Why does a child in a wagon seem to fall backrs w7s:qqj(4x3jpa/)1 5p cz pfz:sbiward when you give the wagon a sharp pul5 a/ psjc1)prfjq7z3wq :px(: ibssz4l forward?

A box rests on the (frictionless) bedtqh )rw64,i-16y xe fs6g(i ulb)vje h of a truck. The truck driver starts the truck and a iuqy6lhsw6t6h(-1xeev)j)4 gf ,bi rccelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces act3c ):skih)3ze2ybkq ming on it? Explain.

Only one force acts on an object. Can the object k2gbe; )z*ktwhave zero acceleration? Can it have zero velocity? Expl z2)be*tk;w gkain.

When a golf ball is dropped to the pavement, it bounces back up. )jhmywq/m69c3jz, 7bo q .rdk(a) Is a force needed to make it bounce back umbw9 7hc6./ 3kjd,qyqr zjm o)p? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the4oaf u5e2ory6 6 c2 no(:gmnsn oppositrs(oyoa mc4n 5fo u6:n2g26ene direction?

Why might your foot hurt if you kick a heavy desk or 3e)cko0eahx m ixv.4pbf7o97 a wall?

  When you are running and want to stop quickly, qj(b 0by;fdl0r x/m, tyou must decelerate quickly. (a) What is bfx 0jdr (l0yt bqm/,;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 speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectiona9fe5 w, s4bo9-yaod2aupx 1r(- roe j of the same thread dangl efarso o-2eo-db9,px9jw15uraay 4( es 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 your answers.

The force of gravity on a 2-kg rock is twice as great as that on.h3m+,c+ ng*no km fpdx-)7 nsqgvjk6 a 1-kg rock. Why then doesn’t the n*cm3gmnns+v fq+x)kj.hg, od-p 7 k6heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resuepp (lyp*ws sl .s(d/:lts if the scale had been calib(w* d.slp/ pls(ye:psrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attacf v3gfm4d/uokd 2h+5qhed 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, or (c) decredhf4/3 q +ok gdvu5fm2ase? Explain.

When an object fallsya1y az v.)0t-kv*pteqjbu,8 y zt+1j freely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite foyt,q yavj +p)kyzu-1tt ae 0zj. bv*81rce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when yo/s)yk7);lbc m vxwg;wnp3uk3u are on the Moon with the force needed to lift 3))wwm;uykvgn l x;psk/c7b3 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, ea3dd we*v*oht (ch team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win?vdw 3o*(*ehdt

A person exerts an upward force of 40 N to hold a bag o1c9rz lu yjaj4*fym 0(*awn/ cf groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitudec yujcr*y04j* l9z/1mwafn a(, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on thze90t u3 .vldre ground, how large a force does the ground exert on you? Why doesn’t this force t.9 d30luver zmake you rise up into the air?

Whiplash sometimes results from an automobile accimy;wb.43a rzq dent when the victim’s car is struck violently from the rear. Expryb3mza ;w.q 4lain 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 truckom,4da (h 0/,jp9v hed)dorqj. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accel)(0h/d adjd h 4pejoo,m v9rq,erate?

A block is given a push so that it slides up a ramp. Afterutsk ,k 1z/nt.(k 2ada1+lwjd the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on thus(dt, k. aw2+11dkk lj ztn/ae ascent. Why?

