Why does a child in a wagon seem to fall backward when you g)a 9sdb1r8x *v4jxsmuive the wagon a sharp v) xdjur1 9am*4 xsbs8pull forward?

A box rests on the (frictionless) bed of0a kiuqudk( i ez4o7+wp;+nh0 a 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, 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 04zhdi(ow p 7+naq +keu0u; ik

If the acceleration of anzf n3czc:n8w.: jkz 7v object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the obad fr cs: u8zh,0,lgnr3ut*-veard1: ject have zero acceleration? Can it have zero vel,l8v thf3sdrec:1g a,z uand0:-* urrocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) I 5kk,sax-0m,o xfp3) jt*ifpws a force needed to make it bounce back 5s 0wx, oax-*,) pfmit3 kfkjpup? (b) If so, what exerts the force?

If you walk along a log floating on a lake,mbq2jv , y4hn9 z/9) jfnpbs;s why does the log move in the opposite direction9b 9nj ;s4nhs)j qmv2,bz /pyf?

Why might your foot hurtpl5le*+;c e jg if you kick a heavy desk or a wall?

  When you are running and: r yuo ssky1f/j+h56z want to stop quickly, you must 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 speezsry y5hj :/6+fk1s uod to come to rest.    m/s$^2$

A stone hangs by a fine thread fa,ei3rsz 3z2 ,bn -tpwrom the ceiling, and a section of 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 break: below the stone or above it? Wha bit2r-znw3, sz ,3aept if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kgnub -w1q* w-yc rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rob1ny -cuq *w-wck fall faster?

Would a spring scale carried qkjb6 ui1 9i qt)5yl/jto the Moon give accurate results if the scale had been calibrated (a1ku t6jbqiljqy)i5 / 9) in pounds, or (b) in kilograms?

You pull a box with a ca 5rufxk g6/g,onstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the hor/u kxgf,ag 65rizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely und7iwxrbsj:(/ m er the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on tm(r7x/b:sj iw he Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lijvrxhl /:(+mhi,nsiq83c l7i*r ct,cft a 10-kg object when you are on the Moon with the force needed 8s:lijicm+*c r3 hlv t n,rhxqc7,/ (ito 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 team in a tug of war (Fig. 4–37) p tcih *a6t3/byulls with equal force on the other team. What, then/hy at*ctib6 3, determines which team will win?

A person exerts an upward force of 40 N to holc:f./*rmx n-en)wr ul 8zgc) kd a bag of groceries. Describe the “reaction” force (New k rzng/n-*c: 8cx.lm)rfe wu)ton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on-fv dk rwmg y2m -52w;wgd1dr1/3 icrz the ground, how large a force does the ground exert on you? Why doesn’t th5zr-1 wfmi2d gr3vg kw; c21/ryw-d mdis force make you rise up into the air?

Whiplash sometimes results from an automobicgk0 vbg d mqn3pr1iv8 d*;hx/p3sak29hf9. ole accident when the victim’s car is struck violently from the rear. v sn 8g ;9.d9digvcphakm0f r2 * b3qhkx13op/Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, l1)zlz1c f/ff79w6 z ,ctwvevbpr31f t3bprvt/wf 1vwell)f, cz 9 61 c17zffzhe 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 thas;pz6 p:k5tpahj 8h1s t it slides up a ramp. After the block reaches its highest point, it slides backzhpt;1j5 skhs :6pa8p down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined 2r;n69.kseb;rsljrh5a :5xe lb 5,ozckf/x yplane? Assume the mecj ezl,r fx5sc55k/hn e sao6ybx:r9 2l;b;k.rhanism functions properly, even at an angle.

  What force is needed to accelerate a ch 1dv4 cysn0-fqild on a sled at 1.25m/s$^2$?   

