Why does a child in a wagon seem to fall backwardffyj ep2,zts f0wc45pyz/(szd-3n )s when you give the wagon a shar4 wzp yszfe2 d3p,-cf(y) jns0s/ftz5 p pull forward?

A box rests on the (frictionless) bed of a truck. The truck db6+ vj1qa06wbw 9 ktkxriver starts the 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 standing on the j9a1wtvk 6bq+0b k6wxground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acti dnseqd3+ltzgd3 n:56 ng on it? Explain.

Only one force acts on an object. Can the object havl //*k8kll xmvd;h5n -gkmo90 hc/udve zero acceleration? Can it have zero velocit - 9d ldgm /k*l/o0x;l8hkvmvhuk/cn5y? Explain.

When a golf ball is dropped to the pavement, it bou*8qcuki zt*dn lk8)/ qnces back up. (a) Is a force needed to make it bounce bad8t/zn )ukq**kl8 i qcck up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does thzek/q 4mh 23zxnlob(,e log move in the opposite directiokehn3l ox(q 4b2/ zmz,n?

Why might your foot hurt if you kick am+esr)- ewq73ej82: rtzm uhu heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicklyca .,n/a9krj k. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum /ka9,arcjn .krate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, anjs *i3hbi9h)pco7c; t t3ttj4d5 ypv e56ci k6d a section of the same thread dangles from the bottom of the stone (Fig. 4–36c)5d*4; 6h tojiv9 5cjhpci6tpy7tsibe3 t3k). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as greaongumn dk 4.+wpk: 2.rt as that on a 1-kg rock. Why then doesn’t the heaornw k.4+p:km. 2udngvier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale had 1m4oxjja) l08w6 gzia been calibrated (a) in pounds, or (b) in kilo8jz jliam4ga wo) 16x0grams?

You pull a box with a constant force acre4s.x(uzn m51 ed*plmoss a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does tem px*zd. 41sl 5(enumhe acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the inf5wk-cg j-snv 9 x 3go7mbb,9vyluence of gravity there is a net force m9bbovs c,m- vg-xgn53yj9k 7 wg 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 move?

Compare the effort (or forxmx)j 2i u*2nvp +pt)ece) needed to lift a 10-kg object when you are 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 given speed on p)*+m 2 vte n2j)pxxuithe Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4eriic( ao6g:tpmz2t 43g ,ljy r;0.nz–37) pulls with equal iogt0 4.ay2eir:tjcn ;z3m(g, lzp 6rforce on the other team. What, then, determines which team will win?

A person exerts an upward force of 4-6z :f(wv3x*aay cg gm0 N to hold a bag of groceries. Describe the “reaction” force( *ga c -6x3agymvfzw: (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, h*yjto-bu )0gzvdg pda/ 4-,c row large a force does the ground exert on you? Why doesn’t this force make you rise up into the abr gu0 y*,t)-oazpgd-j4c/dvir?

Whiplash sometimes resucdmm t/eif7(z. yqpkn,)1w23 ) ukuuqlts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backwadkumq)1 (2tcyuzw,en 7mu.3ifq/pk )rd in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truckn-kjq0miw--h7 z6ehmo dwru.6i *bi* . When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. Whatm*ie--qhuwjo di-m hkw. 0 zbri*66n7 force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches it*l./4m vmfv 6 iwbem)ps highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the asce6vemi/.p* mv4w)lm bfnt. Why?

What would your bathroom scalcpye+spv99boy ko k) 1; . lw/r;,hewle read if you weighed yourself on an inclined plane? Assume the mechanismc/. hsobl;19 9o lp;+,wky)yr wkeevp functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1j/i/ gig-(wp5iubq 3cbn:vn ;.25m/s$^2$?   

