Why does a child in a wagon seem to fall backkaw mx36 6vfhfyf6;e,9qku9*f84pm8rz w uxzward when you give the wagon a sharp v6 yfe9z3 wfm,8z hx xamkk9f*8uwpq6r4u6f; pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts thdewofo d9/. 1x)( 4qi8us tsgjttsp4+e 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) by Mary stadsju (8 ./4wtixtg+9) eopstdqf41osnding 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 fornis96( e anaec16,dti(owhe* ces acting on it? Explain.

Only one force acts on an objec:1heuj:vvlto2;u0ds5u )n3 5h zfh art. Can the object have zero acceleration? Can it have zero velocity? du0 2v5uhnreja :;zt:u1fsh5 lo)v 3 hExplain.

When a golf ball is dropped to the pavement, it bounces back up. (a)i4othp01h(/2ip j ol b o*yon)tga/b4 Is a force needed to make it bounce back up? (b) If so, what exerts oaog j*i4l)t/yop4 /(h0bo n b2 tiph1the force?

If you walk along a log floating on a ablqn)7 in9+6:houdc lake, why does the log move in the opposite direction 9ld ic6anbhoq:n)+ u7?

Why might your foot hurt .hjc87-thz kfzci z b47af/z92lz2 rc if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qu vaxrm:a.dh9:h 7 2inuickly. (a) What is the origin of the force that causes you to stop? :arm:9 2.ahxi dn7hvu (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread frp:kmry 71c h)8 xzf;ca9mbgs3om the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a shk8yfsrc; p:zam739gxbc )1mlow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as zr6n.agocg -iqi 5 *,xthat on a 1-kg rock. Why za-5x ci onqr*,6g.gi then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scaler ukjw y6n 5.k(nja,e8h-ebq6 had been calibrated (a) in pounds, or (b) in kilok wry kj 6(,jn6qah-een.u5b8grams?

You pull a box with a constant force across a frictionless table using an atva lzdzox5suy8c.5 xsfmoige; 9*.22 tached 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 zogi9a..25 s ylmzxf;de8 ocv*x2us5 (c) decrease? Explain.

When an object falls freely under the influence of gravity there is p59pi*dnd a3 qa net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth m5p i pan3qd*9dove?

Compare the effort (or force) needed to lift a 10-kg object when you a (j. bd,ips+tl4uesaqa3s3 3n re on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a sanjs4+e p l(,3iatbq ds3.u3given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of wa; ::*ti m 8bw,lhajzd)z d4ohfr (Fig. 4–37) pulls with equal force on the oth, 8fozj:b mwh);dz *:htldia 4er team. What, then, determines which team will win?

A person exerts an upwardeu0*yq og0:d nf:;cnn force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it*0nedqo :cu 0f:;ngn y is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground j:nuv22d/jcu 8 rtg/aexert on you? Why doesn’t this force make you rise up into the air?t8dn au2g/uv jj/c :r2

Whiplash sometimes results from an automobile accident when the 2,j(dh(v obswb y++oe victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in obds+ ,b2 ((yj eowh+vthis situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acce95t;i5fuqy bqylpwx,w6ouxe/1( 5hu lerates, the crate remains where it is onx1w wo6 p hux;ty55ubqfq 5(u/9e,yli the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blocxl6 f3f6z+k vr1wu w6ck reaches its highest point, it slides back docf vu6z 6r3lw6kfx1 +wwn but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weigh(q4ecudh- bd*ed yourself on an inclined plane? Aschu4bd*-dq(e sume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a cx,s/vl+ gy+22skncwl42lg arhild on a sled at 1.25m/s$^2$?   

  A net force of 265 N acc11ouwe :v 6qbuelerates a bike 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 withstand if it is used to accelerate- ftodddaxy 422o7d7bu+sj(y a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofccs6nc pq;5(u a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg calbzgm: /jp9):vc hzt4r in 8.0 s if the car is traveling at 95km/h? 4:v:/)l9bhj zptgzc m-  

  What average force is nw pdva*(p1:hkud* r0geeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along th0ar:**(ugpvpdhwk1 de barrel of a rifle?   

