Why does a child in a wagon dxd7)iiwsdne)bn ,5*rw ,w,0 eyror4f +3 zmnseem to fall backward when you give the wagon a sharp pull forwarn y5rd 7 ,n we)wsrz)br4fi*ox+,dimn,dew 30d?

A box rests on the (frictionless) bed of.3,gj8n+klqmq txnz0 a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discus+klz m3x.qgntn q,0 8js 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 ne +c bmjl ,;ytos1k1dn+v56 hnum2bv,o forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acce36g)hhby(le aqbjp k0fh62ave / if d1f j:i,)leration? Can it have zero velocitydgbklh6 , j6()2hva iab f/:yf0jqeief h 3)1p? Explain.

When a golf ball is dropped to the7d3 bsge;q/t pt;go 1q6 v+ip)ecmq -r pavement, it bounces back up. (a) Is a force needed to make it bounce b g;+/1tqe-3vmrb 6g7dpqti) sqo cpe;ack up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move wbyo8 . ve,ju;-qpff7 in the opposite directioj-yuwof; 7,8bv p.q fen?

Why might your foot hurt if you kk aofa*9z ywy +4gi.y)ick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decez8iagkkk+ n81gw j 5bb 2-;t1q rsew6wlerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum ratnr6- 2 k absztjgw8kkew581i+gq;1wbe 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 section of t-iy+jw6(q u tphe 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? u jwyt6 q+i(p-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 6/gcj,3w(g:fkn sdvu as that on a 1-kg rock. Why then doesn’t the heavier r,(uvf wg:6nk sc/3jdgock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale had +t1 vcxj :fg;rkryyvn5, 93ul blxfju r,yv 1c:5y ;9n+gktvr 3een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a qnw frwvl* (fth0-:+ efrictionless table using an attached rope held horizontally. If you now pull the rope with the same forr(0*wv-thlffeqn +: wce 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) decrease? Explain.

When an object falls freely under the influence of gravity there fvbe.b+hlmt g0ugyt6e.-j2( is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the(2mlj ef tybg0-euhtgbv +. 6. Earth move?

Compare the effort (or force) needed ty,i l2w09 i lf1zt qjavc*6:zzo lift a 10-kg object when you are on the Moon with the force needed to lift it on Earthlqt9i:6y zj,z*clf2w0i 1z av . 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 (4c7xssypurit45 z 4mthird law, each team in a tug of war (Fig. 4–37) pulls with equal force o45yts(izp4m 4 rxuc7sn the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descri)xa 7jf9sw7qobe the “reaction” force (Newton’s third )awf9 xqs7 j7olaw) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how abj2 6j fie9f+large a force does the ground exert on you? Why doesn’ti + 6fjej2ab9f this force make you rise up into the air?

Whiplash sometimes results from an automobile awos9,my wb /q(ccident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems towmwb/9s,y(q o be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelera v:v5c1p/pqzi tes, the crate remains where it is on the truck, so it, too, accelerateqzp iv cvp15:/s. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches 4gija -og87vlits highest point, i j7vgilog 48-at 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 if you weigab(ith l) 6ilneruf96z z+ +6mhed yourself on an inclined plane) l ble96urzai+66 fhtm+ni(z ? Assume the mechanism functions properly, even at an angle.

  What force is needed to ac;8phv+y jq6ihcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N zu tzn.n) dc94dad5k3accelerates 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 use iv-u:w)aql, hd to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a aim;ju7*qu 0a1dj; v5cz o u2r$76-\mathrm{kg}$ 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 p:a )(ocgi5 eb1100-kg car in 8.0 s if the car is traveling a:bpiec )o (a5gt 95km/h? -  

  What average force is needed to acceleh:zvsq-d0om: rate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifqh: vos -mz:d0le?   