  A net force of 265 N accelerama p 02 tt9ovgx+t/ k*wx,vcc4tes 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 tj0imcg+2qgqqk0mk2rw 90g -l o 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 sa;vs8 xaib+8$76-\mathrm{kg}$ 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 sto5rv+,h+ + ahgtp2vgzwiok/ g10ql(m l p an 1100-kg car in 8.0 s if the car is traveling at 95km/hv2+gmkhl +51hwv/(0 aor+igqtz,g pl? -  

  What average force is needed to accelerate a 7.0nuwktd 7j1+g:kdid rsa) y*; 70-gram pellet from rest to 125m/+i jtn :d;u)y1sak* 77dkwgrds over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of /3qmakenmp; -the water with an acceleration of 2.m epakmq;n/3-5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 covepr )j/k rngq,rus:ff)lsl 4vv +77fv7f z81cyr 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 designed so that the maximum accelerationx qu+8 qeh/*c20zkmdflf e-f/ is 0.0680 g . What are the maximmeqfhkd0 q/2+*8lzc / x -fefuum 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 eleva3b7ac*5d1h sc z* fqthtor. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the e csb7 ahq d51z3f**tchlevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength fjes26w r19d6vsjxi+22z w rk of 21,750 N. What maximum upward acceleration can it give the el2sf12 r zs 6vd+ww jr29keijx6evator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling o*c2/z e-z go8aebt8zsky divers (mass 132 kg including parachute) when the upward g8a28o* bzoz- ze et/cforce of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a hous/k k.pmzy.*gqe 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 tk/qgyp.*mz k .he 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 t n+ wp/waz02uq*np(mn o the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weig*n+ pu2w( wmn/qp0anz hs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dilptc5y ( pg2rr- v2+x.b 0wrfxagram 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 diagram of a baseball (a) at the momentymf/az /yyl ma/)8x*b it is hit by the bat, and again (b) after it has left the bat and is flying toward thez8/l)xy y /mfym*a b/a outfield.

A 650-N force acts in nmrxz7 +yts-ng-vc 5v6h *qw4a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your -vyh -stnn5rx7v 4mzw+cg 6q* answer with a vector diagram.

  Arlene is to walk across a "high wire" strungu nj b3+nr8*-pa)cpuc3nf1 m5 f4xary horizontally between two buildings 10.0 m apart. The -x mubpn5u c f*y)3p1jf ca483a+rrnnsag in 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 by a massless cord from anot o(qw 7kho*o1pher 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 144 g5ieket ;6tb.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at uh1v7x/xd2s0zh ga5r McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fhrsx0zd uahgxv 5/7 12orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-w; zf guen,1k8 ve 2evc+8 cb6fhl3fl:47 . Determine the ratio of the tension in the coupling between the locomotive and the first car81ene lc2 3zf+l f:w,v vgfh 6ebu8k;c $\left(F_{\mathrm{T} 1}\right)$ , 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 herse;7e/e3 /-u3t 6kzizenyhh rsw ,o hk*ylf upward using the bucket-pulley apparatus shown in Figry * ,uh;k3ohk3sn ehy-z/w/7t i6eez. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a raceygy d4kd1e +tfx) e+5z began, 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 block (mass4x has u,ui;s6 $ 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 arelge dtbtah2g 5rjl/3h fr so;;96/ x:w in contact with each other, :29rbo gl r/jx5ht dl3tg;;hf/ ew6a sas 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 initially 1.80 m above th+papvx m. rj( b7b)(m.umg5zf e 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 them bp..mr a5(mpjzugbx7v)(f+ moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tabx+zmk9w d1 fqs,b9s mzc 0u8-qle are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body dia+xucsq mm k9-wf9z z,s0dbq18 grams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a(b/jn c6/pbf7 ir /7n;uoipp p 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 ss 7yyi)8 uzrekl7j3.gtart 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 acceleratincj wx*i h4u 7dkxyfx4h594v-bg at 0.20g. What minimum coefficient of static friction must exist between your feet and the flo hx jd5-hcub7wx 4y9fk v4i*x4or if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffipy*u *fo 6h;6n wimsf m+,5rafcient of static friction between 6f6n,haw5m*p;+rfiu yosf* mthe tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemen-b4uidr t2m(a t is about 0.8. On how steep a hill (maximum angle) can you leaveb-4tmdiu(r a2 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 atj1:p.ytn al (z -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 obf/i(jlw mzi)hdkqd7 e7.4 8 on a 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 d -dprv9o 90 4lrwb-j,xe r(zfvery high coefficient of static friction9brd4f,(re9 roj-wdzxl-p0 v .

