Why does a child in a wagon seem to fall backward when you giv:bm0 4l0d3akoy2k: xob suct 6(rax o0ua5)fle the wagon a sharp pull for mft(2)aa:0uo br 50bksa l6y4k: 03xx duoolcward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the tr;lx6nbp,y.bo 5aw q6suck 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 senya;lw b 5,x.o 66qspben (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 objectcl9j x1pohw0ky6 x(p3 is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Cc+o1 8xvw7p 4ffl s:muan it have zero velfmxlp74fuv c o+w:1 8socity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forcei re a2l lf(1iv2a,vp3 needed to makef( ,li2r ap1ia 2vvel3 it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does a9ei/i3hwsnj3ns:p ;b f g pl 28,w*smthe log move in the opposite di:isiw* s383b jw penfmhs9n/p g;2 ,larection?

Why might your foot hurt:gio08h 9llk)d f1j 4rfhmmhi2v+ d m2 if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you mu zbocetr 4 4k b;nnk6lnuo5-.,st decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimator; nknl-z 46ckue.5, 4 bnobte (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a 0m/ol ggjs3pfz -4m f5section of the same thread dangles from the bottom of the stone (Figg54j-fpm3/f sl0 g zom. 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 rock is twice as great as that onl 2 31c(ol6soch;if dgw; kme3 a 1-kg rock. Why then doesn’t the heavier rock fall fasteofwcc3;2k leo1sgh;l6 3m d(ir?

Would a spring scale carried to th*j g+3ml3r efabhs0*qe Moon give accurate results if the scale had been calibrateg3s3 qf* laj*+bhm0 red (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrosk6ccl+n f2 +y)adndh2 s 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 the acceleration of the d6lhna2fn +c+ )dk2yc box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely uu4y4(5yg mskw nder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by N4wgm4suy(5k y ewton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needa i6ylbz bhd8d5 qh(c)*or94xed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force nea)b4 h*dxq 5h6l8 (9cioydrzbeded to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (F1mbgfs dw,a+p4g vna ds9x8;/ ig. 4–37) pulls with equal force on the om;sf+vbaadn1wdpxsg, / 489g ther team. What, then, determines which team will win?

A person exerts an upward fk( aj-bxvhdc- 6 -*x:rwn(s1 7kq.ldk6hwvyq orce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude,-h(aqwx.(kk-ks rq6j v bx7*lwdv:6 y cdh-n1 (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still 6 tm w64wagvogg-r7j )if;5yton the ground, how large a force does the ground exert on you? Why doesn’)if m4g56 ; w6 yv-ottrwga7gjt this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victs)0kp y 19d2d i-(hvmidnat+qim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in thdd+dn hip1 02tvq)ya9 mk(si -is situation. Is it really?

A heavy crate rests on the bed of a flatbed truck ujwrd,c3 6hdk 0-sf3lq30: 8u bgrfyk. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force r h3uu:k3swl d-y,8 6c jbfk0d3f0qgrcauses the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesld3 qj- 0mv+8) rbh.to/yvifo its highest point, it slides back down but the magnitml i.bjqvfy83r)-t/ o+do0v h ude of its acceleration is less on the descent than on the ascent. Why?

What would your bathrz 2z (sqj4zh1 ficzi18oom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions prop1q4 fh1z 2j( isz8zizcerly, even at an angle.

  What force is needed to accelerate a child onv:hg el;)4xrh8dpqf qj4 xa55 a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 8rn e,sqz.i7lnd312gt; d,cxy qv j ;q2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it i2-( 7q xnqjken2 nr5mwrtm95 buz7a3qs 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 off,y4m6hz,rver,* 5 a b qpjoa7 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 chh8f oe: +(ksnr.8qgstop an 1100-kg car in 8.0 s if the car is traveling at 95(8.8rh esoh: n qcg+fkkm/h? -  

  What average force is needed to acceleratezo:l+ 05 qci80mbavks a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the b+0bmlzo: vqs8cia5 k0 arrel of a rifle?   

