Why does a child in a wagon seem to fall backward 9d3su) abgn: :,02itj;lb8 iw mc gqeowhen you give the wagon a sharp eg): :0 miq ;9ltadcwngj so23b, ubi8pull forward?

A box rests on the (frictionless) bed of agfyysdjwk(9q(i 03b 1 qscv3; truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of theyk(i0 cd1q gb93;fj3q wvy ss( box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forcey i nd1p64w0,h tv+ovdf3y5dks acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati65pi bv ewx0aje8p-b :st/ gi:on? Can it have zero velocity? Explawjap:-gx:s0tvieb/ peb8i6 5in.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forcei edzah4m:)n/ needed to make it bounce back e dh nmz4a:/i)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 oppos luw0vlxyuxx,r6c 7/ c7d9c4eite cxdx y,uv 0ue769wx l7crl c4/direction?

Why might your foot hurt if you kick a heavy desk cet ha :ru/5(nor a wall?

  When you are running and want to stop quickly, you must decelerate quickly.k0e+makd ; c9*9uot4c+lv d tk (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of decelerat;eut dvk*m0t kol +4dc9 k+9caion 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 s;fl/ov nr 84 *wietu.wection of the same thread dangles from the bottom of the stone (Fig. 4–36). I*;8f.ve il4oruwn/ tw f 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 great as that on a 1-kgqt9q :fnk6 :bv 02t0epaw; zsu rock. Why then doesn’t the heavier;u 2z0 vqef :w0paskq: 9btnt6 rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scatze 3/6dck*) z+( grg0uaefrh le had been calibrated/uc azetg *6 +re)(0k3rdg zfh (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acr6*h+dhp tv(iwoss a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an w+thipd(6v*hangle 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 aqwuma oj4 9ae0 yl*afjs fg*0i+j/0e 2 net force mg es*qw2 jme* lioa9f fjg0 0yea+4/0j uaxerted 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 objeww/5dyi,o ug9ct when you are on the Moon with the force needed to lift it on Earth. Compare the forceoy5w /,dw 9uig needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third layo4yrh-y(u9/ihtd* zk jk-o * w, each team in a tug of war (Fig. 4–37) pulls with equh**dk/ok(y-j9 iyhyot-4zr ual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to g9jr6;x8sg0y.cbr a ,br nne1hold a bag of groceries. Describe the “reaction” force (Newton’s third law)ben, ycg1r68bj0r.nx;9a sgr 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 the groeoxi3.25y rw 4il xfc0und exert on you? Why doesn’to f4ie50c.2 3xixwyrl this force make you rise up into the air?

Whiplash sometimes results from an automobile accident whendv 8v 8vgvz)k* the victim’s car is struck violently from the rear. Explag * vzvvkv)88din 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 b41lapg;dqswu-w y/ 6 truck. When the truck accelerates, the crate remains where it is on 41g;pq/6lywu b-wsda the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that i bjh25p s,jkv,sxqn/b *w y)5jt slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration iq/,bs v *s2,kp )5yhwnj5jbjxs less on the descent than on the ascent. Why?

What would your bathroom scale read if you we qy/./6fwz degtk43k iighed yourself on an inclined plane? Assume the mechanism functions properly, 3wg.q/kdk z yief t4/6even at an angle.

  What force is needed to accelerate a child on b4 ilt-mn,su3 a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikbc+0i*6wf8 h ynrlt7je 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 wi; uec o /wj*rk ruy8wtj+ 5 x4a.2xnjx53mhc4ethstand 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 a z;nrviva j r: .ypc9x;1+q:hw$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s gbu;nz0e( pq8aey1+g tui i:6 if the car is traveling at 95km/hq:;iu68(eg+ti n zpag e 10byu? -  

  What average force ismfx3 zc13 x fu3u-lc/v needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along th- 1fz x3cxvlf3 um/c3ue barrel of a rifle?   