  A net force of 265 N /hpg jjhrpnzeu/ 02cnm6ta)2z8g 2 ;b accelerates 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 ro s ,6hde:r 73jdgowgw6s6c0u lpe withstand 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 of jad0u fbkc 8-x+zhvac 6f -npv*5o1b;a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car k2jw-eyt7 q z)in 8.0 s if the car is traveliq-yj2)7wkez t ng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gramacyc 8e6 3eak; pellet from rest to 125m/s over a disa8ae3ekcy c;6tance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out:4;3a+ sa9+fbijdp ns qf g7tf of the water with an acceleration of 2.5q3d+ ifb7j:sp +nfs94ag ft a; $\mathrm{~m} / \mathrm{s}^{2}$ 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 quaivb 2zy2l f)f(rter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the mk3dm.zbop;e )j.u1b*kg9 l qkaximum acceleration is 0.0680 g . What are the maxijukodp9q .mgk* 1b3e )lb.;zk mum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. Whe3azlxzh1d; z7: x x3z4xqfvl0 sso:2t rp f5p5n the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the difppzhr zx 5:alol t1f3d :2;54qvxzxs30s 7zxrection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a mgtuxse //;zj5:scsnd*y)3ut3seu o8aximum strength of 21,750 N. What maximum upward acceleration can it give the ej/nesu3cu8tg :sx *3 t5dzy);o/s s uelevator without breaking?    ( two decimal places)

  (a) What is the acceleration of tqznq.g3( ar qk,iv; 0v s7s:x8/tsfw awo falling sky divers (mass 132 kg including parachute) when the upwarkr; g ws/ssnv37tq:q .8aq0xi,(vza fd force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof s- rr44yhd -e-ih m:p3vrhf6mof a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.7 hpd4rrfrv h -4-63s -hiy:emm0 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 rek -rlew-fg15 ists on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley we- 5wgrf lk-i1eighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball n8l,l*m2i7p) vj(s mnkq tf* oplayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagrazh ) pv1hkvuhq93*o f(pcen3/m of a baseball (a) at the moment it is hit by the bat, andho pfve9/h)( v1z3 uhc*qpnk3 again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. Ay2)itn3 g ribsy-s6*q second 650-N force must be exerted in what direction so that the resultant oy32y)ngt qr bi -s6*sif the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizonhp b0:.t qkj(btally between two buildings 10.0b(hp:. ktq0bj m apart. The sag 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 zu,r/95mjxh i/: m 9yiydrc 2k 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 14p+:)6nos;ovn f2gio mzn(3hti ,iqx(.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new locati kq45w gg:5/8qjqm m(d3lbjrwon at McMurdo Base, Antarctica, as shown in Fjqjq5 wgm5l mw(d /483gqbkr:ig. 4-46. The 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. 4-47b:s 0s9 nwu.oj . Determine s9o0n. :b jwsuthe ratio 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-pulley a;nybm9- 4ppym 7ar7pc pparatus shown in Fig. 4-48. (m;m7r-a4n yc7p9 p ypba) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 656xt.mpf)8a2 cghb u2 d$-\mathrm{kg}$ 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 bl/bo zq9c vkil*0fs00 r60rshwock (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 horwj v/8w vb, y xx0,vs0ygq0l*bizontal surface are in contact with each other, ay jvqx/v0 y xb0*lv8wg sw0,,bs 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, ym; ssbuky;2c*5tx q7and 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 u;xk* sstc7yby;5q2m its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on ae242e wgti)zeql 6 s0c frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body dictele04g2qi z2 es)w6agrams 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 fricti,qnp. mhym 8,ron 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 nlvq7j)j ao0 mp2)a3 xxa0 7fz 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 0q:yt+q74d6,tdhh. 2 uhwxavi g u7h-i.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slidttad76uh y, 7 :xghiuvh+ qqhi2.-wd4e?   

  What is the maximum acceleration a orodx7s3tm2ih i 5 :6z 6t*:sree)vic car can undergo if the coefficient of static f7xoe2st mo ):s3iv:ieihz rt6rc6 d5*riction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and no d egc5,wl;8 mx-bb7furmal street pavement is about 0.8. On how steep a hill (maximum anglg -5bc ;fd,mb78wluxe e) 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 -4my+ ;ju c4swv0.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 on a roughw;ox/ p w6 2vsgzsam5:)l dn:o 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 coefficienf p5 dc2g,aui2rm z.7ut of static fr, p5id 7ugzf.a2mrc2 uiction.

