Why does a child in a wagon seem to fall backwarey kt0.ec3il8 mj( l7o3cblr* d when you give the wagon a sharpetc0o(3.lec8r3b yl m jik7* l pull forward?

A box rests on the (fricvzdzfei fpp1z.9t 9 --tionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seepfz f-it.v1d9 p-ze z9n (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of wtjlqojz7: tb: /8rh4an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratio64wkzz9 a k-i wql1t,vn? Can it 9 k4wa1t,z6zvw- lkiqhave zero velocity? Explain.

When a golf ball is dropped to the iumdrt x e*hf-zzew51( ac,:8pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so,5wu az*1 fmtir-8(zxhdec : e, what exerts the force?

If you walk along a log floating on a la2g s7jykkj9or/ .hqw nowm6. -ke, why does the log move in the opposite dorogjk9/k7wsqh6ym- .j w .n2irection?

Why might your foot hurt if you kic w/sldab(f0 t/ ,qvj7fk a heavy desk or a wall?

  When you are running and want 7/w-xgcd1 dltvl 0*vj 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 maxim-tg0vc* /ll17dw v jxdum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fineu(omic e/:f3h(p8x7m qemt8k thread from the ceiling, and a section of the same thread dangles from73(muomq 8xc ee / (pkfh:tmi8 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 grzl0fov:vs * v222br;oz ba e2yeat as that on a 1-kg rock. Wh:y ;z 20*olsvvebzv2 22rabof y then doesn’t the heavier rock fall faster?

Would a spring scale qag v1 zy;tj1 p5oq+ fdf(dr),carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, v odrf ,) (+;15zydfgqa1jqtpor (b) in kilograms?

You pull a box with a constant force across a frictionless table using an j3be3alw x1b -cls,/ x xv9zm5attached 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) reea1lw5xc-xx m9,33 jbbzls/ vmain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influed5e*g5f;tv euu e) 2wcnce of gravity there is a net force mg e u;vef*g wd5e5t)ec2u xerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forcenz(2/)n v ubxvh94lla2 nefb,) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the forcn ,4fl(v)uh /nbab 2xenz v9l2e needed 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 (Fig. 4–37) pulls wit2x 58:u ,cphdg 7qfn k3eypco9l;ovh6h equal force on the other team. What, then, determines which team will 23c oy7d8pvl kgqxuhh6 ;9enp5:of,c win?

A person exerts an upward force of 40 N to hold a bag of groc w1ur*tsc+0hp:pymjrq:4 xp4eries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, a:cx 14spr+ qw*0h rtp :p4muyjnd (d) by what object it is exerted.

When you stand still on the ground, h g zhji/0p.j1gow large a force does the ground exert on you? Why doesn’t this force mak 0h/z1jij .gpge you rise up into the air?

Whiplash sometimes results from an autom2j: m5zam7n wbobile accident when the victim’s car is struck violently from the rear. Explain why the head nwa:jmz5b72mof the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the b1pg/bk1*c9mwc tarxg,4ega (b ,+hpded of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, s(h a gcmt 1dg xa/,9pgk*bcb41+p wer,o it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it sdbx1obm3v96k:e d *nelhi71blides up a ramp. After the block reaches its highest point, it slides back down but t1x e k3lvh d91dbb *o7i6enm:bhe magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if ymy1 +e:d ah pm2h;t;pmou weighed yourself on an inclined plane? Assume the mechanis; a;ephyh:mtmd1mp2+ m functions properly, even at an angle.

  What force is needed to accelerate a child b8mneidrbx;ps7.8 9 don a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratc+br+ r 3s/t *+dkgx,p dbr(zqes a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960 -d v;moz -iptdfiu*(c.qcq95ih02nm$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o1qf5 q: lplal;f 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 c2qb 66jg21,ofoojcf hhk 8k5h ar in 8.0 s if the car is traveling at 95km/h? j 2ogo , 5ffh6qkok16chjbh28 -  