A fisherman yanks a fish verticd z+:vx.u 55ll/jd tmkally out of the water with an acceleration of 2.ddtl mv u/+:zk.55jx l5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quatifdr;2z)r s58q vyk 4rter-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 tohl-ki -0huqpf-t 6 q7o be designed so that the maximum acceleration is 0.0680 g . Whuif-6 tlqhqkp- o0 -h7at 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 elevator. When thg l /tik.hkts90 ,fv j:. m:z2yd;ocqev1hku+e elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and fimij.tc +,uz ;y v:9hge/tlkf0.:kovh q kd2s1 nd the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a m.vz/.ys*a:w 1yeowk nm b: p jnao(5:aaximum strength of 21,750 N. What maximum upward acceaszoek my (. 5nvwjp ya/ab:w*n1:o.:leration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration d4nml xbfg;dy+56x7tof two falling sky divers (mass 132 kg including parachute) when the upward force of ai f;t+xb5nm d7y6gd4 lxr 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 rbtjf l8 2mem-ted /(0the roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over anber-e ftm0/d (lt2 j8m approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests onh2ttn d.;n l, yvguk *l(u5p/r 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 thlt/dv uyl5nhk2p;.*ur tgn, (e 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 dmui3tjdt 52o (iagram for 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 diagraieowld c.7(m ,m of a baseball (a) at the moment it is hit by the bat, and again (b) after it hadcl,i w .(e7mos left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mustixw jhko.-( pa.5s3knh15dll be exerted in what direction so that the resultant of tl nl pkhkdhj .-55axo(w3.i1she two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildiyq9n ;vzj /tipxw :9njs:b+6 qcudv3-ngs 10.0 m apart. The sag in the rope when she is at the midpob q 9cvpn ysd/tu;z:j +:w963nivqj-x int 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 s zf an9q*66hmhanging 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.. gza9y:9s*j3 9c -abc rpm+jv8qecsy0$-\mathrm{kg}$ 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 nen7 z,5ynvqgfd*9g 92 lk d9m4j5 w:o(vfri lbxw location at McMurdo Base, Antarctica, as shown in Fig. 4-44ryldq*gb7f95 x z ov :2vn9 kim5ndw9,j(gfl6. 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 isdcpshh 0h* b)t 9yy0s9 pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first ca th9 sp0y*0d s9y)bhchr $\left(F_{\mathrm{T} 1}\right)$ , 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 u6p/diw8,wr o)vbya1 wpward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to rai wwvi1y,a/bp)d r86wose 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 begk(9e5)4go 9no 4ugjl(uupa5afftr) x an, 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 b/to5e vf esa,md x3/t/u 9tb6vlock (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 contact with each otny pj:* j(-mbdher, as shown in Fig. 4jynb m j:p-(*d-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)g83 az/ufmmlp n4du9ally 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 him9n d3 uu4mgf 8pa/)zlt the pulley.]   

Suppose two boxes on a frictionless table a2rs/nb4u9eg7q rk56oqv rkeumcb (m+;qc*+p re connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension qm 5 c/c surv7g+6rq e9(m2+nkbqkb *rp;4ueo at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frictimv p2y-u*8oawkwo ;0pon 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 required to start a e dfln1; (l10ama y*bw5.0$-\mathrm{kg}$ 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 minimum2kkae gu5n mw :d5*seo ;w9,xl coefficient of static friction must exist between your feet and the floor if y ,k5dg: a*;nmw e euskw9o52xlou are not to slide?   

  What is the maximum accelerat)to;w */y dkimdj0(1 bmees:kion a car can undergo if the coefficient of static friction between the tires and the groun) 0wsiky (de1*m;omkt/ bdje:d is 0.80?   

  The coefficient of static fricti:fn 4t6* z o*exo 4(zao5arkepon between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parke rn*4z*oaezp:(kaxo6 5o ft4ed?   $^{/circ}$

  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 -4.80 pdye 9pjr6v v *l3f6as;cd, -0ptok y:$\mathrm{~m} / \mathrm{s}^{2}$ 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 rorltx g6urg4vj+ it,k b;88aph6 -m )qough 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 aspha h cudsj7,;uhl3 ft-pb.zn- z,lt surface have a very high coefficient of static friction-td;zc-jnhbp,z.7ufu3h sl ,.

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 fr*a0vji1cz*0 vj tow3y+0 fi qbkis;j3l,6h v niction 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 ,j0o3pt0a oma(/jks ohave to have to prevent any motion from occurripjoj /k30tsa m ,ao0o(ng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fx i25: vtsbp*nxfxtb3n 56xo. loor. How far will it go, given that the coefficient of kintvx 2*n xxpsfo6ti x5nb b5:3.etic 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 jyx3 jg:q pf; te18n3lon a horizontal surface 3f8e 3 jqt;y1p :ngjlx(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 coefficient of static favhbhb94ruf28 .3jr q2hdy. qriction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truc.rdu8by bj9fq2r2a hqh3 4h.vk?   