A fisherman yanks a fish vertically out of the water gvm9hi4*ugl4zqw*x2z+7i okg h /mn2 with an acceleration of 2.2giz 9o*/iwkm u42mh 7hg4zn+g* vx ql5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ppg 7w8ixl6oo1 i/wkc9nx:f 07 bmtnmp)8lv 2cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designe nkc c3ai(t xvuu3r;1)d so that the maximum acceleration is 0.0680 g . What are the maximum anax n) u (kit3r3ccv;1ud 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 t n34i 3;zgxxa w56zjzz jaxg*7he elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the dir *n zz453wjz6g;aax xz j3gx7iection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximux9bu/m)d b2+;xl3tdco h yo- -puotq* m strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? oxm;*/- 2hlutp+ o9dxob u c3-td)ybq    ( two decimal places)

  (a) What is the acceleratioh4 19(;/xjjqvs.aawlupnz0 fn of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fou/( f4sp aj.za9uwhqn 0xvj1; lrth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a 8lflse)jya* q.ch-n 7 mj/cx5c rd,z2house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs /lc. hscy5cmajf8l rq2-e xjdn7z )*,) 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 tabls70 3kbd*o c, 0ob,z7p ldkscde. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-4 p70ck0l sd,z*,d boc3d7so kb0). 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 a basketball platxdo /l9vqx5:.k6fj7bv3m y iyer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body rxy mnh*)1 ikgxl n,(*skkf3 -diagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward they hxxk1ingfs )r-,(*lm kn*k3 outfield.

A 650-N force acts in a northwep(u15(g qfoc;9m(c ltdld:f 7zw8ej esterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagr7:gc u e9t(5wo;pd1j(fm e(cd qfll8zam.

  Arlene is to walk across ry5 .d7q g0jdv /up3+fvqh:ova "high wire" strung horizontally between two buildings 10.0 m apart. The sag in 7jvq.gydd vqh0+f3 / prv5u:o the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by9rl vmp8ybcjdqilc1u)gk -t - /b tg0-3t/8 qw 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.r4wff +a47g5r0*1 vyzax cpfxfe(fl( 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 neiffxg 34-wykw7 +x6l0f ) aoadw location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces f iwax- 4+k)3 xoy0gdal76wff $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 tvf7ovgn piww1::o tp8tw. j9- he same mass behind it, Fig. 4-47 . Detwo8- 7nwv p 91pwjo.tg :fvi:termine the ratio 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 herself upward using the bucket-ph iki-ub6o8o8ulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise oohib8 6ik -8uherself 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, ; gq f:g85 nb0gzb)q 0mlw(ii0exwo:ea 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 gj9w8 vq(w *0x1v5vq(gduzt hblock (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 aw*a-:)nzo y *dpz28wu hjn)qure in contact with each other, as shown in Fig. 4-5wq:zoayn-zw*dh8 p)*nuu j2 ) 1. 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. 1:15 coi-dhj3v4ffq -gizi(nr va6ds 4-52 are each initially 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 ag: 5df(ijv14z-1vqd o-r36ifsc nh iheavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictiononfodv:4 mfus /5q vs*8l+-tn less table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration oft8 v*5lv nd-n/ 4+m oqs:offsu each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frictionyj)7h1xa ay s,auth5up+ 84ml 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 5.olw c(2yxlfr2 pclx-a: t1em,7.i*c o0$-\mathrm{kg}$ 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 minii/8 oqkz+wo 93a+ewzgsa om0*1 e;p yimum coefficient of static friction must exist between your feet and the floor go;++130/zzs a8epyqwa9 i o*wkmo ieif you are not to slide?   

  What is the maximum accelerationwaw4-+wl;qdaio3jf hpj4 c*: a car can undergo if the coefficient of static friction between the tires and the grou a*4pw:hwol c4qadf i j;-+3wjnd is 0.80?   

  The coefficient of static friction between hard rubber and normal street pave-zd q0svyckb8m,c95ue zx2c2 ment is about 0.8. On how steep a hill (maximum angle) can you leaveusymvxzk cdez, b2cq0 -82 59c 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 -4.80 (yw:tb33ggjt;/+i 7cimtqi pid,; ok$\mathrm{~m} / \mathrm{s}^{2}$ 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 ayv9; z9g)xbog;- 9qisbvsc 9f 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 have a very hig i r)zd gu8ng1n.u:/joh coefficient of stati1i uurn8g g /.jzdno:)c 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 frwtp 0+b.r uq)diction 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 f)c 8 .c7m4i:omriuftwould box A have to have to p.tm : 8i 74ioumrcffc)revent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push (jgs ahy rk8y ;o1c-p1so that it slides across the floor. How far will it go, giv;oh 1r81 kpgjac(y-s yen that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and attej 0(iz cea6 nu96*zk rest on a horizontal surface (F*k uez966 i(ntce0zjaig. 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 carryingycw gojur- l59 h +6iydvws6c8;mb: 0c 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 having the crate slide against the cab of th lbmiy89j;h w c g6-sc0c+6d5r ovy:uwe truck?   

