Why does a child in a wagon seem to fall backward when you givez (g/j h yubl,g,.j-fx5 ljwt30bio-t the wagon a sharp pull forwar bzoy3f( 0 h.,ujgjilgtxbt , /l-wj-5d?

A box rests on the (mfpa,mwh7mg 7+ 9gjmk7 2d1h gfrictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. 2 k m1ag7mmghpm gf+,79dh7wjDiscuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration ylv z+ g-fcw90of an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerao61r5xnscb mkn0w;4ztion? Can it have zero velocity? Expla cz4nmrs;k6w 15nx b0oin.

When a golf ball is dropped to the paf2y3af, c sm3evement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If se s3f2 ,c3afymo, what exerts the force?

If you walk along a log floating on a lake, why does the lotpz+,(rv/y uj:lzzu:g move in the opposit(zu,yl/rp : +vzju:zte direction?

Why might your foot hurt isbslnhz/ 5/ k.s o6ry.f you kick a heavy desk or a wall?

  When you are running an6sc qxr c63tqtc2o5f, d want to stop quickly, you must decelerate quickly. (a) What is the origin of the force thatq6xofq5tc crst6,3 2c causes you to stop? (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 t e/ i0uel:pob0hread from the ceiling, and a section of the same thread dangles frob/ ie0ulep0o: m 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 slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock0p frp-;;p)wtes tt,k is twice as great as that on a 1-kg rock. Why then doesn’t the hs);t ,ppr0et; -wk ptfeavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scl;dg17dt qdddco81 u.ub6e 9bale had been calibrated (a) in pounds, or (b) idb;1 9ebc1l6d dut ogu7qd8.d n kilograms?

You pull a box with a constant force across a 7d uwlxe 3*) c4:;zf:cnrtmvr0v,bq0s/e dkn frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (witlw mn:7d be ;v * ,3cdk0) x:ruvrtcnqf04sez/h 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 4n nzyunkdh;6-/9 sds influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite for9z /;4kdsh yn-6dnsunce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needr 1j 1oxzog-m68t/wyt(2qjn7 0q w 6zkguc g)ped to lift a 10-kg object when you are on the Moon with the force neo / 1k2g1m6jp zgzuj7w-r x6tcg)(tnw0qy8oqeded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third(u qm i7py-jw. law, each team in a tug of war (Fig. 4–37) pulls with equal force on the ojuq7.my- wi(pther team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bnp7)w2yv)9ibx bc ,jifv ebo ;,.lb h1ag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object hp2i,7c. v)bfe ;1 bjyixb )bolv9,wnit is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on yi c 1:oaappy1 )i817apgpafu/r* dxy4ou? Why doesaco18y)rg xp ifd *u ppa4pa1:/1 y7ian’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s ckf)* wiyfj jyub9w 7v2 h2v38lar is struck violently from the rear. Explain why the head of th8v2)w l fy29uh37ijvf*bjk y we victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck ac(r4 kswqt3z8 fcelerates, the zq 8(3trs4kfw crate remains where it is on 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 rat,j/ 0 obew8hj0n y k*.lopoi;mp. After the block reaches its highest point, il.0jotp ,yh*08owi/ejn ko ;bt slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclin,and2,vpz uco j-+.vd ed plane? Assume the mechanism functions properly, evenz2 ,a. oj+dvpndc,vu- at an angle.

  What force is needed to accele7l:sq2ug v2 jerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30):ynpyk5 p9liye pi88$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it isdw (x84ijj ja/tvure 2,* 5bgh 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 obm3us( 4h.1d:w 9 cxquclc-i 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 car in 8.0 s if the car is4), iq,qxornlpg x0, p traveling at 9,pgq)0xl,i,r4 oxqnp 5km/h? -  

