Why does a child in a wagon seem to fall bac:zl- +ma8tn nvkward when you give the wagon a sharp pull forward? :-mnz 8avtn+l

A box rests on the (frictionless) bed of a mw9 d+on(f /fvsh9ru zj8 5n8struck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Dind5 f 9fjr/z8n98wvhu(m o ss+scuss 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 on it? Ex 7euqyt(v;r 7br,w- nmplain.

Only one force acts on an object. Can the object have zero accnbx i9*xs; ;b(qnk2c2 q6zdkeeleration? Can it havbnbskk;nix9(ezx* d2 ;2 qqc6e zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back ucpemc0 y8l .5w+rpdy* b/p r;wek3 v:bp. (a) Is a force needed to make it bounce back up? (b) If so, what exert5 wl*d+ pmpy bk3 r /:vecbr8ypc;e.w0s the force?

If you walk along a log floating on a 97* +vqpg+yifjwxnm j*x9n /xlake, why does the log move in the opposite dv**7x+qpw xm gnyfi9n +x9j /jirection?

Why might your foot hurt if)v0m) nzehj0t you kick a heavy desk or a wall?

  When you are running an1eapa8:s m;zsd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum raz;s 8pam1 e:aste of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from tx .gf/*(8akmh/ zdljdhe 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 perso/* /z8lj.da kdfhxg(mn gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is:pxyc q26*y4ined(rw twice as great as that on a 1-kg rock. Why then doesn’t try4xiep2*6yqn d :w(che heavier rock fall faster?

Would a spring scale carried to the Moons xz42hn0 e2kj give accurate results if the scale had been calibrat2s4xz jk 0h2ened (a) in pounds, or (b) in kilograms?

You pull a box with a constant force q2c.k:z type f,9gl)b9bllu8 across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontbect89,gf:ky9 l pb)ulql 2.z al (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freh c9 (-gbc3szfely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the os-(fccb9zh g3 bject exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on su+ +zkttinka.2zs o00bre :: the Moon with the force needed to lift it on Earth. Compare the force needeo2aus tbi: 0zs+ ez.rk kn:0t+d to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Figi0x out p;u6.hp8y.d n. 4–37) pulls with equal force on the other team. What, then, determines which teap;pt6.n h0.you 8idxum will win?

A person exerts an upwardog 46 s,u kt8.hgooy-s force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerteysghos ook.,gu8 6- 4td, and (d) by what object it is exerted.

When you stand still on the ground, horxgcgc(;jdg wr 14-e:w large a force does the ground exert on you? Why doesn’t this force make you rise up into the ax4rj :c-wge r;(dgcg1ir?

Whiplash sometimes results from an automobile accident when the victim’s car,ej nd a8irm.. is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it rea8 dij .r.,menally?

A heavy crate rests on the bed of a flatbed truck. When the truck accele;z+zn/wu4gr okl 9l7r 1ta x3()vvqdrrates, the crate remains where it is on the truck, sovr)9+;7l4zzgrdl uwnaxtqk 1(3 /vor it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itiy(fw g c0v5blts) 4);x;uyx es highest po svw0cf y4 ()lui)x teyb;g;x5int, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read-l ;i :xwvp*fx if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at l: p x*-fvw;xian angle.

  What force is neededu ka mdp**fta+ p9u:*o to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik*3 ufcuhugk 07e and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mus amog9t.5 5dcg en14fhfx/, lzt a rope 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 ov 8 jgpzi4r0csy1,m489eql ;i0ueqb zf 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 requirdgv uh/w.1bvhad r( iy z6.*b)ed to stop an 1100-kg car in 8.0 s if the car is tra.d6).ygu ahi*v1/wz r(bh dvb veling at 95km/h? -  

