Why does a child in a wagon seem to fall backward when you give the wagonja(0u; 5cyai v a sharp pull forwara5j0y(; viacud?

A box rests on the (frictionless) bed of a truck. wany( egg ccij79l;92The 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 t 9(aicwn;g j2yl9 c7eghe 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 of an object is zero, are no forces acting on it? Explaiu- yiwb)r j,l/n.

Only one force acts on an object. Can the object have yp;a gr83dwx)1 : wrvtzero acceleration? Can it have zero v :t8vrp ygwwa1d;rx3) elocity? Explain.

When a golf ball is dropped to 3ojx4cv *v/6r;at w py5lki .dthe pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, a3v4 i xyk*c.twjp;/vlr56odwhat exerts the force?

If you walk along a loghumf, ni cga)d1ph*6 ( floating on a lake, why does the log move in the opposite dir*h(du fhn61 pm,a)igcection?

Why might your foot hurt if you kick a heavy dessy6nvv up36 ,woqjqf, )tq0; nk or a wall?

  When you are running and want to stop quickla4m w( nul7yd3y, you must decelerate quickly. (a) What is the origin of the force that causes ylu y7n34mwa (dou 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 thread from the ceiling, and a sectiourw gjsg)48: /5pecndn of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person givejw:)gpe4g 5/rcnsdu 8 s 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 an- z5rq+8,hm/*ff y)tqiw sgrc f65iks that on a 1-kg rock. Why then doesn’ttzyq fqicw+ 6rk5fsrf5mn-h i8)/*g, the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results ifls:gth/r 61 ydz( ao4b the scale had been calibra 6zrgsy41ltbda(ho: /ted (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionlesi 2 egv/uvj6ax*x1x ;bry- u/ss 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 box (a) remain the same, (b) ine x; jvxurs/1x2 /aug- *b6ivycrease, or (c) decrease? Explain.

When an object falls fr+cs wez09j0xm eely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the om+ec9j0 0zw xsbject exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) neeby54v;v3lvm rded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg4 ;lb3vv yr5vm 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 (Figw90x ex5okr0)9 lhi :cm.rhqo. 4–37) pulls with equal force on the other team. What,cri0qw59e) h x loh9:o.rmxk 0 then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groce.vw7;kxcg80ec s .xrl ries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direce.l8; cgwvc07 rxx. kstion, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the grra bz;tq:4iw(ound, how large a force does the ground exert on you? Why doesn’t this :(4iqt r wzab;force make you rise up into the air?

Whiplash sometimes results from an au8m)f .ca/q sf5fk c-fbtomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in qf ccf5 /.f- ka)8sfmbthis situation. Is it really?

A heavy crate rests on the bed of a flatbed truckq04bi:yxy-f j +t ba9j. When the truck accelerates, thbtqj:-yix f4 09bjy+a e 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 ramp 8z 9x 6 ezmxnn)jqt6n0.p3kvl. After the block reaches its highest point, it slides back dnxezlnq)93z v80txpjnm 6 k6.own 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 yoursg q/)frk5;;uj r5vl phelf on an inclined plane? Assume the pkh qgl5ru5;;)rf j/vmechanism functions properly, even at an angle.

  What force is needed to accelerate a childb0a9rw :o 1wrm )vaaq+ on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates j kbpe7a/(*h 4c.)c8e*msixmblj/jr a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand/-lnesc( p(jq l: +7xuku4 ky:u(ps ns if it is 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 o6(c+;izdmef6;,l rq tw ihc 3nf 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 8dnt)7.oxml.g9c85g-0btg-vvhbdsl l 3 zf m 1100-kg car in 8.0 s if the car is traveling at 95km/h? --hl.mgv d8g0lb 3gvml 58zoc).n f7t x9td bs-  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125o.vto3/ my3 v ffb5;7m mw/mstm/s over a distance of 0.800 m along the barrel of a ri3 mf tyom7ow5bv3mf.vts ;/m /fle?   

