq.i1f0oi ltk0iywthe driver decelerates fri.qt 7ws l4suokoyif01 05ekn66b7 ni om 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 n w9/dp;y n6gf usn/w(ezrb(+(sk1fom is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a coswc * d9(rc.udnveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary anwu *cdrd9 (.scd 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 .,fg:bp+d0 jisra8j9 qzjs;t 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 kg (some -2 -mr1.fuegd z8including 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 heart, at /+2ab t* )fk;*i,tlerrpy(x3v 9x1sihprfepeach pulse approximately 20 g of blood is acbef,ir ri2rf;hs kp+a1/x9*x()3tvp pet l *ycelerated 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 7v:qn0k 9k i-zuyapqzd2q:+/af r8 ulcelerationq:i: +dkqk 7auanz928q0/ r-uvz ypfl is no more 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 earthquake ej65llpbzpv7c+ j(m45t 2 wynis a , and if an object is going to "hold its pl5 bzmy+t542vjppc(n6ell w j7ace" on the ground, 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, examior psd.lbg (4u.p01nj4;n tejning 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 befores 4b jo;d t0lr4j.nuenp p.1(g 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-4ol s b1hd*l-x3 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 reacheo1*d 3-sll hbxs 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 drav-cii7*n vz3stvge u+hzz1 v d*251r opped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of vez i1 2nhz* *-v iztug7csv3rd1+5av What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch w mav 5b(jzraz n5,mhpd359 y k59m2ltmhere the effective coefficient of friction is 0.60. Will th5dt( 5 9b5 v9lh5jarm na3ym2p ,zkzmme cyclist 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 redesign of a hilz( ;u5ryt ymd*em6;a jly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to ay(uermmz6 5t;j*yd; 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 herm: olg.0 bq gat*id/gm;zj q12 watch from a thin piece of string while the j;ag0m z1 id2gq l/ bo*.tg:qjmetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarketmemplj,).a: y x +bev., there are to be several ramps connecting different parts of the e pm,a yvmbl:. )jex+.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 ( kfd3bscx bi h12+g10;a8amvamass M ) using the pulley apparatus shd+gvh0 i 81a2cbb1m sa k3x;afown 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 3h5xxp-nekiywc5ml 3z 9986kv.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 chair6ajeq0b p8u:0i3 6cfyzkk iy1t ,ude :, an engineer considers the following se zdeu8fbeaty q:yk0u6:pk1ji3i0 c,6 t of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mas ;o6gv v:-x y,ulql0oys of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar len lcf68ba dkjaokk0/ 21gth. 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 ovefo06d1k 8kcb j/al2k ar a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1o hkmo t14v sic6dd4;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 buildin nf ,xah) ip+u sz-uw0(vmb)a(g 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 together ;d wrnd7lniese8+ 3nmt :zj4+are ascending an ice field inclined at 21.e 83dzldmeri; sn+n4:w +t7jn 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.