A fisherman yanks a fish vertically out of the wa*tm siypx .gf-.0zy 5oter with an acceleration of 2.5o*5mftx-ziyy.p g .s0 $\mathrm{~m} / \mathrm{s}^{2}$ 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,nrw a*)jw l ;gd (oozp6ar5.y-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 designehnh5ol8gd z ,6d so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces th 5 6h8n,odzlhge motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When ta0ub*w /u 5ld v2*bu1oreq r9qhe elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevat*/e1uqq*u r29a d lubwv50b oror, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wh yurt 0q-pbsx:u *t.6uat maximum upward accelerupb.0: ytq-*x u6urtsation can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers ( 9a+1o 1lamifwtuap)z qjhxgl2 -0g*,*m9zermass 132 kg including parachute) when the upward force of air resistance is equal m911*m 0pgi2azoexqt 9hz,j)l l*+ rw-a gaf uto 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 high. When he strikes the ground,yp w+r;d)(w/keyx ki8 hu3 pk below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding lrpyk/u8 +wx dw kp)i(,;yhke3egs) 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 box runs vertp, 2( prh- 6bcavbehw)r(/ zmeically 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 s,pp ew -2b rhh6va mb/(c)(zreide of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playemmz 1(z6l czqssxi8: 7r
(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 basebadffyx .ul6j:n y(12zc ll (a) at the moment it is hit by the bat, ny.z c:lx j6ff uy(21dand again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. o i,: 2/vsndz ubw dblq7.f)5tA second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vec:vdindbz /2 qou.7wsl5t ,b) ftor diagram.

  Arlene is to walk across au1-6va7 b w(zrc bi;l)tkh7sp4jnv)- e;gmoq "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rozecb (wav7smgb6q-4n;; vj-u 17 )i)krltoh ppe 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 another zwqx0 i7e)-qjdx29fr 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 14.08( e1ksfu...reifmc4 j,fjhwfquz7 -$-\mathrm{kg}$ 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 vyq( 7ts;ib/ v,zow;c, Antarctica, as shown in Fig. 4-46. The sum of the forces /(,y; cz wvst;7oivqb $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 s7fc27wtq ola7 txpp09ame mass behind it, Fig. 4-47 . Determine the ratio of the tens7aftt0qx c7p7p 9w2l oion 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 us8v4b rsym)hv5 7cy (x2u giof2ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at c x mvvh rg52ify7b4)oc82(ysuonstant 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 behclhc6y3zlw: u 86mgb (s8a:es7 a(nmgan, 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 ( bpt6m6y 18wmn3 .zzkdmass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contf0igpy9 ,v;q6faa4l tact with each other, as shown in Fig. 4-04l;g yftaa69,q pfiv51. 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 Fin - cw2owv/-3cy/o0 h7d .ubwo+wk bscg. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch7w0dowc2w3nob - h bso/.v+ /yc-ukcw" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cbuaew q03 9-rdord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body ud30 -aer9 qwbdiagrams 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 p5w9s3ogvp+k kh )5 vifriction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.67o 4du u3femt0$-\mathrm{kg}$ 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 stan01d .xad8; 2jf+ eupmhyu0uueding on a train accelerating at 0.20g. What minimum coefficient of static friction must eu2 ufe ;+xh.0u01ydajep 8dum xist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient aaq8f8mn8xq;+ hw5zfof static friction between the tires and the ground is 0.;zfaa 5 qfx8+hm88w qn80?   

  The coefficient of static frictiojmoi dmf+ c oiq7,d(4 -qbkyi5+: x7 78fkpiaxn between hard rubber and normal street pavement is abooxa 7:7d+,( +j mciyb kq4dix fiq8-kimpof75ut 0.8. On 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 decelerater9e twy*2y4ue9 ;fbcivewu56 at -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 onf2 f+cxzdsshm:d8q7u 1 9; vox 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 contacix5)uam a-zltfuh2*6 t with an asphalt surface have a very high coefficient of static ff*h imu6u z)a t-x2la5riction.