What would your bathroom scale read if you weighed yourself on an incli+*3p:vn4p;g6yz3vnmvrb:2 eyxvi pe ned plane? Assume t vyeb2zi4p nm3gprn+e*vyv:6;: x p3vhe mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on s z.e2v9eiv ,ha sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider)* /c* oobzc e:j5lt 9zswnx;d g4ecy0 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 to accele4t5gxl5n ;a a 66cvovqrate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ga*ma ;qcf4m,ercqg3. zww2,$76-\mathrm{kg}$ 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-k9qkvou-s vg4v)p7f h8g car in 8.0 s if the car is travelin8hfg-ks9v4pu) vv o7qg at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pell 7jsrxj tz 2i )g89+ .btxuqx3i38fqglet from rest to 125m/s over a distan7 qi+gix xt9xr3t )g3qb8j.f2zusj l 8ce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelera9u /3y)y(vqr1mvae o47rbe p btion of 2. 9)ypo 1u /yab e(vbqvrr473me5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cov-6g1lntr rymra n0718+mcv2ah ) ixqxer a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the m y1uxj6 b3(y0ykj o5gwhiu+*lyln,j - aximum acceleration is 0.0680 g . What are the maximum and minimum forces the 1l5y6nu u+oyx ( ,0jyiw*gkbjh yj3-l 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 elevatz4-s h9jsfxh- h g(oy(l0h ,ttor. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelerationgohhjs -f4hxth -sy9ltz 0( ,( of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximumm tumq8i3 yml(71ja4 f adc92m strength of 21,750 N. What maximum 1jmfi(ult79 2c4y 3mmdqam8a upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f9(jhw05p-vb2itemr h aj 0s7srt k2i8alling sky divers (mass 132 kg including parachute) when the upward force of air resistance jwi h9v 2t 5-tksijhb 7r ea0(m20sr8pis 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 high. When he strikes the grou3ag p7g - tnua5v7j3vynd below, he bends his knees so that pv7-ay3g7uja tgn3 v5 his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N llyp;f4(e .uk rests on a table. A rope tied to the box runs vertically upward over a pulley 4.yp(lf;lkue 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
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baske 4r3;y; mh)x6sru s+/v0gl mob/opy fstball 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+c+24v+c8hk)rev4-mntffgru c nk7ql (a) at the moment it is hit by the bat, and again (b) f4g+c +r nhkvq4ck-mf7+2 8vncrtu)e after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N c lzw*zxo+nh) pv*9)wforce must be exerted in what direction so that the resultant of the two forces points westwa*z9z)o xw+nlc v)phw*rd? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "h9s;nlxb8 e0i2v7f9pf o ggyw +j0 8jlvigh wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she iw088e9p+ojb7lf ilxygjv;9fs 0 v2 ngs at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from anothegads-/rd l6n0 j 9 r1muiw,i.qr 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 14.0/ i7d1npc;rge $-\mathrm{kg}$ 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 q,ip8(4rouq4, tm tsp8w lde/ new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of theqp4lsmo84t (q,8rp/,w id ue t forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 . )u+.:r paar4 x p1nw2o 1wy-oiyn ff3wDetermine the ratio of the tension in the coupling between the locomotive and the na3+ -4xo1yo .wyauw21)r :nfwrf ippfirst car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus showhgpcu6lrw- )xa r4f20n in Fig. 4-48. (a) How hard must she pull downward to raise herself slowlycafpgx )2wr4rhl0 u 6- at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race be7 tv.5lsvthomz;+. b rgan, 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 (fni 3tmv:7ux 7n-k/tscvr) y2mass $ 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 frictionleelakaua u5: 9+on7xhz1( q2 sbss horizontal surface are in contact with each other, as shown in Fig. 4-51. A faq (lea u1s95nua2:xobh +7zk orce $\overrightarrow{\mathbf{F}}$ 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 Fi jtdql k:j-rm/z4q z)(g. 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 s:4rl-)z jq/(d zjkqm tystem 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 heavy cordb;x93kk6cgi o5n jvy 0prs-o0r;d y+i of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using thb-v+jdion y ;p6r 9 xskcg30i5r;0y oke 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 befgb 1u5gtiuzz)m. l n ro*3a.2tween 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 st i7 gpi-l2caf6nk3x 9 :kbw6yky*os 3-pg0jl sart 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 acb575d ( w lic )7zhmnosafz1*dcelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and theomz5i dbas1fn7z5 ( )7dc*whl floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffwftrxjo p3r1*f ,wm3 +icient of static frictionwfp+mrt,13 * xjrofw3 between the tires and the ground is 0.80?   