A fisherman yanks a fish vertically out of the water with an .jbhr:y xpa/-y,oz0c acceleration of 2.5 b,a po.0hr -cxj: /zyy$\mathrm{~m} / \mathrm{s}^{2}$ 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 evhud4a; 5bymet r/ z,mq6l0 ;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 ke.:+ bo7n;xwi owu z2bg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supponzb.wiwx+:ou7 eo2b ;rting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. Whens5v(7+ cenkkr the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleratiok versc (5+7knn of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maxim6is99xn7/vd ju le(e)mjs g,xboy1+sum strength of 21,750 N. What maximuse /dgy)i m us o(9e6nvlj7,1sjx x+9bm upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of z)mcj.l ym2rd1 t81wy4gft3utwo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance izr)yftu1.2ym3tlw14 d cgjm8s 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-mzebz6t8ejfv*q p/3r lmeh6*2rbcte2,c, yj7 high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding jcc6ybj2*p 6q b8z z 2tl hrfre*e,,temve/37legs) 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 resf0s8gofs(j 0;3hzb sub ti13c ts on a table. A rope tied to the box runs vertically upward over a putzc;0u0i8bhs ff1j(og3s b3 slley 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 basketba7)-a*t i/jlfig a nqa;ll 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 baseball (a) at the momevw )pni*98xq3,v pbrp:isb9q nt it is hit by the bat, and again (b) after it has left the bat and is flying tov3wpqi: bp r *si q98),pvn9bxward the outfield.

A 650-N force acts in a northwesterly direction. A sex jqee)ysk0w0 t+u7 q3cond 650-N force must be exerted in what direction so that thetqe+se0ku7 3 x)jyq w0 resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hoh+udt k1k* .ewif6h1gixg1 i6 yxevnm30(q+a rizontally between two buildings31g x+kh.eag610xki(y iqe1m f+ h*u iwn6tvd 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucke1 pr/xby wr;cgpt,95gt 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 14.0((0q bw+de72f xsjo qi$-\mathrm{kg}$ 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 u p47qx* u7jf ygxj;m(new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The*yj; mg7ju(px4q fxu7 sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fb(vpau09, ec.b z )etzig. 4-47 . Determine the ratio of the tension in the coupling between thvbzp9)(.cubz e 0 e,ate 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 the ;p7kk6 (atavj-23f vxxth1nx bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she vvt3k;x7kj2 1 6f(a pax- thxnpull 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 b wjxnagt1 7p9abz 7si9) /vly.egan, 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 blocwn .u+)n9d6b91m dp-g flf uvvk (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are t pn 3 byp8 x;a9apvf(4* 4jtwoj5j4lzin contact with each other, as shown ip95awypnx *p;b fl 3tt(jzj4 a84j 4ovn Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the ground,y -jw 09fdvg3by4*/pzrso/h o and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ghp0ry fy o4jsz/9-3bg *ovwd /round. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table aq*t4c ) 0dzhndre connected by a heavy cord of mass 1.0 kg . Calculate *hdd 0)tzcqn4the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic frictionnlh/0x0p 01uj g; uhtnbvnh *0 between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to)6ilovm k 0imdh 74o9f 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 st221kad6 mzs( xxw y1 )dtunwr3anding on a train accelerating at 0.20g. What minimum coefficient of static friction must exityswxr d)wm k 13nd612 x(a2zust between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the cq )wf 1;g isgewk,/swc8)f)cd oefficient of static friction betww)8 efwf /qigcs;dgk, cw1s ))een the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubbeux*j oe y9rp-hn mas+3k1 37grr and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you ljxm nu r3h3gr9yk17s-a e o*p+eave 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 b3-w/)w/lqvep p;jfo 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 uf (-kw:nok+yk mi9 k-lnco*k;lt(7vrough 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 wit)w rj. giio64pk2v2pdh an asphalt surface have a very high coefficient of strj p24gvk piio26 .)dwatic 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 frit3// apmr5g dwction 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 4-20skfsbk+v6 t3 9) how large a mass would box A have to have to prevent any motio +ssf36 tvk9bkn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Hltoe*s,f2 4 bfow far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial b4f*2,tle o fsspeed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in congus,5b) e ml y6,0bhntc:aah-tact and at rest on a horizontal sur 6a),yteh:u5bgn m a0bl, -chsface (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 static fricta s*blmnwii c s6eq,b3o8,);uion between the crate and the bed of the truck is 0.75. What is the m,a)i3 u;e6s8* csblo bwmq n,iaximum 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 inkxiq.) z 4g+ z7x4afpx your driveway, which has an inc.qkgx4fxi) x 74zzap+line 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 acmf4w2 :f:rlxj)lha86 be.na 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 a plane tilted at an angle 1zex +nhx g,g2 $\theta=22.0^{\circ}$ 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 speebu-x8yvrrsa3vs uvj l0 t42-/;yg;an d 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 t+i sxfi;y stjgop c.2:7:l gl3op 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 place against a rough wall by someone j- x - wgunk8d7ua*fx/pushing on it with a force directed upward a-jn7 8*u afwxkuxdg /-t 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 projecti0dq3u kn s,y,y3d:9lu:cfrg oles as they melt. Consider a chunk :,:9u, yy un r3sl0coqgdd kf3of snow at 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 for an automobileor0(y8t6qlh (c; uuyz traveling at speed v is et (uzc8oyu lq6 (0ry;hqual to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when mvu/c2; le dv9the driver decelerates from 45 9 m vd/2vlcu;e$\mathrm{~km} / \mathrm{h}$ 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 c+twgn wsjo.4gg;+*jgobr t 681 wpp3an 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 the pajjj1 r; f4:lldcking 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 distan1 jljrj; ld:f4ce, 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 kinej9h k.w094v6zlgj f mutic 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(5uh0+g ,ehdvlo 7st 9uh b +yr8i4gue kg (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 heartja8 hx t*ps;+evx54 d-q-08ov vgm(cu 1vkpsd, at each pulse approximately 20 g of blood is accelerated from vsp180hs m xv-c;kjd qe a(p-*o+5 d4u8xvgvt 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 deccgo0 sw ewlr9tgood xu6x(m:) 4r0 ,6veleratio4v o0 , :wg)owxr6t(m9er6olcxdu s 0gn 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 acceleratio o;de)0p 4ejax2eed1cn produced by an earthquake is a , and if an object is going to "hxc 0ed1e)ejp d4 oe2a;old 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 involving twooe(0wk1bf xzkra hf/v+8c j*0 cars, measure 72-m-long skid marks of one of the cars, which nearly came to f 0h81c/z fobwxk+ajv0*r ek(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 eacj.xb9xij+q 0;px2j2sw 2ywzn6 l rj.lh 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches rw.i.lx22j pn+yl;x wjj02b 9jx6zsq 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 95 4vrxrh6lrbPisa and falls 55 m before reaching the ground with a speed of What was the average force of air hr 46rlbvr9x5 resistance?   

