Why does a child in a wagon seem to fall backward when you -qe-bm f-x5 fwgive the wagon a sharp pull forwam-f5qbwfx - e-rd?

A box rests on the (frictionless) bed of a truck. Thorqf1+2xntgq 5 8-xoc e 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-x8 5ofqgc+rnt2o1q x 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? Expl8-v3pusnq/rs n 8xtj li1jb 54l(j28xt6wakmain.

Only one force acts on an object. Can the objecuj (x.j6vi+ cqt have zero acceleration? Can it have zero velocity? Explainji(uj.+qx6 vc .

When a golf ball is dropped to7f)lhn -uhf tz +*/q, nncr*s3tg/ qqs the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exelzsu ncqfhtt*-r3h,/n ng/ q7 *)sfq+rts the force?

If you walk along a log floating on a n6biz3sdu :-xgea 0a4 lake, why does the log move in the opposite directioze 3b4aainds: ug06- xn?

Why might your foot hurt if you kick a heavy desk or a gjb-9yuumnoz q,*9fv i g7(c+wall?

  When you are running and want to stop quickly, you must deceleam:j0 pe50eu qii90ujps5 5ybo /cw n*rate quickly. (a) What is the origin of the eujy0b0imu/p5*p o c5s9 jeani0w5 :qforce that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thre/v ct l3qn knuu27k94ead from 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? What if the person gives a slow and steady pull? Explain you4n7ut2ec / uqv3kkn9l r answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-0 wy0*p*hdz: / szppwhkg rock. Why then doesn’t the * y d 0/spzpph0wz*:whheavier rock fall faster?

Would a spring scale3eqfkm:u: q-qjo m01r carried to the Moon give accurate results if the scale had been-u0q fjqkomerm :q:3 1 calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a 30xaf )cz: dof a(d 87aonxg6pngy;l5frictionless 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 th37dfp6:g(d8 l0fzx)aang ooc5a ;ynxe same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of b+ qf /-a7imd 8qbmy7ngravity there is a net force mg exerted on it by the Earth. Yet by Newton’s thirmf a-8q7 bdniyqm+ /7bd law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) neq/ c 4cprk pkb*7;+a2yhigt:zeded to lift a 10-kg object when you are on the Moon witcp 7 pk g:q;+/rzy*bc4h2 atikh the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, e;t1oh*, grl5nb*/-du ae r fpf36uzhgach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win 5p6;fndlh3ga tgouh*r ,f1-/*bz rue ?

A person exerts an u9+yjt,ri9:jdbqbq56h d r2 r lpward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (q9triyj2j l:6drbrqb 5hd 9,+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 the ground, howprtfnpk *dh5ohh cr70ea9 .9 4qo*if; large a force does the ground exert on you? Why doesn’t this force make you ri7 9 roe*.fat *phc0;5 94p rnfokdiqhhse up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car i *dv gnf*:oeg (hp5ar2r 6qt/ds struck violently from the rear. Explain why the head of the victim seems to be thrown backward *rf5(/ egoht*d2 n:q6rag dvpin this situation. Is it really?

A heavy crate rests on the bed of and k ;)y-yaxo2 flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What f k)2oyna x;dy-orce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block j9 w2r6kevca-reaches its highest point, it slides back down but the magnitude of its acceleration is l-v e 9ak2cwjr6ess on the descent than on the ascent. Why?

What would your bathroom scale read if y;8v4:l 2d9 bb5tqct 1fnu mzdoou weighed yourself on an inclined plane? Assume the mechanism func bvnctq8tuldfzm92:15; bd o4tions properly, even at an angle.

  What force is needed t4odx:whv/yi4 t, f(hto accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a biurd* 7 xt,m*b)oc/ xt3vaz v7ake 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 ro8yw nq87ea/ q bpo-dt.pe 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 a ;vm )5kdih q4lbbes;3 $76-\mathrm{kg}$ 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 if the car is 9l rjb8 bwyi9.traveling at 95km/h? -w.9rjyl i b8b9  

  What average force is needed to acceleragce /mnb:2k7 -piewjj 5b ,ey*te a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel ne jmc57 kgi j -ewp,yb*b2/e:of a rifle?   

