Why does a child in a wagon seem to fall backward when you give the wagon a sh 6a+;y5glnp/jal5r waie(al0 arp pull fo5j0elpw l yra/niaa56la(g+; rward?

A box rests on the (frictionless) bed of a truck. The truc h2rgjl q.tp84 nbrr-;k 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;8p-.rj 4qnlgrrht2b 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.l+nxn3*0qryvmv1 83p d1u 9ise b ucp acting on it? Explain.

Only one force acts on an object. Can the objectu n4n;i1h2i 1bmioany+. e4my have zero acceleration? Can it have zern4iehi11n.y2mb4 na uio +m;yo velocity? Explain.

When a golf ball is dropped to the pavement, it bounces bae;ah kfl j3/g(vf0i1xp .a-mh ck up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the f0 h(f e /vj.p-kfm1hglaai; 3xorce?

If you walk along a log floating on a lake, why does the log move in the/yz ywv*mj*r/w- jkr0 opposite direcj/r/ywy-k0* vrwm z*jtion?

Why might your foot hurt if you kick 7g z(,kys,a ;8g r3cj +kulvlaa heavy desk or a wall?

  When you are running and want tmdaft *f n(f*l6vu86u-rojj6 o 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 permf8vdft6jrfl j *a-nu* 6 (ou6son running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section o: yqwvn.:l6e pa+ ):iohahq,rf the same thread dangles from the bottom of the s.ivar o:wea n):,h 6qpl:y+qhtone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-k,mqr u4r*q1y kg rock. Why then doesn’t ,4*uk 1mrrqyqthe heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resultscru 2d q0co9f: if the scale had been calibrated (a) in pounds, orfqcod9 :uc0r 2 (b) in kilograms?

You pull a box with a constant fxrs6 f wq h8r(h.fg6*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 horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, fgq r8.6wh(h s*ff6rx (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity thvz ;+rnwu*qxd.s;k7t ere is a net force mg exerted on id*z s;qwxt ;u.rn7 +kvt by the Earth. Yet by Newton’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) needed to lift a 10-kg object when you 4oq9+g l9ii0 tn0xjlg are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objectqn xl+9ggti0jl4io9 0 horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war eljt :,zj(-lt (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win?t tj ,l-z(:jle

A person exerts an upward force of 40 N to hol9oxmev ::: l p 5wxhmyo8y9um-d a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what objech:ul o:w p8vom:ye5 9xy-9mmxt it is exerted.

When you stand still on the ground, how large a force does the ground ex+d+ubw80p t 4.fsaawiert on you? Why doesn’t this force make you rise up + 4uwa8.0bd wf+saitp into the air?

Whiplash sometimes results from an automobile accident when the victim’s cav n+,ur;ah0 ielk3tp i8 ut:d3r is struck violently from the rear. Explain why the head of the victim seems tpei :+ t;0k,8u3ln vhtrai3u do be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trucv e ;vow+k7p:2iuqy.io9 2fwck accelerates, the crate remains where it is on the truc7ve:y;pfvw wki.9 u+2qoio2ck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push azj)o1 khvsmv9; qu* (jo*gq9so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent tha a;)o gjm *s hq*vo9qk1u9(zjvn on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclinl0 jrizc6+v:0ut fey./da3.gff rm-l ed plane? Assume ltdyfre0irav. :gz-.mcf l+/j6 uf0 3the mechanism functions properly, even at an angle.

