Why does a child in a wagon seem;c1 xu6fs,r d+ + +e/z/,yovwwz lzvvt to fall backward when you give the wagon a sharp puld/z; w,z1/exrvofu w+,l + v6yvtscz+l forward?

A box rests on the (frictionless) bed of we,mo( /p oc47xrl(zra truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, il xroz,p(ro c7/w(me4n terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero,9n 5denudam+ * di3p79jsc7q nxw7.z n are no forces acting on it? Explain.

Only one force acts on an object. Can ib4 6jgr:c/i6 k mwc(pr5s2 5 xfhqg5vthe object have zero acceleration? Can it have zero ve (:ws6 5h5kxjgrvi cbqg 4mci5/p2r 6flocity? Explain.

When a golf ball is dropped to the paveme nior2l0d2ol e(3crn/nt, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what ex /(2 rdlenl32cno0ir oerts the force?

If you walk along a log floating on a lake, why does the log move in the opprtfw5; kr8 if,osite d ;ir,8frtfwk 5irection?

Why might your foot hurt if you kick a heavddga y t./h)-iy desk or a wall?

  When you are running and want to stop quickly, you mr08 ngzz4y 2fwust decelerate quickly. (a) What is the origin of the force that 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 rg ny4fz0w z82rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section od pf/ kpwqv62:x+ clt ez7;w2mf 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 brem/vwdk+p;f 7ecp2tq:zlwx26 ak: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg roc1.nh9qywgt v8, dc(;aku wa6dk. Wh ug( ty 8v;dnwkawh.1 ,6qd9acy then doesn’t the heavier rock fall faster?

Would a spring scale carried to thsic1uep*yxw+ez + h7 exg nwn5(n98+ye Moon give accurate results if the scale had been ch9sewn51e yy8 xp cuei+n+n*xw(g7 z+alibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attw u7y,r h78ahnxrkcf*x t,x/ *ached 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) incrxx7n k7trhxwcf r8h/*uya *,, ease, or (c) decrease? Explain.

When an object falls freely under the influence ,4,a1umry.egykv)4up**h xcu nn ff; 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 opu ,u)n 1a*fv 4hypf*.y ;xmku4g,ercnposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed ysx c:)s op8z qw-trld3n-g/eg m(-q0to lift a 10-kg object when you are on the Moon with tqx mwzr-t-8- e/s)d :3lnpqc (o0yggshe force needed 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 law, each hq a2fnd3d; ojkq677:izawarj5 :b:h team in a tug of war (Fig. 4–37) pulls with equal force on the other te3 a:nadoj daw i6zh2f5; 7jrq:hk7q:b am. What, then, determines which team will win?

A person exerts an upward force of 40 N to holdx)w 5o7 fac:3ewj:poq a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a 7owajc5:)w :qeoxf 3p) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the grounzxibsfs475c7 d exert on you? Why doesn’t this force make ysbf5z7si4 cx 7ou rise up into the air?

Whiplash sometimes results from an automobile accident when n(p/ wdft qq57)fkzi(the victim’s car is struck violently from the rear. Explain why the head of the victim seems z()k nqi/ 7w dfpftq5(to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accyfs3 0yw/qsbl;q+ q-we+z:rx elerates, the crate remains where it is on the truc3sw0q; e- xfy+z:ylwqbr+ / sqk, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftl/::akd d(h kver the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the a/ (:k :klhvdddescent than on the ascent. Why?

What would your bathroom scale read if you weighybl sbt9v *9r iod1g;yiv *u:2ed yourself on an inclined plane? Assume the mechanism2rb ;9byvito:9 i*svg1yd u*l functions properly, even at an angle.