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 kinetoq2d 977f xze to-j 2+ vihw1/5egudzbic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-h.lz.qyza,o/ 20) how large a mass would box A have to have to lzq ,zh/o..ay prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it sd en(-o bcx en36tl-p(bd2).kk1at fglides across the floor. How far will it go, given that the cc addb2k 6tf--( lnp )(o13t ge.bkxneoefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg at6l ,g q: szr6+hwya8znd 110 kg , are in contact and at rest on a horizontal alsw 8 hgy:t 66,qrzz+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;5m n8ucc2dtq heavy crate. 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 cm5;uct 82dqn crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whiyy vhqi(2k+p5ch has an incline of(yi kvh5y2q+p 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 a9de1sart- 5et* j,wy,mw 1lt s 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-n -*5v ipqve.g55 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 initiam y3qz re9v8qbz2n. (lzj3.dj l 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 reachew6rq1)yd/w*e tenf d*s the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a+.ycmj9we0rg on)9h x rough wall by someone pushing on it with a forcx r)jn9o90.m+gcewy he directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can beco9ed 3iy 9k 7z2+wmvza2no ac4ome dangerous projectiles as they melt. Consider a chunk of snow at the 9edom3+wya vik9 27z2 nzoc4aridge 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 wz5:7qu x0yqk automobile traveling at speed v is equal to wku5qxqy :70 z $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*d:qk7rp)m*cbi- z+zwh(lt w slides forward on the dash when the driver decelerates fro q )cdi* -rm7+h:(* zwtwzblpkm 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initmuq+8:mkxarn e4 6f5vial 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 ybo/y zaj2+v2ca+ q7i+pvu7 qfilled 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 dizac2+7 +2b viu+7jqqp/a yvoystance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fcqr8p3ftl5ul j+ aj;/riction 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 654jyau2pj;5m f 60rl cr 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 mammalianbo/ p.b prn7 j0qxvbm 8/i:u)n heart, at each pulse approximately 20 g of blood is accelerated from 0.2qxvb :nrm bpn/80o.u 7 bi)p/j5 $\mathrm{~m} / \mathrm{s}$ 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 aop2bq a.- ena;n automobile crash if the deceleration is no more than 30 " g 's." oa 2-;baepq. nCalculate 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 accelerahqdtzt2dk-;n9gv;sl rd+lf jl5 6 l/*tion produced by an earthquake is a , and if an object is going to "hold its place" on the l+d; q nz-kdl6* rtsd5lhf2/ltg; 9jv 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 involving two caosu4to3sray05 ),orors, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficientota r4sors5 o)uy0 3o, 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 hilf )0qzjb3frc-r-as 6 6- dcew6p8 kdaal (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going wh pqrjr -83a-ebc6)wc-affad0 6 zkd6s en 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 Tontjtcp74 1hlwu w*; z0wer of Pisa and falls 55 m befocj * wt04z7pw nlht;u1re reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stvf c1hbpoz2a-t y gu8la-1td-/pr ff v. z,5/veady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from thvz vd -z bh- /avf12upp8.5a1yf/rtl g- tfoc,e muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working ong3 3 go)clf8lc the redesign of a hilly portion of a city. An important consid)glcf g3 83olceration 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 physics experiments, dangles her watch from a th rvkl:j 3)4bphin piece of string while the jetliner she:4p)jh3 vbrk l is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there c9o47h kon/ck 3okhr ap3 0+xoq98b zoare to be several ramps connecting different parts of the store.oo r okknhqz 34xk/po ca97h+3o8b09 c
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 pi/-yj a-rfjf -fano (mass M ) using the pulley apparatus shown yffjfa r-/-j- 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 4 wi07sxoyr jl kf2m85ekt+o53.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-restrai,m:el1 jt ej4unt chair, an engineer considers the following set of condiet emj4 :1u,ljtions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 66so0rs-0)d erx 6mdf z /d.whk(wtva7 )0 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 similar length. Karen') 2fse;r-u7ofxf .ctws 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 (Ffew-. os;tff7rc2 )uxig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill'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 boatohxg ,.95fdgz 7lpou , is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall build :zg, ug6(gdpvt6eg8ko ek yd3kw1*i, ing is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climber+/g1g ppgxr4)d k / t3cjeqqy6s who are roped together are ascending an ice field inclin)p+6/k g3x 4degj 1g/rtqyq cped 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.