  What force is needed to acceleo sd4(f .+iueg,y1kcbuk bt5. rate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike aqfwo r mwc+gw98y +r;pk 60g7lnd 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 if it is used toib)pwk( f-j/8m sxp.a accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a wxz3jb dx+ )l5 qctcsc(il5rie y77:: $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s+qovn7f1 seb;8iu5 a)cav n9b if the car is traveling at 95km/h?fec+v9 n;vb7a a8)uioq1n 5bs -  

  What average force is needed to accelerate a 7.00 ;mxxeru7df9pg2 )e( c-gram pellet from rest to 125m/s over f ;x)9egrpd2m uex7 (ca distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratq*s mg9j) )uw v9qi9wnx*va8lion of 2.5))ul w a9jn9vs q*m giq9vx*8w $\mathrm{~m} / \mathrm{s}^{2}$ 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 j.a -whsye:pe gj 6bm1b-.pj1ck (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 mheet q(1*u jj5+ drqy:aximum acceleration is 0.0680 g . What are the ma1u 5 *tqej( yeqrdjh:+ximum 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 bathrodsaoxm:2t/)p hi)mif (90r nzom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accele(0 hfdosir/n )a:9zp)ixmmt2 ration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevatbu52v 0iyt.0fg zhytxj( (3qtg/z,rq or has a maximum strength of 21,750 N. What maximum upward acceleration can it gihr gq35gxttb.y/j0 z(2,z(0iyvq u tfve the elevator without breaking?    ( two decimal places)

  (a) What is the accelerationtu;8ncluwj r ilif5d(27 r6zv8 b( fa0 of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is eqi6u rwat 0cf f7 5nbi (vzl2udl(r;88jual to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he stdb( a7y3h k;wb apu+4jrikes the ground below, he bends his knees so that his torso decelerates over an approximate disw uk7+3y(;pdj4ah abbtance 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 tih. i; bvnmzvu5.a zzh15 0ywj;ed 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 weighs z1 i.y5jw5.mn a 0vb ;zuzhvh;
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbdq1/gj(g+xdbhcxh6 8h p8g 0nall player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a basebal lf6x 5q;)lli e)gv9.pk xgs+rl (a) at the moment it is hit by the bat, and again (b) after it h ) qvlr ).5 ;6xkgs9lg+plxefias left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N4i0.wg j e08m 7ahppip force must be exerted in what direction so that the resultant of the two forces poinej7iw0apgip 80ph m4 .ts westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bui c sm rd+vyvg(:t2jw/1ldings 10.0 m apart. The sag in the rope when she i/w1gc+y(svd jtv 2 rm:s 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 hanginge0s uw6b 8(bhm by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1)r bm+/jxzsaw9j3cs:4.0$-\mathrm{kg}$ 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 wiav0 ,45efyynew location at McMurdo Base, Antarctica, as shown in Fig.0wi5ave, fy4y 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 pulli-xwd (93ez(qenf;m 3 cc 7srbcng two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplin3b;w 7ezn fqmc-9((xec c3 dsrg 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 herseybm:fg4, r: bboi-wmh1bu, -zlf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pu,-:by,b4 fm g: i1bu- hzmbrwoll 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 rac w3i9xfs 56f,t7kkvpme 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 block (bjk/; kmf-z :e-:u3xsv l1.smt pujh1 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 sur/-ex3kfw fva4 face are in contact with each other,xfak3-/ 4e fwv as 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 0x*(f4nb/d4obb j k lkin Fig. 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 heavierkkfobnj* 4ld(/40b x b one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cordn30kt7 bj;py *i z.gph of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diag pj;0 hzpiyb73kn.t*grams 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 fricew43/e )mlp)lz x2b jction 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 t b;dm;zd e+ 2ywq(mmki(wr6*lo 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 stane+ y8l0tho2ysding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor +yletsoh2 08y if you are not to slide?   

  What is the maximum acceleration a car can undergo i ucsjat,. t/iz;7o0paf the coefficient of static friction between the tires and the groo.0t/zp ;7a,a cu sitjund is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemvzn 9+vb s69u;mgv;az ent is about 0.8. On how steep m;9v;zavgunb 6vzs +9a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at 4wwk; axn)n *v*;a -vwn yp0 ,drjiin5 -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 on a rough o ufrz5u26u/ z30$^{\circ}$ 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 vern6s66mu8bgefo1y s6 jy high coefficient of static frictio jns8g of6s66ub e61ymn.