  What force is needed to accelerate a child on olot)iih6 zfr -:o5 -sa sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rid jq: io(1ya 9)wo1ogxzer 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 accelkb3l+ 4k);nr3o:k frm g8w+enh3 mbbf erate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of p8g8;yz.qdnyw9 ay 8eru 9*f/t jorr3 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 sthc* bigeay53l /p*e: lop an 1100-kg car in 8.0 s if the car is traveling at 95km/pl/i*c 3 lg*5ae b:ehyh? -  

  What average force is nt thmz v+mzxlnq.2qcp:l+8d xa,k,08 eeded to accelerate a 7.00-gram pellet from rest to 125m/s ,hlm++ :xtqp08x8lnmkq,t dz vzc2 .a over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out 7/;+tda j g3b8 kr9rapqaki*w of the water with an acceleration of 2.5 ;t+ adbir/*a7k89q kprgwa j3 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track 9x (*ef+gzetv1-p qx z(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 4850b7w08a+h.yrrtap2 yd kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting car7+0 abypw .adt2rh8yble? 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 elmj6u xevnd- e5b,: e*nut.ed +evator. When the elevator begins to move, the sem, -d:exvn*e u5. j6btun+ed cale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maxirr ( 4ri*eev9 lg khuy-ioez.p:n981qmum strength of 21,750 N. What maximum upward acceleration can it giv 1nu8rlzeroiq ie.9g9k*h-:r 4vy(pee the elevator without breaking?    ( two decimal places)

  (a) What is the acceler6xj*y18sau6o l9jghds0l lp)ation of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fo u69jy s*agl hl s0ox)8j1l6pdurth 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 high. When he strze))vz a(r) qqhf0+hh ikes 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 tors))hvf0+h) zhqe qa( rzo (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the w*xx7 9g et.2d5oixqq 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 pullex9.x*ed7 q2 toixq5 gwy weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body di(rbzcl:sz+rz+5 2v vdagram 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 moment ityz:v 4xe;xk t4 is hit by the bat, and again (b) after it has left the bat and is flying t;t z4:k4 xyexvoward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must bep6x:q-owv+ic36 ith8bnk6 g*:wi fnr exerted in what direction so that the resultant of th3rox v6 iqi8 k*6b-6g nf::nwih+ctwpe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildinor*e4 2s sz 2pv*bf1bmgs 10.0 m apart. The sag in the rope whe1bze*smbr2s p*o4 2fvn 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 byh0x skpf-0o s2j/mle 4vd ,wl; 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. , o0zkg;/orhc :q.elc0$-\mathrm{kg}$ 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 lod/h q cox 0jg/(pc-fh7yzxu/ ;cation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forhxpq; xu ghy7/c( j 0ofz-//dcces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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-p25;p koc smd pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car cmps;pd 5o-k2$\left(F_{\mathrm{T} 1}\right)$ , 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 hersepug y 49d)fzak0i+9qi /yxx+ hlf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard muqy+ig9h x/p9+4a)yz dxufki0st 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 race began, a.6d:pc4k tmzkvzh:8 k 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 (macih0kc-.fjj r +h eh1hcs4x 5ge.3ub (ss $ 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 are1j- cn) ug-ph;d;yj ne in contact with each other, a1;dng)puyhn cje ;--js 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 the ground, alh4i/q 4ud8cuwx0( tw d:qcx9nd the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assum(lxuw0 8twqdd:qu4/ic 9hx 4c e it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cordcpt nv7qwvo g-j 6d2olhbw4. hf0k, o08cn j,1 of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. jwh4hjnkb-0,v.o7 60c cg1,of2 8ndpvltwo q4-53. 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 kine*po 0hbwa-3c 6g xfc;ftic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start q7qvg/:70yon: rjm ada 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0 wmsi+yo1p;ep-wm2ui+jt 96f .20g. What minimum coefficiefsy-jiw9p+ mtou6;pime 21 + wnt of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accelerd(2u of gfvl+)ation a car can undergo if the coefficient of static friction bf+2of glvdu )(etween the tires and the ground is 0.80?   