A fisherman yanks a fish vertically out of the water with an accef2m(wkp 5grzhv+ dk-(leration of 2.5 z-5w (kr 2pfmh k+dg(v$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile track (402i0lv 6sp,6gwmjgq9 1f $\mathrm{~m}$) 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 faud3 /e(syb5 designed so that the maximum acceleration is 0.0680 g . What (sdye3ab/uf5are the maximum 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. puy6h8 *rr)gq9f)(euy wd 8ldl e p6-uWhen the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weightrd)quh 9 )reydpye lg -6u(w*u88lp6f. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator 7nqwov/ ,2 mlzhas a maximum strength of 21,750 N. What maxqom7n, l2 zw/vimum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelera,1xrwbl uq /65yhzt u;tion of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth ofq/bx;6 h uy,zu5tw1lr 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 tl4 )y3 36el1dyvukh jpaag 3q-hjm5j4 he roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate dl3 3ydlp44ajjjk36ghqe u-h)5y1a mvistance 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 p)ljo h1fez2v agyf ek b5)yc418qb-b44vj 9 ztied 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 pulleyejf9 eyqzv18f5bz4 -c4by 2pov4)kghj)a b1 l weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pla se g1z1xdxz35yer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the m fhua) lzo c7i;l8s8:uoment it is hit by the bat, and again (b) after it has left the bat ch; :78f 8lul ozsi)auand is flying toward the outfield.

A 650-N force acts in a 2dtwi25rh/h6 /aoapasne8 zx k405qu northwesterly direction. A second 650-N force must be exz/iakh r 5n/t26sxhoepa 28w 54auq0derted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strungmm-gw-o/ su. u hgu72h horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint 7g u/sou2m.h--humgw 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 hanwmv1w n 9i,3muwnq-g9ging 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 14yg d h4gnqr; xal/0//v.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 location at McMurdo Base, Antaggq8y3rzydvtq h0: t7 tj o659rctica, as shown in Fig. 4-46. The sum of5g qt zt 80qgt:h9j3 6vrdo7yy 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 ist-dsq+ b7le(n pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratieqs(dl7n+t b-o 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 up:wte7f8 ynf b(.x,kkz ward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speedk:7 xwf ,.(zfnet8ybk?   
(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 f;wwk.i w/qwd,kz ( /+w 3g )g)wxnmpp 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 blocuz;vs( hc lf,ip e,9:qk (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 ek(liqa sy zks350 c,)yach other,3 ssqyyk ki0),c lz(a5 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 in Fig. 4-52 are 6q-o ho,)ari u: t ,ng25edwsleach initially 1.80 m above the ground, and the massless frictionless pulley is 4.l) u6n,rq5: -woehg2 asto,d i8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are c, tft(muoy ;3feoxlp.f9(l9b8 imv e +onnected by a heavy cord of mass 1.0 kg . Calculate the accelelti99,( 8xp bfo(em;.+fvoetmlfyu3 ration 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 kineticyc(5/fp4w mh. ph4xdf friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to sta+w oe ebe4v)z1rt 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. Whag5 4rssxd., f6a1qjqr t minimum coefficient of static fd 6aq,xs grj4fs15q.rriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficie6ay-ofz/j 6t.yc q0bynt of static friction between the q.t j6f0c ay-yzoy/6btires and the ground is 0.80?   

  The coefficient of s e1-agqqkv73 :mb /mrl 0cwh1btatic friction between hard rubber and normal street pavement is about 0.8m-g03 bcwkr7h:1/ e bla1qv mq. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4d vg0a5,g+)y xd(bmvk.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 lt fwd8 -e.c+orough 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 coefficient jyjn r.,v0 meaqrec c6-m+e+* of static frictione+ , +cjv6-aremr c .n0ey*jqm.

