Why does a child in a wagon seem to fall ba:/5xq;lsr9muv ;px rlckward when you give the wagon a sharp pull forw:uvmqxsr 9/xp;lr5l;ard?

A box rests on the (frictionless) bed of a truck. The truck driver starts t /(xodz*yu/ 0jhbks(mo :4 ndqld 1iz3he truck and accelerates forward. The box immediately starts to slide toward the rear ofl(n u03zj d(dyoo1m /sqkx ib*:h/zd4 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

If the acceleration of an object is zero, are no forces acting:-jj 4 wemo(1eqw qml) on it? Explain.

Only one force acts on an object. Can the object have zero vtm*j nrqxy/w: wbx5) 0lgy 2:acceleration? Can it have zero velocity? Explain.l q:g/wmn yt y)x:wr*bx02j5v

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forlyr0lm7 g or9d( r qw-y29emt9ce needed to make it bounce back u-rm 2y 9yg(lotewdl90rrm97q p? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log os) m),yma zh0a tu73smove in the oppositouzh3),0a)ssa m t 7yme direction?

Why might your foot hurt if you ksw v*8.piq*(a /nz88bruzu zk1f5lbwick a heavy desk or a wall?

  When you are running and want to stop wc ob;5 3ql oeqjc dg.3s.71voquickly, 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 spes c3vd.. q 1wolo;q 75jo3ecgbed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the c3pxo z1cp9 or15c(zmoa 4.w sceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a personxpcr5.1mc9 oc1 p4zo w(s za3o 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 twiclq+wr4wpt ps8dcq1v/ h3-r 0yhus ;w3e as great as that on a 1-kg rock. Whytp/p-ywh r33w0rq8wc;l4suq1 dh+vs then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale had me8 0xluiu,g1qn3mid by, 79 bbeen calu1mqy8i,u0bn dg,x l 7m3 9iebibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friqr9 8wme b2l9gnxq -zv0 9ze0jctionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, 9n-em 0vj 9 2rql x0gzzb8weq9or (c) decrease? Explain.

When an object falls freely under the infl6to q 4o2cvci6uence 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 to2ovcc46 6i qthe Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg2*zzxapvz.l/ h0d/f h object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a gzh la2/*pd.xzf h0v/ziven speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls wmahums2n6u k2yma4 uj1( 4 j-uith4u m6m u2hmsjnuja (ya24k-u1 equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocerieua1;;7)v:wyf bgjv brs. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (drvf; gwb 1a)yv7;: ubj) by what object it is exerted.

When you stand still on the ground, how large a force does the ground ex4l76 p*z pzfujert on you? Why doesn’t this force make uf7l4pzj z *6pyou rise up into the air?

Whiplash sometimes results from an automobile accidy42w yjtpe-v1f8q r nxbkc67 (ent when the victim’s car is struck vyb8- 7fpxyr(e 2wjt 1n4v6kcqiolently from the rear. 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 thsa dh pkc:0v,u b0z*7zhggu85e truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causd c,z5* 7az0 khgbuhpu0:gv8ses the crate to accelerate?

A block is given a push so that it slidaw2i5i,e/b2pxeeu ( gj+ rn1ses up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is leeixunbp, e 25sg 1+jarw2/ie(ss on the descent than on the ascent. Why?

What would your bathroon t es/(yd.zt(e t4z8im scale read if you weighed yourself on an inclined plane? Assume the mechanism functions pro.i e8s z(t(ttndyz/e4perly, even at an angle.

  What force is needed to accelerate a child on a sled at a1h :t d5r)lty 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at.yn nai::hvd) 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 to accel na7)gd.x0jpm erate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight op6b 8o1yoo*a c/f *mjsf 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 in 8.0 cu 4z,5*)mpdpu pl -ves if the car is traveling pld-,) vuc m54ppue*zat 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fromi,bixpuu bc)6i2ac vt3*ah1i)p2z.h rest to 125m/s over a distance of 0.800 m along the bu12 ia 3c u)*v, pihhbz. ca2ib)p6txiarrel of a rifle?   