  What average force is needed to acceleraty dpnqyfy4h 7.nm k(kpqg-*4v o8 +6ote a 7.00-gram pellet from rest to 125m/s over a distancdy .4pqpfkmtv( qo8hynk nyg6 4o -+*7e of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticall90p6r rnl9cjczc eyj4a g9),zy out of the water with an acceleration of 2.5l e9cc4rc ,0y)6rgj99pa nzjz $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile tra 9k)nek pj22yuhw ;r4mck (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 maximum acceleratios*0/5-q sucn3ye vulgn is 0.0680 g . What are */n- uvq5g 0su e3lyscthe 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 t.hk942qb lle, s:a5tp3yjuz 3mz,rascale in a motionless elevator. When the elevator begins to move, the scaley4.klql,5p:,e3b 9hatj zzrtm2au3s briefly reads only 0.75 of the person’s regular weight. 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 maximum strength )+vz tfv h:x.csoj7 1-pkmny9 of 21,750 N. What maximum upward acceleration can it give the elevator wi+1-.zvk7)y fjt sm9pc: xo vnhthout breaking?    ( two decimal places)

  (a) What is the accelerati3 ogm1/psd0/j yfaapkew3 c )d+0 u8slon of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of toays c/0kdp) 03wa 1ml8us+pg3def/jheir 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 3h3x j1o2d yefd;9-l9 f(v acsd dl5k6z.9-m high. When he strikes the ground below, he bends his knees so that his to12la5dv9l-e y (3dz9f;dschfxd6j okrso 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 rests on a table. A rope x+5xc- py dqf.qh+ c mf4o59eztied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if d.mpfh+e -zco+5 q5x9 y4fxcqthe 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 basketballupy+qwkn:a7n1 g fe4fsp-9j7o.k . ee*jf lt. player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diag+l)jf0jzx35a ;kmdm zram of a baseball (a) at the moment it is hit by the bat, 3zaj +km;j) 5dzmf0lxand 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 650-N force)+0yvu.kju /-zfgqe ;uyz g7l must be exk z -g yufyluuq+0/z;g .7e)vjerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontallygau3 v +sct)j+ between two buildings 10.0 m apart. The sag in the rope when she is atcu jv+3)at+ sg 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 buc 1 5swnn5xvv.qe)p azm; c6)okket is hanging 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/ajbjm5*0,yxr)xw q(naj ; si.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new loey2n. 1wd p 4)ipjr4 e+i4r epco4pe7jcation at McMurdo Base, Antarctica, as shown i)yw1p i4o rp 2npc ij+jdee44 4re7e.pn Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behcsao fd 1c.(y7 (c)s .kaz*wnoind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locoo1ca.kfoaw c n*.(7s z) s(dycmotive 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 tobukdw .8e-a ;he bucket-pulley apparatus shown in Fig. 4-48. (a) How har. k-ebdao 8wu;d 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 begaon(;k/wclry /vhjz /mns;* g ;n, 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 (m37t up9af0 nvaass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contaciuy 1+5byojn4 t with each other, as shown in Fig. 4-51.yy15bjo+ u in4 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 the gro 9*:hsn ,lp6f6 hgnbnqund, and the massless frictionless pulley is 4.8 m above the gblh6hgn f*n6:p9nq, sround. 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 heavy cord of masux1)h 4f7vqum3vcm/l 7 qr9sz s 1.0 kg . Calculate the acceleras73uvq 9)qz7fmrulvx 4 1ch/mtion 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 kie uhbzepl74q(,hx 0 :rnetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required -wgaa8rklc5gn;( 7 bf 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 pm3wkr.s- nzu9 3v hu8train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the flsh38zwm.uk 3p9nvu- roor if you are not to slide?   

  What is the maximum wc*pd)cc: m 8o9r9wnu acceleration a car can undergo if the coefficient of static friction between 8wuc r:cp* ow9nm c9)dthe tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normazv b gc14 ha/11vkdh7hl street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a vz1k 4/7d 1hhvg1ha cbcar 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 decelerateile)kj7+by05pqt tt- at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30+ 2.t6fobuh nrmrn49j$^{\circ}$ 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 aa9lh ,o giu*p81dc :sbsphalt surface have a very high coefficient of s,si:a gpuc 8bo h9*d1ltatic 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 kinetic fri ob/q5su0gb+jo i5o , 0jy6rudction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a maa14(y.w73w 7 o (q ugj(fkvi3au pmfcuss would box A have to have a.1y 77upkmu4(wcgvw( qi ffu a(o 33jto prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far ay bt/2 c-b-po3vq/jowill it go, given that the coefficient of kinetic friction is 0.20 andtvbq/j3bap/ o-ocy 2- 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 on a horuzn02y gk3y9n p2x99vhul0zo 1mx /wcizontaxkny 1u u2zc90zyhgm9l oxnw0v2/39p l surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of s/f0v,/s ttmk ztatic 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 th/ 0k,vfz mtt/se crate slide against the cab of the truck?   