  What average force is needed to accelerate a o h:hfut y-ubuvuvr4*(r8 e/8 7.00-gram pellet from rest to 125m/s over a distance of 0.8oe8b *8uuy/fvh:v u(rthu4 - r00 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelera8 ed.j86 5 jajuebblg-tion of 2.58eg.blj8dj juba65 e - $\mathrm{~m} / \mathrm{s}^{2}$ 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 opwgqco;h :elne*9 rarb 2**55b( biy (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 s7ye qg+gj +ppq.uy1 :zo that the maximum acceleration is 0.0680 g . What are thegyp u +g7ej:pq. q+1zy 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 elevatorp;m67e; tr ispe+ csv4. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weightpete7rmcpv;i+ 6;4 ss. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a slit40wy 6 k.ut:dx:y maximum strength of 21,750 N. What maximum upwd:yxs:406k.w u lytitard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg oxuunvpcpt wc /*3 bwkv)2d* / bx0;3rincluding parachute) when the upward force of air resistance is equal to vu)ctr*30 c ;*xow bn xwkp/puvb/d 23one-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 amwxukif56lnn1xw,;5qr t i. ) house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance n,)iwmku 5tq x6 1ix5.wf ;nrlof 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 tied to the box runxb+ *x ypg.vvjr39r;s s 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 p j+;.rs*vxy9b grv3 xbox 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 pi1r ,1mvj 3)jdmhw (npm3+xnc layer
(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 base q 3smfuaqtcx;; -b54js ksh15ball (a) at the moment it is hit by the bat, and5 5sb cuathq4k3ssxm;1j f- q; again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second )t i: db2z (wdmy5ck(n650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your anb c( ):yd(t2d5iwmnzkswer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw e5ff8s6j (sdezb1j/v een two buildings 10.0 m apart. The sag in the rope when she is at the midpoi6e jfs8e5svjz(1 /fbdnt 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 hangingm1f k x(pw6 u0ni-m:m 3lbttz: 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 14a 0u w(0aq8jgt7iqal ,.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 hox/78mxi8s mejusing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the smi x/mxe87 j8forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 ot bs o5xl0j bhzzh)ka48 6rq0l4-5kpzf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling ba4 z4oh5b-6z lzb0)x 50kj lspkq8thretween the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using th 8v ajr.m3jbiv-, zof.e bucket-pulley apparatus shown in Fig. 4-48. (j- bji3fraz,.8 vm.v oa) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, aj73 lugppvt +c04o9i x 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 (massqun2(z qv1-2hd hi;zfnvk-b* $ 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 hum4vcdq 0gvp :fk0 )c*orizontal surface are in contact with each other, as shown in Fig. 4-51. A upm:cv0 *4 vcdg f)kq0force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the grk- oqrh.w84*gnjm*baound, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is relegq* * amb8.-wjoh r4nkased? [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 connes)m ,dn m9iat1cted by a heavy cord of mass 1.0 kg . Calculate the acceleration of each nitam)19ms , dbox 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 35tda3kzvu r +- i:cy309 ja 2 dauyjuftd3/ki-0$-\mathrm{kg}$ 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 svcu2 sg,ynkvhudi:r9 /;2 6b to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerumv:mbcm)42d2lnp0 v jv g,1qating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? 0,jl4m:p d 2vbv) u1mc gvqm2n  

  What is the maximum acceleration a car can undergo if the coefficient of :x4t 23dn9mhq1iexb/lbr)f*-pp vh e static friction between the tires and th* h3i:q)lmpbxvd2pnxf -4b e 9etr/h1e ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemeka89m+yo 7t jrvfe3l: nt is about 0.8. On howv79r+:aeyoj3k m tfl8 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 -4.80 4b i3z) xozfn83m7 zi ya29*qnwrvh9h$\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough +n0dcs o 7pj/c 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 coefficiegfokxfu k7f6 *s yu*,;ozj .4vnt of static frizv j sx o;4ffg y.k*o67k*uf,uction.

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 fby ydht 65yui )uwt*,jc .ll z:n:b(-rriction 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 (fr+ruoc/g n6 (Example 4-20) how large a mass would box A have to have to prevent any motion from occu/u6g f(r+ro cnrring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across threy8np5e5+ ge *k7wwhe floor. How far will it go, given that 8+*yhene 5gw5 k pre7wthe 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 owf n7p ftt3vfuji/49+ n a horizontal surfacef ui+j 47t3f 9fn/wtvp (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. b4)))(pjab9dltkry p The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab ofrypa))(4d9 )bjlp tbk the truck?   