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 -3o;5 s-p .jpw,,otxxjhrr;u,exkt x tr z1n5friction 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 4-20) how large a mass would box A have;pt,vyx1ila z ff 8ykz9s/1d4*jqk+d to have to prevent any motion from occu taq4kydd1 f1*;9l/fjz8+vzspkixy,rring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push45y:2)nwz8u viw*+ qippbj uw so that it slides across the floor. How far will it go, given that 4+i n )pu zuwjwv5:*8bqw2yp ithe coefficient 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 and 110 kg , are in contact and at rest o6 .h+5q c2eq(q67 kd tkogbxgpn a horizontal su(6g 5 e.tqcxgo2hk q7 +qp6kbdrface (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 cf 4 j6rxv8qjt09pups /arrying a 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 deceleq jrp pf9 jt4/v60sxu8rate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car sey.,ug8et q7 in your driveway, which has an ine t.e7,y8su gqcline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a ::i 1ew:(od3ex vf gob28$^{\circ}$ 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. 4-557,p)ngr -rnvf/ j r m(*d-v-d8efsmgc 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 initial speed of ex5s4l4l xb0 c 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 t8nhw3rp4d) xhu 0p/(f l1acgyhe 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 rough wall by jga 7*co6a cy8v3gdz/someone pushing on it with a force di* cy/odg3aa78cgj6 vz rected 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 vdt gi 67dre6-dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitct id d67veg-6rh 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 automobil83a7oyuiiw9 g w-m-nse traveling at speedmuso83wii-yg-w9a n7 v 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 s(dx0dhe hi nm6*z8l.7eyh b b7lides forward on the dash when the driver de eb ld8m0y6.behih x*( dzh77ncelerates 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 mua; o39ihh, 4yh6u vs. yjv0kd 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 conv0xkj+5 d nxh-)irdkou, 9c*jx eyor belt from where they are filled to the packing station 11.0 m away. The belt is i0)knx5j jxr-xhid, o9+*dk cunitially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction between gep l.e636um w1b qukmm:+x )d$m_{1}$ 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 bicyclm k p g-ent3zvq+ k-o/n+hcnp. 8cqx75e) 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 mosr0;b)ml+2 ck7ndu zrw 3/tvsdel of a mammalian heart, at each pulse approximately 20 g of blood is accel 0lt/dswb mz;vsu+rkr) 32cn7erated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable ch),yb95xwch teance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a )9wt5,hxbe y c70$-\mathrm{kg}$ 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 pr v42io iihee/3oduced by an earthquake is a , and if an object is going to "hold itseoi/i2hvi3e 4 place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving)ar)k6(+pk+a kw6aauv xpi3e two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. Thex6pp)r e6(uaw aa+akk) 3ik+v coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling downey*1pr:0o lk,h 8 kdhe2ux,tm a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore fr, * uxe: otl8rhkm1h p2yde,0kiction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is drlsow)dr0v- 2 lopped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground wi2) -ls0wvdl orth a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch whero,zn8d79rvp p2 qjj o*e the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what 7nv9j8ro*pz2,p djqo will be the speed upon emerging?   

  A city planner is wow(r34 v6 zn5llz uuf8q/cxz.ogf ac 3-rking on the redesign of a 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 1100 kr6af .cc ugv x-4nuf/o 5(zzl3zwq38l g , 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 tc7h;1v0uivu dhllm5wg0g q 1, hin piece of string while the jetliner she is in takes ofg;07id5lu 1hv, luv0qchw gm1f 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 are to be several ramps connecting differzy0xm;ql7f2iut(5hgi t)fd* rp ( ye2e g)m* t; iu27x(5peyfd0 lhyir(2qzft nt 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 tdze r9 8/n 2q 0waglan9g.l1ynhe piano (mass M ) using the pulley apparatus 8 e0gaydqlnnalwz1 9 .n29g/r 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 acceleratinda1tx.8( gbhyg 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 f:09yy p 3 gtkn6ypibdf) do-q5or a child-restraint chair, an engineer considers the following set of condi6gi)qd 5 3py 9-ydp:ynbotkf0 tions:
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 660 metric tons (660,000 r;tv;hh c*q3wb mv7euo0yu22 $\mathrm{~kg}$) . 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 j1 + lg6 vxk1k;.tuhwcof similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climbe luc+hk.twk g;xjv116r is more likely to be hurt?

A fisherman in a boat is using2a3 zp: .mnd a;/fru:e l:pqmxx kx;v) 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 kcp z9zg ygl/r49pbagt; ) 1b:maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are a-lfjkczl)3 xh+;2d/, g xcb ndscending an ice field incline)fxg-k dcl+; bn ,/ 2jc3hxlzdd 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.