A fisherman yanks a fish verticallyg a(5x,te ri6x u.j9r/6qx7 dxbabv,f out of the water with an acceleration of 2. x56 eag7r. i6vdj qxf9x(xbatr/u,b,5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile tra w +1w9p;doyeu o20rpeck (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 thatseym+b:4ju-ww aj 4v: the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the s: +b4m4ejj avs:wuy w-upporting 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 motionlesjcg u01b2c,4bgqq1*k o2q okcs elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calc211b 4gq *q0c quk2cgbo jkco,ulate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevatog+s(bm4+; ad yyrw uedg mc0*/r has a maximum strength of 21,750 N. What maximum upward acceleration canwd0ageycr 4*;mu+/ +sb( yg md it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratiowpr+ 7/ wfw,tqn of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-ft/w7,rp f+qwwourth 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 grouhdk sro2f2s2obj)-8 fnxm10z d51mcp nd below, he bends his knees so that his torso decelerates ojfdz-xso)dopm1h220 2 nb51s r8cfk m ver an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs v:6,q7yl ii, hzwa*kmwertically 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 si qw,la6wm:,iihkz*7 yde of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball p x0va3bvxlh, 3layer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagra65xgif /q0e j4rie.9f 3n h:i rlqm,uom of a baseball (a) at the moment it is hit by the bat, and again (b) after if0:ilnieg/u5m6e 9fo4hr iq.3jq, xrt has left the bat and is flying toward the outfield.

A 650-N force acts in a nor4 :*o g-rd/m ly3irqoothwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with-o*gi3yqr4rm/l od o: a vector diagram.

  Arlene is to walk across a "high wire" strung horizontallywag c(tfle* r,o po)*: between two buildings 10.0 m apart. The sag e oft)wo *:(ga,c lrp*in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another 3.2a*z c3aa( utt:$-\mathrm{kg}$ 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 14.3myp4f h(2r)61r*4,utpkab dsyp q yji r/d.l0$-\mathrm{kg}$ 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 locatio8qxq ;5umbfb5 n at McMurdo Base, Antarctica, as shown in Fig. 4-46. Thm855bbfxu ; qqe 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 pulling two cars of the same mass behind it, Fig.ln/i ;2qn 8d)7s7snc.am l ,uqpqj ;pu 4-47 . Determine the rc; ) q8m, ldqsu;l p7pian/7nsjqnu.2atio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley327vrh gl q-wsb.sw 5m apparatus shown in Fig. 4-48. (a) How hard mw7s2.hwq-m5 vgrsl 3bust 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 racu piaw53k1:vnd 0 t3lfe began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a blockohfs, fh, 62udgg33 *8os8eyu 8k xxzm (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with;r g8h gktjt.9 each other, as shown in 8g.tt g;jhkr9Fig. 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/wfo3 ;wot9ckf7e: dg initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. c7 f3;f dtkwwoo eg/:9What 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frs,mp6(h i )ym/b1pvkcl. * +4ejnny udictionless table are connected by a heavy cord of mass 1.0 kg kp1y yms*bc,m n/)6+ih( n ujle.d4pv. 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 friction biou* (5 ivo,la q6.nshetween 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 requirju q 7y ,;qsh7xp4e6jmed 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 on a train accelerating at 0.20g. What minimum col air*a.u2ka dfz(-r7efficient of static friction must exist between your feet and the floor if yoi*z(r72aa ardul f.k -u are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffis)l r3k3 gjscx, ow*eo, my0w5cient of static friction between the tires and the ground is 0.80xssw 0y )3kj5,wc or,o le3gm*?   

  The coefficient of static fricti5 ;of.kr;awci 7ss+alon between hard rubber and normal street pavement is about 0.8. On how steep a hill (maxwi7kr;+a s a; .l5scofimum 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 vyp (a13oorz j-h /7pj -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 1 fl+ w/xu(u.b1k7nyumft , hyon a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high c :kn9 r9tufa:uoefficient of sta99k a:: furtnutic 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 frictioudhe+( az.ow ,8c4z ,g-pqukwn 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 (Exam,goha7p. j*exa2e s bu t13c7hple 4-20) how large a mass would box A have to have to prevent any motion from occurring? Ass7h c o,a x2g7uae*1j3stpe h.bume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. (tlc0*;x wgc:-nbbh4 4inynt How far will it go, given that the coefficient of4bttxn*-bilhnc;0( 4g:ncwy kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 1k u6*fmfbx 3:br ij1y010 kg , are in contact and at rest on a horizontal surface (Fig.0 ijmbk*fb:f1uyxr3 6 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 c+ i b:9tywkyqr7 kz4t2rate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slidb2tyi7:q 4wryk 9+kzte against the cab of the truck?   