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 kinetimn5em+0h/8aej 8di;n)hzt;1 n zxy o lc 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. 4-3g3:-u:;l w ncnl3kcbq 2 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurrbu3n cql gkn-;w lc::3ing? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acros mzbqv4xv xe0k8)a97g s the floor. How far will it go, given that the coefficient of k 8)v 7xavbm 49k0egxqzinetic 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 (8mo6b fj6jyf,2j-zf8xan; t h5nbyz kg , are in contact and at rest on a horizontahf2a6xz (yzj-tmf8jnjy bb;86o5 ,nf l surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static :g cf05+e mtxpy0:uj pfriction between the crate and the bed of the truck is 0.75. What is the maximum ratetumpcypx 0gf:je :0+5 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 driveway, .0spb v0ogt q 0qe1(/o4koo kdwhich has an incline of s0o k04vpbood /0g(1o.tq qke 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 n+ro,k5g t+sy+wys0u) i pfmu0 mue/ 8a 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 rq1)s5wnozg1te3ybqi:,f 3e 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 initialj1 c fo-52ctz 7pp/p3m kwkmu4 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 top of the steepest hill with a3qdmripgr/ep l;8 5hll0 2w5a 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 ag5 orfgftsu6.3fe4og /ainst a rough wall by someone pushing on it with a force directed upward at 285sog6 t3e.4rffgu/of$^{\circ}$ 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 r: 05zzouv bl1gtfd) :doofs can become dangerous projectiles as they melt. Cu5:f1tdd zozlg0 )b: vonsider a chunk 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 stoppij534olfupb,.5 o hfo hng distance for an automobile traveling at speed v io o fou3j4 hpl5f5.,bhs equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the d,lyesino:: )s95q xo yash when the driver deceleratey9xq),sy l5 e:oni:s os 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 gv0/1tai3q(nn r s91b zt kv3lkiven 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 belff3ezjf i 36usx6tt )+t from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficientfet36i)x 3+sf u6tfzj 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 betwee gkaa e e3/bnlc. 0f/ekxj.)(tdap)j.n $m_{1}$ 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) 8d8l p/e9do2g9ai +xvacun;l t 0de4*.qeqwdcan 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 simplifivpf3if*ngvrb:g41+ j ed model of a mammalian heart, at each pulse approximately 20 g of blood jpiv+*b:gn 4f1 r3g fvis accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if thl*e,bt2 3y0 qr xjv-tue deceleratt 2v 3eyrjxu-* lt0,bqion is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquaken a:9 :+zoj.nsukgfx;,9oqf2 myo(m m is a , and if an object is going to "hold its place" on the ground j:ano;,.9f2ng+ omy9mm :sq kfo(u zx, 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, emf8i. u u.n,ycxqb x6.xamining the 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 kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that c xnb.86muqcuix,y ..far assuming a level road.   

  A car starts rolling dotq1 ,mqxc e6(mwn a 1-in-4 hill (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 reaches the boxeqct(1m6q,m ttom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dr7z0y(o q2rc fj dwkk4.c xu./popped from the top of the Leaning Tower of Pisa and falls 55 m before reaching th zr 0xpw.y 7odfj(cq 4.2kkc/ue 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 stretckm8 :w1t pv2s8;fv c 3lniow:oh where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedalcvn8:k fv3l;powmti1: w2s o8 if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign oxjg8 + 7nym(2ta b7tmznp y6hoy:) ri1f a hilly portion of a city. An important conspi8ga 6xmo)(n17yyn:myt2 rtbz jh+7ideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes phys)unhw1:b6 r:.m s c:du uyb;ojics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport ( sm1 d;)6.ubuj:c yun:o:w brhFig. 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 con.o l brbr tlodl/5708rnecting different parts of the storeltlod0.8lob r/b 5r7 r.
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 the pp vz) i--afk0ffy;6uvullefi60vuf a-pz)v; f-k yy apparatus 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 h f9;6rxh3kgn:.ne jw 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-restrain 7mcnvt 98znejmcb.f +;mo;4lt chair, an engineer considers the following mjt84cofnmc +e 7l nb;z.m v9;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 Il/*x u 5sr0;ni sk6scytalian train 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 sa79s 24 z,d tlppyzra2yfety ropes 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 fzyp2dzs97t,ya lp 4r2 all, 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 " 10-1 kpjx;3)le shvm;p;)nq l4w+g$\mathrm{~b}$ 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 maxe)h.vnbt8kcu * tt ne;y6 ;k3hb4lbv+ imum 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 are ascending an ice fieldu0*u x e5vydra;a3p90 u f*qnv-uoc9z(ubu )e incline0;u (9y quu u* u5ar3nve)x oczpe09bdf-uv*ad 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.