  A cyclist is coasting at a steady speed of 12m/s but entemqccspp 6q w(nmk8 :+m -f:7fars a muddy stretch where the effective coefficient of fn6spma mq(-q pc:mf:f 8c k+7wriction 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 on the redesign of a hilly portion of a city. An hdy)q*g*p-wd n)wnw mb) 8f(q important consideration is how steep the roads can be so that even low-pow n-w(w) )dmd ph8bgfqy wnq)**ered 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,ota1w,4 f 7 ;k/gniurq 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 string makes an ang,uai;4fnt koqg/w 71 rle 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 sep d.*kqzc z*w*veral ramps connecting different pa*z zcqw*kd. *prts 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 forcg erv/1q5dve)4v5lyiygtw;-nup y95 e F is needed to lift the piano (mass M ) using the pulley apparatus shown yyy/ 4r5e5piv 1 )e d5vt lvnwuqgg-;9in

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 acceleratin/cs)lylu5p0nwt7ax*fn oszsp ) a 0+,g at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a ch-1 mnlq9n+d:dt dhbvr1. nv n8ild-restraint chair, an engineer considers the following set of conditiondn.9h+dt bn dnq:-m v18rvl 1ns:
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 2sq0y. z p+ixjm3 :37rezkhrvmass of 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 lennfhu+-u:pk 1/gn,k oy gth. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m ahkon+u1gku, : pf-/y nnd then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "h,oajx-ahty,vf78 vnz8zt+8 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 bui, ;ar,s: y 3q;xoxn6ql9mwo jalding is allowed to reach 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 arem,d oflwmd-0eq/a6 tp1 :w7 vuc//dvi roped together are ascending an ice field incline,amw:vmo pi dedwl7u0 qv1/ 6-ftdc// d at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.