On an icy day, you worry about parking your caatm8 80 ew+bl8dp tgbx-5jo p+r in your driveway, which has an incline ofp+p-g xtb8 o5m8t+djab80w el 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 2)dapkok3y9v486dn/ uuwl a ul a24k3f8$^{\circ}$ 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 as ejsse1hg iy. p5jq:.*zi*/ pngle $\theta=22.0^{\circ}$ 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 init0 75r1tsfx0ab prf6bv ial 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 speed of 6.0 poe-s6dx5)4g jj hhdkb59v,o$ \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 again ey8+sl1n3kjj 2ahx2q;r8 n tjst a rough wall by someone pushing on it with a force direct28j;8 jl1+t jrenahk xnyqs32ed 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 dah6m x;z:t ,zu+jl/nscwa9( :nb t+zwmd 0*dvg ngerous projectiles as they melt. Consider a chunk of snow at the ridge of a roofmdnl 0gaxd+z:(v9;+t* jwnus ,h:/tmc 6zwbz 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 stoppwb2a9s4uu2+: lw mwjying distance for an automobile traveling at speed v is equal ws9mj b4lua:2y wu+2wto $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 dashboaru() y,ea :e:x.w thmaqd of a car slides forward on the dash when the driver decelerateaq,:maxe:( . h)twuey s 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 m2 1bosq,5jlcc is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to t/sd c 9voq84hxhe packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid xqsv89o/c h4d transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction bjegzm,y 74np 7etween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can nl.p 9) ps4womcoast 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 appr z)z a/m7sa*zloximately 20 g of blood is accelerated from 0.25 /) *mz7z slaaz$\mathrm{~m} / \mathrm{s}$ 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 th*wzwwv 3 fj4 5z6vmxs3e deceleratwzm6zvj33w s4x5f *v wion is no more 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 producgrkskjr. 0;lb5 h(b k4ed by an earthquake is a , and if an object is going to "ho ;j. blkr0( bk4sr5gkhld its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident (-t.lz qkvmjge+:u,l involving two cars, measure 72-m-lzqtljug(v. m+-:ek l,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 travelz2rg4,dvkxn,-- vj tb ed along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore fri4br-n z2vt,-dx j kgv,ction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Towqz-q+ fwd :3gxe, zrc0er of Pisa and falls 55 m before g fz,e+- cxrwz3dq0: qreaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stead (+ 3m1rgiucpybo :hna+l4 7sny speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having (7 yh+nrm4npa:gbio1s +cu l 3to 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 cix;g1+zyg9uc,k* tjfs7-p gi wty. An important consideration is how steep the roads can be so thtx, pc;wg- z9+jy*kfg 7iu1s gat even low-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 experiments, dangles hevl37zi lh+pdumy cv0+4yr v 6(r watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58)v4udl+pv 03v+ lr(hzy76i ycm. 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 supermark0s-fh1 2/wq: mmw kcabet, there are to be several ramps connecting different parts of the0qfc1w w/:s2-bhmakm 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 ks;23v9: p w(qdb onc)tc;dwxto lift the piano (mass M ) using the pulle;2c9 kbdw(p;cq nsvx ): dowt3y apparatus 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 5 v; n3ird4rv(sovi9 h3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-resv3xa5 t 6r1 rrilll4.ltraint chair, an engineer considers the followin .a536 itl1lrx 4lrvlrg set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of mwv4x algm;o 3v6 opst29ua;(660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's rt+o * :rv3ndmoope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm drno3vm*o +t: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 ixvi;e*wv+s b o*,tbrs :;hcu*s using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reac*d a4vs)+hpxcmh 6r8kh a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascenrqtf9ay *uap*84uv; a ding an ice field inclined aqa8*ay 9fap4tur v ;*ut 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.