A fisherman yanks a fish vertiyi qf;2lco,)i cally out of the water with an acceleration of 2. )qol2; ,cfiiy5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-8qkc/zix..dng i01gh7zse* e 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 9eoa9 0 yaimh.the maximum acceleration is 0.0680 g aaeih.m y0o99. What are 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 xw )97+dfi g2z)eu okdelevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculatf2) 9x7+godkwe)i z due the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg ecuau54.,owf r levator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elef a. 4uoucw5r,vator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclk s-qhd9l ++8.ozwhya uding parachute) when the upwa. yw zhdals+ q8k-+ho9rd 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 of a house 3.9-m highp3.rthsk*eou 8,lg rf/ mlvlz0;v 3o5 . When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance oo ; uot*z,frlp03lh5s3.l e r8gvkm/vf 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 r+; kst kunej/(jl0np .ests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung fps/.+ ltu0;nkn j(e kjrom 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
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player 6jsld)xq: 86eb jy ig(
(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 moment it is hit by th/4 onqkdqrm6*9xc q-sf v+6 the bat, and again (b) after it ha6qq6+*kdftv - msxqr4 n9h/co s left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A seconhr+l far :-;4 ca9j6gcys1srm d 650-N force must be exerted in what direction so that the rg:lr 9asca-r4j;h cf6+smyr1 esultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "him5nqwn vbw6)1 t8+ooo+ib+jl fdf5 0xgh wire" strung horizontally between two buildings 10.0 m apm d +x5o lntf o)vbboqn+56j8fw+01wiart. 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 15wt ,aioq 3zpzaoa2* 4m03nys0jxr:mda2fo 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 14.0y(lu)hj:p l2n n.k wz3kj+ t5q$-\mathrm{kg}$ 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 Mzto9s ( axtidk,(5p(h; xntj2 cMurdo Base, Antarctica, as shown in Fig. 4-46. Thejp xiz5o stx(,9th((n ;t2kad 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, Figngug6 x8m r 4j:k9z2zi. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car 8:g9 u2m r6k4 jngzxzi $\left(F_{\mathrm{T} 1}\right)$ , 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 u4og1 6rw+2cqe1sjb i gx (q7ersing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant1 2bx1(oq+e67r r jqgeicgws4 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 beganyqeujcql gah *jvic 7bgb4):q4;b.+/, 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(+u j+wakvxfp n73z v3s6,p kaxs::ar (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 ik (sguz-x:t.(ma0 ah c 2ox)jwn contact with each other, as shown in Figz txjck2.h-o0(axus gam w )(:. 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 theun3kifxz3+g)hh tg j)jp b;.+ ground, and the massless frictionless pulley is 4.8 m above the ground. ;3h +xjp 3nki)gt.bujf)g z+h 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 connected by a heavbodafu ,k;r; jd4uf/2x fa a;)y cord of mass 1.0 kg . Calculate the acceleratfr;fu,d ;auxdaab/ 2)jfko; 4ion of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a 3j9 6meq,pdvya n :28zbo.9dap5$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.f3 nukx(sbajj7,1k bmt2.pz :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 accelerat -7p(tusq2u vk3b1p;wr0iwwh 0 i0tasing at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you0(b-s 2wi h0ku3wpiv 1wtqr p0;7t sau are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of statpom+3p1(hchlx g4ho 1 l1+gpbic friction blbm hhgo hglpp+11c+1p( o4x3 etween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber anxrp bq+,wbl9: d normal street pavement is about 0.8. x9 b+wqbr:pl, 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 -,tw opn2uke9- 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 re,yw dn94xt..:bf lub cst on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in con*ehlz /g1zw qfrw p151tact with an asphalt surface have a very high coefficient of statiez/ fhl15 wwp1* zg1rqc friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetiek twb )wrikiwe.+*1 3c 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 Figz.2s awk1ko6k . 