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

  The coefficient of kinetic friction k/-l.* 3fdfb 5cx tyikfor 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 wouloxhq-xvy 18eiun6 u;2)8 q(t;zkhougd box A have to have to preventu68o 2uh ix1 nhe)t ;x(;gqoq-k8v zyu any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that a+gh.s,ft g5wit slides across the floor. How far will it go, given tha wf5h.satgg, +t 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 kg9 j1wbcs8 4mqo and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54)1w 8b csm4jqo9. 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 cu0gml igv r-op76w:4 oarrying a heavy crate. The coefficient of static friction between the crate and the be:7wlo4ogp v0i6 -urmgd 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 truck?   

On an icy day, you worry about parking az*wltoj7(fl)w 3 8 l 0z(ebnsyour car in your driveway, which has an incline of 1otslj l 7afnw)l( zb83w0 (ez*2$^{\circ}$ . 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 slidgrx;y.27wtx-p5v g.)heq zche 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)hwum *smb zzo9u f.j8(.fl(q lies 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 speednpf c4klq 493*,a rdts of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest higfup j.8z/*cu 6q8a4k1(js1etn pwd hv7:ne ill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a fnjx 9sqai4pdy7.9ce,zw *bdx* 5 o ;sy5 xg:krough wall by someone pushing on it with a force directizsx bxc** o:d9fp9g de4w7 y,;55yjs qx.akn ed 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 di 98 )tj-qykm;,sdmhyangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a p9tyqkyj im hm,)8 -ds;itch 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 automobia,f +5 swyo3jxle traveling at speed v is equal 3+sj,wxof5ya 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 forwr/l z1jm40 ghc on7cc8ard on the dash when the driver delc4 / r0zgmjon1hc 87ccelerates 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 iniz7 pv cofop (w0mp).*btial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from wher zqjx9 lf6 dlh+k2h9p)e they are filled to the packing station 11.0 m away. The bel2hqdp+f xlh69 l9kz j)t is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction betwxdq;w.imugg8 zb.e 1( een $m_{1}$ 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 (inw,vvjb, vkr:su .j;6o-kp hx6 cluding 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 i1o zy6m1wn6i p z)qg6heart, at each pulse approximately 20 g of blood z g)onpy6 m6 qzii61w1is 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 automobisk9 -maw+ f3.jx*pfjs le crash if the deceleration is no more than *3pf-m s ja .fwk+xsj930 " 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 accelera1, bc 0*zlmu/zpi(nq k63fgp htion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must lf,6p3ckhz(q p bnu*1gi 0m/ zbe 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 a0 gy80a51 jwu6hcipqof an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction betquha cwgy1680 0i5apj ween rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hillt,);i.yl3 cif5p6 )vzaifmxn (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 lm6f;)z .pc i , 3y)nif5txaivreaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pit48hnj2lbi;) tr . eg k7dok+wvyz*i2sa and falls 55 m before reaching the ground with a speed of What was the at o+bh7v.w;nki 2t*zyjk r l) i4eg28dverage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a )*iz8u3 +teg qnky0lv muddy stretch where the effective coefficient of friction is 0.60. Will the c3u)yv q8+zgek0 tni *lyclist 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 hilly pty jne z(57e:v5(h; cuzj6zy tortion of a city. An important consideration is how steep the roads can be so that even low-powt5:e;ye7 jz jct 5n z6zuy((vhered 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 ey,k.z2uqr:pq8 3s m vcs- u- pk00k2p8 ktapewxperiments, dangles her watch from a thin piece of2z8.k0tk8 k2psp3 akqus:yv-w rp0pcu, e -mq string while the jetliner 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 several ramps connectch92ieksg.vb6,s7l ts/ o5tm ing different p,e 5ls sgitc7.kbmh26sv/to9arts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass Me5jf;m 0: evno ) using the pulley appara f;e0o5j:nvm etus 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 v2sn seltw9)p:mksl 4q5ot:/x )sz: v$\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer considers thw:h j 8xox mm7*3il7qbe following set of conditions: :h7o3lwbx8 7 m* xmqij
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 metrw+ 8f:9fgc5fd( c yukvic 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 rzx.+,t-sv yyz m5rjp 1opes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a 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 .x- + svyzyzmjp1r,t5'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 boa 9g a7b+ksg1 9d.thcw h3a(fjtt is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a mk aemby,3fve3 9u0( bjr 8gjy4aximum 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) jfji+)g0mxp are ascending an ice field inclined 0gpj)m+f) xjiat 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.