  The coefficient of static friction b(ivjfok;+6c vyw9j 2p2rxl9aetween hard rubber and normal street pavement is about 0.8. O f2px9r6j +avil 9wk co2jv;y(n how steep a hill (maximum 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 at -4.v6v2dh7njm,d0 0 bipyd4(zo p7s so m280 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rmwz2 d6k7aex;) dy hsd ,yg75nough 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 wy5yd5vn*v ,x)v. uahhave a very high coefficient of sv ) 5hywd,.yxn*5avv utatic 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 frictm 2+tpm/m7x e9yq85kb8lvoob-o 27j lmxv)idion 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 4u* vwj cpxdmqy);e1 .ac;xw) gcd;x0 .-20) how large a mass would box A have to have to prevent any motion from occurring? Assu );d0;p )j;gd.x c *wq mwuxc.x1yvecame $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesf: , ,sghvk/nibzf+xp+ 03d 3qbi,oge across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and pbq,3keg ,ihv:3+fix/bzgfd0+s o ,n 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 on9;a+b7yf tio1y bl+yq a horizontal surfacfqio 7aby;yy 9+ ltb+1e (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.n4.s r)( spg xsyn6h6 okbcg7ss+tpg+h0u t6 7 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 decelernos 6pp(6t77h6s0 r +bg )g.y+kssgxhc4nstuate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry aboe4 0:dkoix* zqa7g+*y yadr9out parking your car in your driveway, which has an incline o0e 7zq r4gyad+:dxo* *i9yk aof 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 sl:)lnwsia)z 7r ide 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 planvv7xph v.o1mi5m)c 9+vw pkl )e 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.xtq6w +tpc,n42 xuha28u-nuw0 $\mathrm{~m} / \mathrm{s}$ 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 speed-e(mlgey uy(, of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someo;a.upjgv:/vod c8 qn*ne pushing on it with a force directed upwuocg*8 a.;v nvp q:/jdard at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as:fz87r0w.wjcx) jy xj they melt. Consider a chuxj.wf 0jjy:rx8 z7cw)nk 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 yux9 k3q, a5 -7f0bjjlit cs+yautomobile traveling at speed v is equal to+ac- qky,tlyfub05x 9j3 is7j $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 tlnv-4 smeh vt,z)d9ih)d n /e1he dash when the driver decelerates from ei,le h d )4-dsnt9h/z)1nvm v 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 7d- z cyfs67gjm is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt fro/krpf/z; dl7hm where they are filled to the packing station 11.0 m away. Th k/f ph7l;zrd/e 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 coefficienrjvn6w4 seujf,.m3p nwnu 761t 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 9tqzdg gf1mkmt2+l.x6rx z1-) 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 simplifi;2r8e s hscmk5eh,bv7e1 r/vled model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.2e/sh52erkh e ;bc,rs78 lvvm15 $\mathrm{~m} / \mathrm{s}$ 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 reasonab;6v-u 6pz xxhale chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on h ;x6p- vz6xuaa 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an :ba46v q.f tv/3rq vlhearthquake is a , and if an object is going to "hold l6vva.43q/: vbfr thq its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involvingz8 1r( xl/ykiq two cars, measure 72-m-long skid marks of one of the cars, whichz/ y8(kxq lir1 nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-aie k /m zw9,)1k6efos4 means that for each 4 m traveled along the road, the elevatiw s9/kaf 1)i kzeem6,oon 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 and falls 55 ino32k5zbdg,92akn(,t cikb n5zi g2n 3a tbbd9ikk,(o kc,2m before reaching the 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 mudg geptq(wh: ky+m7z,kp( ,z od* jxe55dy stretch 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,7hogt5,:,wp d(m y zz(*ek+kgj eq5px what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly po5gw) dry+/c yfrtion of a city. An important consideration is how steep tc/fy+ y)r5gd whe roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics exm72* vekdm 9lbpp:;/gc8 hpiuperiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport8mv9me;7u ic2 pdk* :ppl h/bg (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 ram5 m1vi- mh0k0xiyxjx y:c1h ,a4j+y swps connecting different parts of1vx1-:jhaxi y,05ims ch0y+xy4k j mw 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 (masss57*zz:vz bfwqmd t1c*o sj83 M ) using the pulley apparatus shown in 5s1mc8bq *ztw z3:*doj sv7fz

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 at4,k:kx1xpq* tq ., sxpvl rcb8 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-restrrmwm;uqq(gv/mar85 :aint chair, an engineer considers the follar /gumvwm:8(rq ; qm5owing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian traio/ ye8h*h jz4tn 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 ropes of simil. kr3 +gtem(m2he. yjiar 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 thame ihjr e(.k+3ym2tg. t the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10fef5orjr , 34wf/jpe .cua.h9-1 $\mathrm{~b}$ 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 reac8v6rpa.ho8 anh a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers wh+xk dt izh7rt+2,;op;ada*x polx5n ; o are roped together are ascending an ice field inclinel;h25rktx+;dixpaod +n* zo;t pxa7, d 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.