On an icy day, you worry about parking your car in your driveway, which h:c; 2dso cgx(ndi+hr/as an incl;hxo /(2dgc+d rs: nicine of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide wi;mcj;aa41.r dl *g pjdth 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 lsvp4 9iiafv-p ,wn0r6ies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 wa 88srsyr 04g$\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a -jviw.,i +pjnri i *p8speed 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 ag;gjuun) . j(dwy x0h ;tu;dit1ainst a rough wall by someone pushing on it with a f0h;1dytuxu(ui) gt n.wdjj;;orce 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 danvgk3y--.ognsygz: zn3 , xn, mgerous projectiles as they melt. Consider a chunk o zgn-3sgg: ,yz- nkmyo3.,xn vf 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 miniq:3l toss dhhdcp6 8mk2wx.x(auzf:* :c/ o2 kmum stopping distance for an automobile traveling at speed :k22:h63a wzxsccx8douto/m sqlp:h(d k *f.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 fo-0 dixlbx2x0p rward on the dash when the driver decelerates from 4xx0i dxp 2-0lb5 $\mathrm{~km} / \mathrm{h}$ 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 initialflbg1op2q5v td2f- (w 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 condo m*(x82ljg cveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the min8 c2j(og*m ldximum 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 kiji ep8at4w9f0ur -(sf40xhj anetic 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 (including the bicycl*r vtm, h.*xi)ox 4+fwai,xdoypm6 ; re) 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 mammalian7 x(or+q wn3)ajol 4aw heart, at each pulse approximately 20 g of blo+ral joq7o(3a 4)w nwxod 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 chance of surviving an automobile crash if ii-ceo 9,8qt hz4yzv1 xln p1,the deceleratzvi1, nlx 8p,ey1t94qi z-ch oion 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 accelerati.biye8 l;(jpg.fh-s f on produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of statici (lb .h-s.;ffgjp8ey 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 an accident invq5g-bb cx, x gwax)pi:(cu32lolving 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 initial xcx 3p)2q,(bi5 gg -cxuablw:speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for ea; 1furtg,o/ixch 4 m traveled along the road, the elevation change is 1g; / ouri,1fxt m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppedgcb e)epd;rv-v 7cz( x 3vvm 629i)htt from the top of the Leaning Tower of Pisa and falls 55 m before reaching t)h(62 ceg v7 xevvzvti-m3;c9dp)b rthe ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but (( 4teuh jghr1zpx3d 2enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stret(zx4eh(r pj h2gutd13ch 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 og9phf3vgqe 8l )/ kc.cn the redesign of a hilly portion of a city. An important consideration is how steep the roads can be sqhv.) 8clc9fgp/3gke o 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 fro4v w m f;/(arepjd1m-5w;kbp dm a thin piece of string while the jetaw - dm4pd; ;ekrw5jvf1pmb(/ liner 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 supermarket, there are to be skn at.uq9fi,3;hu*aw everal ramps connecting different parts of;anf,qwthku9a 3. i* u 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 needag( )n 5 v:i zplz7q-bxdm39kded to lift the piano (mass M ) using the pulley appa5 d g:7ql-pvxk)z(zadb9min3 ratus 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 nds+047 gjal e4 csv-vat 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an ;+wq.lsgfkon ,7p4r 9/wkhlw engineer considers the following set of conditionsprwl;sw /kwnqfk7,49gh l.+ o:
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 twxk 2z +w*b,gxons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. 0ckcf+gy42y fKaren'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's rope stretches by 30 cm only. How many times his weight will the rope pull 2f+ yygkc 4cf0on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10jh4il+e) fv 2n-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 speed of 3.5 xv 1sw)+ qn(wg$\mathrm{~m} / \mathrm{s}$ 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 are ascending an ice fiele, huf0 2qxm0yd inclined0uqm2ex h ,y0f at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.