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 friction for a 2g nd.d6wht1a $ 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 Figt50ao6w7it:nd) kk xu. 4-32 (Example 4-20) how large a mass would box A have to hd5 : oxk7k6uiawt0)tnave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. H1: e eug)c ,xze;rnmi(ow far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts 1ci,g)zn uee(; r:exman initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rn *k9db s uxn79owe01)x wvya8est on a horizontal sure) 8k*awxdv us79x09yonbwn1 face (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 stav-;sgfayorrw.0. 0skj9vkc2 tic 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 slide k 0kg.j.;vr-y09o rws s2 favcagainst the cab of the truck?   

On an icy day, you worry about park x-jf81t3*;vyk)po :muwpgdming your car in your driveway, which has an incline of 1 pxo- fugd8m3yjt1): vkm *w;p2$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a sl r1zs qdo;dvv2.80bm5jdud z)u9ku+ uide 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 li tzh +6dca93kpes 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 initial spewzaq5nk8i+ vn,g ;d;q ed 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 *-sh4ukcxydp bf z,0.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 emlvv.t; 2t; jap:6xh7x fnf*in place against a rough wall by someone pushing on it with a force xe*t al;jn :.pfh;f7vv m62tx directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they melt. . ;gz5brtpkc7 Consider a chunk 5gbck.z p ;7rtof snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distanch+wsmpga ; 0btz+jo5- e for an automobile traveling at speed +a mtogpwhzsbj-; 0 +5v is 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 w/.* *u4rduuys f3tr7tessg,0rl au v) hen the driver v/*r4u, u s utd*0.uls3ateysfg)r7r decelerates 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 mast 4,t1mkgsomoj + )3rys m 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 thk m omja6jmk*gr; a..*e67 dpney are filled to the packing station 11.0 m away. The belt is initially stationary and must fio.*kk.repj mmaa;6 md6n7jg* nish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betweu9b6xf(l if,r4 zzwp2 en $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a s)8cey 2ivq o:98gspl 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 approxi 4r.jll;opym5mately 20 g of blood is accelerated fro5l.pyljm4 r o;m 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 chan9i gpm 9,hhtds2u 62quce of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calcuugui62q2 h d9t9m hs,plate 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 acceleratiyxc9jlt)s 9 c8gf6xgt/ywm :*on produced by an earthquake is a , and if an object is going to "hold its place" on the grou)x*9:fgc jgls t t/6 x8y9cywmnd, 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 involn;uamx zj),6m it5ia 4ving 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 ru zamxi6ajtm,nu) 4i5; bber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled: j(gsyf7j 5tg5gg fjt:(7syj along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the tp+p+ 2axcy-ay op of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of a+- yp2 ycxaa+pir resistance?   

  A cyclist is coasting at a steady0s fmrbl 2.i0j speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the fi0s0r l2 bj.mmud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of 2y/ewxfj6 8gma 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. A6emg8 xwyf/j2 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, dang7:sb *w mf06+xhc.a3kv 9,xajbtddk zles 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 stx6xadkd: 7.9cj mv3*kaf b+t0wb hzs,ring makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting differeq v*orqi(ksc 9+ pe5y+ obu4r*nt partec9k roy5+(viu4qp+ *b*oq srs 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 lif p1y h-saf.1ijt the piano (mass M ) using the pulley apparatusiph1f-a . 1yjs 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 3.55dudn0 -v-ror)jmydj, n , p4u $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers thi(e+wyd k3;h,g r1kum e follo 3dg u wke+;r(y1hmi,kwing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 66ezgt ph9r ;*j2xcnk. 60 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 len yj sd0il;wl-s:+n yy8gth. 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 thl:n j-;s wd0yy+8s iyle 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 boatw.jj o2d g7/yi 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 building is allowed to reach a maximum sp s 5 :tvsaoh+lxy zm(gm/i+ 4xdz8g9h+eed 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 togeth;mo+eg-sexo -*km-r aer are ascending an ice field inclined amso xrmk --g*e+;-aeo t 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.