On an icy day, you wa.04ux6vjh*ok7i;c b5 wts ce orry about parking your car in your driveway, which has an incline of 12c*sajw5 hukc exo0; v7.i bt64$^{\circ}$ . 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(-m ny;rtjvw, 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 plane tilted at an angle 0)/h( o(kp q7ha pb suw)qn5ev$\theta=22.0^{\circ}$ 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 initi4obp6rxs(1n q26 hr ryal 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 a speed 1* dqmfia6u6uof 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 placea2;agz4jfrgglrkw57 : 9)e0 bmase , i against a rough wall by someone pushing on it with a force directed upward at 28s je iwz:0a9g542kr7r,;l afgg)aemb $^{\circ}$ 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 roo uaaq/n+qao :,fs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitcha/, qqn auo+a: 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 automobir:cdn6z 8 z imkf6: *u*(whrgnle traveling at speed v :r*:rcu86dm zngn6*iz(wf h kis 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 dash when the dri2y;:( eqad ovzver deceler:ya;2(qdoe vzates 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 myf (gf5lh n6el01dv8a 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 from where they are filled to the pspr.q jy zun) +q/n8c8acking station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most8)/zy cqu p .8nnqsr+j rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of k.iss27l;p fktinetic 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 6*w fa sgq56hh45 kg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxirgs5- aer9y8d 5vq g1bmately 20 g of blood is accelerated f8r e-gyb vaqg5 9r51sdrom 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 c) ymz;ovo f8p-vh+scme 1u75an automobile crash if the deceleration 5 omp7 ;ovz)1vf mc-e y+8csuhis 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 earthquake is a , and (*w.mxw by )rhif an object is going to "hold its place" on the ground, show that the coefficient o.)*xwrybmw h( f 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 anp i1t:e9neq9m : ox:cs 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 pavementq:19o :tcpsximn9 : ee 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 met3kfcj1ly+h (e +m3 ntans that for each 4 m traveled along the road, the elev+e t n k3tfl13yc(hj+mation 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 Leb rk3q,qa.z/:yff*ht aning Tower of Pisa and falls 55 m before reaching the ground with a speed ak.q:*z 3h fy,/qtrfbof What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but ent ; 7tucxhwwwxv+hyd.-22hdq/qs. g,kers a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal.w2q.h;x c/td-hdx k,wy+ h2qgv7u ws if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of oo9;oydt 92i 0 elfl kcptq6-enpi 3/9a 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 1109 f/oq t0kptd9y i 6elnoilc3e 9-p2o;0 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 experipxiuvix9(v acdrw:lc- . l582ments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle o. i2v8- dl ca:9pw ixxcl5u(vrf 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 mhuf+/q0zv2kb vu;y 147 gxq pare to be several ramps connecting differentz4yqu;u2xbvg07hqkp/ v1 + fm 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 (mezao) b0 9,4 obsjuxe)x:se4bass M ) using the pulley apparatuej4e a9ox4bs u)x)0: ,bezosbs 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 acceleratinxmg* /har*9fn g at 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-:q8r iv,nr w pae vm7u)5mo3qi(c +d6frestraint chair, an engineer considers the following set of con8cdwm fm5 : i6qvo+(a3iu7vrr)n qpe ,ditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train huhl a,h-k)qp*4 cng:,,bucl mkkhj49as 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 Karencdks53 , u0 vc4eto)jk, use safety 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. (Expres)ke kc0tdo5,3uj4cv ss 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 usinndgf:m1, /3+i piujdag a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximuma2or6du m(* ceimzsi,3+sp 9 r 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 ic)/8ej vuq2u h7js;xmc: p7hc ue field inclined 7;s/qmj)h eu7u uhx :pj 8vcc2at 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.