On an icy day, you worry about parking your car in your driveway, which has ang+;z(alg 0twy inclinew z0l +;g(ygta 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 sl0yfe g 1kqgm5yh ,o(aiqgwb 52(94waeide 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 angle )jxo, fu +i,vndfx wn 2jx93p+ $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.m+2f,ths/k*hcc1l s d0 $\mathrm{~m} / \mathrm{s}$ 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 olj)q+uy7 o:jz f 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 wa 8/l9nnbenrj5 ll by someone pushing on it with a fonn/8j 5nb9 elrrce 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 dangerous projectiles as they me(sxpo)x cl4xur6dd5 6 lt. Consider a chunk of snow at the ridge of a roof with a pitch 46r dcx(6s5oup)ldxx 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 traveling at srngz 1uz y2*c*3mf 1mnpeed 3m*1mr1g*n yznf2 uz c v 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 dasxu1ne)w79fo 9g b9igd h when the driver deceleratesnud g91gwf)o ibx9 79e from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an i5d-kio u2 x m57f,xdvbnitial 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 co6i0t) )rficoxi(85 cq0s*sa/xtuz sdc oe2 d6nveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero 6rocsszic i/ec0 f)tqa)s( id 6x2d5o* 8u0xt 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 frictio;+l /hzfux b 18jcmv9hn 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 (including the bicycle) can coast down a 6.u/h c lgm.6.zjt 7y2jw0$^{\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.gu/ij*n u)rl7ugqv bg 3sl79 mammalian heart, at each pulse approximately3r9gvngs7iu.bljug 7lq u *) / 20 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable b/ o9vx15 houmdc8ko ul el0+jy1;9je chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force oney uj89o/1el+;d u9k0 c b5jvxhol o1m 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 acceleration87n 7hm jemh)aik7 ov9 produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the h7hm 7vo8mk 79aei)jncoefficient 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, examining the scene of anupkfq/+bn e5n) vhz )e2n1xj5 accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the zb2nv)5nq/hufk1n pxe)5j +einitial 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 m yc8 vdgvyzeql7 rjewp:;88d qd (*;.ktraveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) I8cd jp;dy8ve:vge8y7 rlq.*qk;z (wdgnore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is drovjj c mv7ay*;u,p- f/ 4ym-wibpped from the top of the Leaning Tower of Pisa and falls 55 m before r mb*vwjm-7/uajy4-i;cy vpf,eaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a sqnr3ac uwfm t3,:3mgmj. /1 ;z,)tb1bnwdtjeteady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the 1wra, mf:jqbe ttub,nnd tw/;z m3g)3c.mj3 1cyclist 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 h o9g; u6oyt,bzlb2vy)illy portion of a city. An important y; uovb ozby,6ltg9)2consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin1p7wa3g05mnr)yp tsk piece of string while the jetliner sh )7ym 0nps3k1rwp tg5ae 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 supermarket, there are to be several ramps connecting differmq1wp2fl2w4f* u2 (wvxp1c cnent parts ofp* 2plc42 wcfuww1qm1 fvx(2n 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 lift the piano (mass M b, 6g g9sf8fkv ) using the pulley apparfb,vg 98 sg6fkatus 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 3.5 u-i c1d vc3ax8xj.qy4 $\mathrm{~m} / \mathrm{s}^{2}$ 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-pdhf*6 dfm(jri3qzo:3dh q6c k (b,s-restraint chair, an engineer considers the fol6f3 zf,ijhd3o(d hr6 b-(pq cm*qs:kdlowing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,00 p2 t()b-k 9ul;jpgfid0 $\mathrm{~kg}$) . 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. dp wy5y;j0zzc. nb *p-Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill'snyz5 *c.d wyzpjb;0-p 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 usi*wsirw;k4mz6at 66 b1cp u ,wung a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speeb/z v.xdch 1e: .rbu;rd 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 climbe5wn3jph yg :pzvp6a:vv c 6143abtyn/rs who are roped together are ascending an ice field inclined at 21.pp abp :4c5vg :zav6 nnjvhw 3y1y6t3/0$^{\circ}$ 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.