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motionkks1.z6akw o 2 from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrosixdj9)dba uibu(y vav9t c03:4z.)v es the floor. How far will it go, given that thb9 (d4juv yev iu iatd)3 90a.b:x)vcze 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 opu+ums uo )y57o/c3a hd 7abqk6 3o.mkg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 7u 5pbkc6+q3/ohaoo. u7a m3 )umsyod 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. Th5 dljr*mc0wl(lpo 8 p/e coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slic 5ro*( /lmwl d8l0pjpde against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whichuz)3q46lmso s has an incline o3suq46olm) sz f 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 fn84 n(gt u/7n5rdne xslide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an a1dkj )v:p ww7i0k3sxqngle $\theta=22.0^{\circ}$ 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 anod,bb-+aextm dy2rnz/ (.f7j initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speexzk-n 0mk.if +d 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 byvu9w/y ;6ldxl8b8kqz someone pushing on it with a f9ydq w6 l v;k/8z8xbluorce 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 ro6iu8 s+ygky t1zaekcm, q; cc3h1. p0wofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ri .6e1 8mskp+hz u03,wyica ;qyc1cgkt dge 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 midkvcs7j/5qx 1v phbn0o:o +*csi iwze4*;bm *nimum stopping distance for an automobile traveling at speed v is eqcsj 45zno0dvi:/ e*x ob*phbsmv* ; 7+kwiqc1ual 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 9a7q+gotu sx :p+ gy;pa car slides forward on the dash when the driver de7g+yp9+ s:ptoa gq; xucelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial 7on sfa wg8-i3speed $ 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 whe:kvspo za;1,x3 hfgv +re they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates fxs:g3 k f,1;vpa+vo hzor 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 kb g1t83u: fxh:s z;hbvau2oc2 n4bf(ginetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 qbxrrnjlq iqf2gr4/n4 74;(wkg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximatbw hm a77p +x8;j8l kvrrb9yh)ge:yi3ely 20 g of blood is accevbb8;7y7x y9j r:)kp + le 3h8garmhiwlerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crt s/zy (b)d pyly;t n+scn,1*eash if the deceleration is no mo 1 n,cl sn+ztdsyy;e)*ytbp(/re than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is *4b; oww58h d-xo (uwux/mxna a , and if an object is going to "hold its place" ondwo(owu/;x mu xb w4h a8n*5-x 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 tgo1 -y/bram )che scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assg1r y m/ob-ac)uming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m jppt7wxm n9f dz:6+, ptraveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom af+p6fn m ,7wjzp9xtpd :ter 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 Leani+.fa l iy+gup)b5eep3ng Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average fo y)u 5lbg ai+ppe3e+.frce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy s+x /pi-b +k/iia1ks pntretch where 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,p+xpska /-1 i ki+in/b what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An i1vtm8ahimpe u9bowg / +f(65e h:0yrzmportant 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 kg , 6eyt+wpu/vh1bio:fg 9r m hm08(5e z acan 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 expepxmm82nc8z g /v/l o:m/*idxvvl5 8 svriments, dangles her watch from a thin piece of string while the jetliner she is in takicox/ md8 5m8vvsv*/2zp/n g8:lmlx v es 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 srqc -k8regw/m;g*x)q3g1 w wx 0s cr0 1mwojj3upermarket, there are to be several ramps connecting different partkeg jw xq1jx030)sw*ro8c q-1g/m cr wgwr3m;s 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 thxp4b t.sl28 jde piano (mass M ) using the pulley apparatus sht p 4.bj2ds8xlown 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 g:h646tc ip3f7tt b x5we hpt:at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restr f+ip th5n.a0+q b2swaaint chair, an engineer considers the following set of conditnas.tbw+ih2+pqf 0a 5ions:
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 mc sa5at10k* hrt9 d;bxetric 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's)i8 osb:q )t84qswx,psl )ae y rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for sa4w:oy) a spqbl,es)qt88)sxifety 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 climber is more likely to be hurt?

A fisherman in a boat is using a 4awbhtyh ;17 m8e/b d nylo,689ksiyi" 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 7 ivb1/jevhv /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 ascen -0wsje (7u2ooklfa 9iding an ice field inclined ata9eo0-2i (kou lw s7fj 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.