  The coefficient of static friction between ha d*(724sl klmo1 hrbohrd rubber and normal street pavement is about 0.8. On how steep a hill (maxll( 71hdbho4k *mo2 srimum 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 / n9qnp/oz4 **l7wzbem jxav6 -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 resg)af r s,a-o(b5;w:sisr 3 dgtt 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 contact wit1b(o)i ah h+c-kzn7j fh an asphalt surface have a very high coefficient of static friction.ki7 h -noabc fj1z(h+)

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 e43xx uma:w: ohki 49da $ 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 (Exa26.spy5eul,9r b cb)u-repz r i2qw8f hz+;ppmple 4-20) how large a mass would box A have to have ;eyr,bipl5peuq 9c pz2hrwu sfr z 62p+).8b -to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides 104*ly2 e fexrc7*ksnc dy-je across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of ken *ycyj0lerf7c4 1xe-d*2 s 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , a b.uxq/w5x74vviz:x5bj :sj l4na(frre in contact and at rest on a horizontal surface (Fig ufv:rjz( :xa w4qjsb.b 4l57nv/xix5. 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 coefficiei y i) 5u 6shb8.ujuz0ka:bd7vnt of static friction between the crate and the bed h. b yb0kius)jai 678d5zuv:u of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which hmv4a)baz7wbo+ iq) r9as an iaq )4oir)7+b azvmwb9 ncline 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;z n(qj (d3in ./-juqydp)bby slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a98hbuvjw/.sx 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 (kiumhz 2t u)kb- *9ec3.0 $\mathrm{~m} / \mathrm{s}$ 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 th96 fhzp kehysn5ba .mk,m.12i e 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 someone pushing on it with xzr 9-up.77(khl zkppj /d -fna force di.drn/plf( h7kzpx -z-kp79 jurected 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 theyer hkduw*-2+ e melt. Consider a chunk of snow at the ridge of a roof with aw 2+* deurkh-e pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance b4rgu( jq1cp5for an automobile traveling at speed v is equu5j(cg qr4b1 pal 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 das; z9kj3(q 3oe7cowg.jwzhm9 lhboard of a car slides forward on the dash when the driver decelerat.w mq9wo;zj 9cjkog 3hl(ze37es 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 giy:5zczuq jfxh :9e3m-ven 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 f 79a zh 3mh9ta,..tckw/nula-ak.ikfrom where 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 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 mi, 7fi .zt k/la.9k. -hntk3umwhac a9animum 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 frict3s)iq/ r5 j3 zg 3jeb37rvlolfion 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 kg vkh r 7mbs1-tw)/gq o+(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 pulsekwrh + kodd232 approximately 20 g of bld dkk2who2r +3ood is accelerated 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 crash if the decu*ev:yp*( te)jy, kgbeleration is no more than 30 " g 's." Calculate)euk(vg, bjt*y e: *yp 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 bhhb(,/u8 yz 2 +agpwkxy an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction wit8 w, xa uzgp+bh/2k(hyh 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 a4kc: wh1 sgprt v jxr306ffe*of02. x; bcem+zccident involving two cars, measure 72-m-lo00f6*mfbt2e f+rc ev:xsjz3ok ;cphw g.x 4r 1ng 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 assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 mapiq2kq**bj b *liw:o7dy2b8eans that for each 4 m traveled alongq7di bk8i2boj qlya*b2* p*w: 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 top of tap/ u3lhp:6j7rah0 kln kzc4.he Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average for0h6 lk7/ 4c.hzj3k: pan prluace of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but entfr.326- z0jl ktnc vgsers a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge tns03zcl26j gfvk. r- from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a cn4ckif k1yt + 4; -tk5frxr0mxity. An important consideration is how steep the roads can be so that even lowm -k ykn44x0xf;1crk5itfr +t -powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics o.;oi7 bq oh2dz 9sit6experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the strdis.bi 7z hto o;269oqing 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 co+ ,1rhrg 2ziej/a2gzxnnecting different p/2aj hr 2zg ze+rgx1i,arts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) usind) aet *(igr1pm,7wuz 9a; y,j qhfhj9g the pulley apparatus sh q7gpmi wajre9a ,)zt1h* h(9; ,ujfdyown 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 atoi 5y,t ie oqx5i--ms: 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-restraint chair, an engineer consovzoa./ ;ju sh0rk18biders the following set of ca; h/b.ks 08u1rzojov onditions:
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 to3 2, mq;o/ cmwmivn(wrns (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 simi6x j/-2vhr0 ma7dcxfblar 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 cjrhf2076x/ -camv x dblimbing. 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 alv28u l. y.umb d4wnp6 " 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 /w,po*u16 fy:w bfbko 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 asc:n h 9oxkbr 4v 0+ t45zd++xqeszw.qwoending an ice field inclined at 21. + o4bo hv5r4:zq .xkw xs+nedzwq+0t90$^{\circ}$ 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.