  What average force is neededvyvu.:1 ixk2 uuu5)0hyo;crj to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 05o:u1.y )0 h;jk2 criyu xvuvu.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration otv ;o)ii.g6azt ulz a(,: uu7lf 2.5)a6u z z7v.;iauu :olg,( tlit $\mathrm{~m} / \mathrm{s}^{2}$ 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 covern1:d xv+eo-rh*lo* tr 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 acceleratiol29v)vxduj ajvj+yj jetk b,4..s+ x6 n is 0.0680 g . What are the maximum and minimum forces the mo jvj,x ye+46ltja)9b.+v x.s uk2jvj dtor 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 motionle:w -e0kj 6mjucss elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, andeckw u-m6 j0j: find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whanhqgpjq0 98kcs ;5d m2t maximum u8gh0s qq9pj 2mn; dck5pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (9a9g(p -l7 qtp o-qufgmass 132 kg including parachute) when the upward force of7 g(-upoap lf 9qgqt9- 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 house 3.9-m highvvj*d: a5xq g6. 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 tova :*dq5 v6xgjrso (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 a,fs6eo:c0 9o3p7ks,nvfaj arests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box,os,fv 69njeo0cf sa3:a k7pa 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 ba5ub ycp3+ b-slsketball 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 basebefiqd.e/ 39c;szl 0mlall (a) at the moment it is hit by the bat, and again (b) after it has left the i9me ql/3.d0z ;fceslbat and is flying toward the outfield.

A 650-N force acts in a northworr q/ +t.0lqtmc1me9gkdr11esterly direction. A second 650-N force must be exerted in what dirmr 1l q1t k.r91/ eo+qgcrt0mdection so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung ho8 x,ckur ph+(trizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoin,h8 xp( tkr+cut 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 mb*-l/155rv c obnvczjassless 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 14.0/fdsq(pnq :k mb8lr*zp e:5s:$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica -7j)/ttmrjlgk.ke:h , as shown in Fig. 4-46. Thekj: gm)htr t-7/ljk.e sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pull)hw e7w1g6 7df) aigwsu,hc:ning two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of t uge1sw,i6h adgc f)7:hwn7)whe tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus spm8*w0nagzf 8;a qc v1hown in Fig. 4-48. (a) How hard must c8 1 0zqg8pna;mafv*wshe pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race beg1v; la fwx 2f*t0x9dtp2z(druan, 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 (mass 0o79r :zl tugky9npm*$ 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 i4pe3ocd 7(b0 ;xjh(x 2sc mxrhn contact with each other, as shown in Fig. 4-51. A forcch(mceox3x ;rd7bh2 x s(j0 4pe $\overrightarrow{\mathbf{F}}$ 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 the ground, adljlxtf0dvo fj-;e- 1 28rgkwt;j y.e::yqh(nd the massless frictionless pulley is 4.8 m above the ground. What maximum ekw (jvx 0hl:fg2-r ey; -j:d.q o1ltt8djfy;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 hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy 3czm;f(tfm)y cord of mass 1ft);y c(m 3mfz.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frictiukc0cb*7 )t.g (m otpnon 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 requir e1pji4fid1x 2ed to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on10,pu/wde(i 2 zkg tks:b-mlv a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you arei zdk-/1t,s ew 0:vum l2(kpbg not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient oeiqg7x9qpiye t3)(o. j -g7ztf static friction between the tires and the ground isit qg77pe. qg-(jez3 9)yixot 0.80?   

  The coefficient of static friction between hard rubber and norwyps0d ien8m bd ;5v4fm5k9f/ mal street pavement is about 0.8. On how steep a hill (maximum5 d v8 ikmm50b9/y;ps4 enwffd angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate atv v3gy msp ez7/;,bun7 -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 onx9,gzhrh6 im4 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 3a91z gi0k-opc tqwz2an asphalt surface have a very high coefficient of static fr0z q3pci2g atzwk1o-9iction.

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 kine3v62n-5w yv lghe)1ulvm9q h otic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (E1gxbvlbd,rsxm*rbw 1 /p*+2dxample 4-20) how large a mass would box A have to have to v1 b*lrx s xbb+2p1 r/m,*ddwgprevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrosssv06fshl37 xt the floor. How far will it go, given that the coefficient of ki7hft 036x lvssnetic 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 on a horizontgbh;e2i 8j8vobd 6 4ykal surfacejo826 ;kbyhig4vbd8 e (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 coefficientp5 p-f- nti y zz6l8luf2p:d*d+em kb2 of static friction between the crate *p-illmktb: u2z2ff8yd np 5 -z+ep6dand 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 truck?   