On an icy day, you worry about parkinr + pxatz4y07h.mr m)wg your car in your driveway, which has an inclxm. a0z)p+4mtyhw7r r ine 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 ofae( 6 sj1t:a18g 1fsl4b2iukd tesumx 143mslide 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 (x)ga2g vjof2plane 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 a i+8hsn3u9ggwk86 hr 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 th,oz mad(oeo; y2px 4*xe top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in pladm8k lsnt y)r6/0.m hrce against a rough wall by someone pushing on it with a force directed upward atlyr/ )hd kntm.s06r m8 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 becthnsa5+vl;j +u7 k3pjome dangerous projectiles as they melt. Consider a chunk of snow at7++uljjk3s5pnt va ; h the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance lps8uk,w*7l y i cpd9/ i.vw7zfor an automobile traveling at speed v is equ 7dlp9lkvi 8uy /wcz7s*wp,.i al 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 o1 la+cv69:wkb. k)v : vcabicnf a car slides forward on the dash when the driver caclcv bi.+a 19vvw:k) 6bnk:decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an ini /xy8xufqy mnlj. -ee46v4l 3utial 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 fromt /mhqofz(e :2hb3g 1c))kalz.dms (b where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero szsz1ogaq/ ) efbmlkt(( :2bh) ch.d3mpeed. 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 coefficien4x3iufnpi2w y* df9+st of kinetic 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 kg (incl ) mb*kr g(z48iu-ao gcyg:i1cuding 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 simplifiedftk3 mypdk2g-z yj a.q)9;5yf model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25a) fpjyt- mykdkz.f9 y2q5g ;3 $\mathrm{~m} / \mathrm{s}$ 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 angr3 lw+ pnf5 4iml*e.l automobile crash if the deceleration is no more than 30 " g 's." Calcu.r+m wlfig4*l peln35late 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 emhq1+zp uev5g0-ze)oarthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groum1 e poh) +eqvzg0z-5und 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 sc3x6 px)r9jmyw rsi 3v/ene of an accident involving two cars, measure 72-m-lp)9/siy3mr vrj63xwx ong 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 means that for each 4 m travelevet 8,nkd7vc ;d along the road, the elk,8nedc7t; v vevation 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 the Leaning Tower of Pisa and .k9,yuav;.h *xboxesfalls 55 m before reaching the ground with a speed of What was the averageu xx*9;.bos. ha ,kyve force of air resistance?   

  A cyclist is coasting at a stl6ka)j * ;zxpweady speed of 12m/s but enters a muddy stretch where the effective coefficz j)px;law6 *kient 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 will be the speed upon emerging?   

  A city planner is working oa,7ojo1p mem lgq ,m.1tiu23tn 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 oa1ommju. 27p3i1 e oqt,gl,tmf 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangs e yp*awy-w9uf7qg 34les 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 string make*uwye 4s 7pya93fwqg-s 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 didin2x j,m c(hv,2p gp))r0vbq fferent pa0 ,2jqv) x,2rh( pbg)mpndvci rts 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 ,0usp1g og4 b:zu)cq oey+qy0) using the pulley appu,qygc 4)p: g0 o1bz+sqeoyu 0aratus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at -cgw k+ced06k 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 considers t b+rhz;bym0* hf3bqasvd+l6)he following set of conditionsmhv z+ dyb 6r* b03s+ab)l;qhf:
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 metricc0xobih35s/riyh o+nca* o86 b lk23b a b*db* 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 dx hgs)0dz ;p1safety ropes of 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 d0z 1xpdh;g )sfalls 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 uia0hc3 p lejctrw (; ,*emp+5ising 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 maxim3o)oq :7tqtu5ewg iqr1vrqs3. / la0oum 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 ascending an ice fid6n3k3ce8-z.u32x nb5y9o: t yurwis2cgmtneld inclined at 2g2o 8 93. 6uxyi n 5unrk3cyb:2 e-stw3ntczdm1.0$^{\circ}$ 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.