On an icy day, you worry about parking your car in your dr g.u(ag4vaakxw9-g) tiveway, which has an incline ofga9-xk t .4ava)( uwgg 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 afgg t8 a/gr mx,/59vcl slide 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 6 n (uzzk:sz 7vr1jaxo58ivc9 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 inio)ber4 9fp-ld tial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the to s0fm3hog+) b9 q4lyx4g9xs3i2n :8f bwetburp of 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 play 4n3 xicf9*pice against a rough wall by someone pushing on it with a for i9p43cixyfn*ce 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 projectile: 21 dxv+jskdmpko(2 zs as they melt. Consider a chkszpdv + k:j221odm(x unk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling wd+8,lt;1x gzlyfl-c (2s nihat speed v is e h , dx ycwslt-lnl+12f;igz(8qual to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drive or o lhvhl93 d/7we.:2mpnnl6r decelerates from m.elrw3oh7 h2no:n dv/p 9l l645 $\mathrm{~km} / \mathrm{h}$ 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 initial spscwo4d,6pfmf x8o2 p :eed $ 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 .pc1f udumy;/from where they are filled to the packing station 11.0 m cf./ dym;1 uupaway. 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 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 coefficientiu 3wtts i7ytl45pc 739(logb of kinetic 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 bicycle) can coast downjhp0 zdy y qf,qf6,crw.+ v-g8 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 mammalzgt :q: )yubpmbk4 uw;h yq410ian heart, at each pulse approximately 20 g of blood is accelerated fr140 :yw qkyguq zhbu4tpm);b: om 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 autdsu 0)8do qx39:cslzfqk3 g 1domobile crash if the deceleration is no more than 30 " g 's." Calculate 9kc :3xold)qgq 3ds0s fz8d u1the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration producey21j m gx56wted by an earthquake is a , and if an object is going to "hold its place" on the ground jgmex1w65ty2 , show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining fvwr,y9-5cb2.6qf(0lal *w khw vawcthe scene of 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 kineticwl,. yhvrk52c0caf vw*a-( q69 fl wwb friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for +ym;q 8xz n l4qfscr3/.w6gqteach 4 m traveled along t3+q84 cf;nmq.qzt lry6/s wxghe road, the elevation change is 1 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 dropped from the top of the Leaning Tower of Pisa ah ;jfc9vmym79nd falls 55 m before reaching the79;m yhjc9mv f 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 enters a muddy stree sptk5922t dntch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will 2d5snt2p k9 etbe the speed upon emerging?   

  A city planner is working on the redesign qr, bl*9x*e1 q;cmfv jof a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can acceb;cf jql*q ,*vme x1r9lerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piecef-to:t 0gv)0akvn2uhm1 g np(dw) o p- of string while t pu10tv nkhw ))0mo:apt nd(g-2- ogvfhe 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 connecting differe r0zz+b(tce6v5fi2d fvdif ec t+( f2rbzz650nt parts 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 M ) using theh,sk2d.kx rs( pulley a(s2skh,kdxr. pparatus 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 )0cr62 d nzzk,w c( efpyo0or)j1y6roz4kiw(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, a8u1(foz s2tt ,.t mmzk:0tlyp n engineer considers the following set of conditiontm(.my stt p zu:k,l1zot 8f02s:
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 trai,g- g6 m6egfa:rtbg8 q 6xg9pin has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety rope7 2d)pj xrh7gts 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 th)x7gjrdp2th7 e force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using804iupw eqw *x 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 tallfcyr2x 5.rmc8m /vd /c building is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbn0zch4 q ur9g+z8(tym ers who are roped together are ascending an ice field inclined a+n (tcurz g94hqz80ymt 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.