Why does a child in a wagon seem to fall backward when you give therh9c wimo 7rc-pwp zn)y0 3l(8 wagon a sharp (0lz m 3rw p9icno8wc )-hrpy7pull forward?

A box rests on the (frictionless) bed of a truck. The truck driv)t*e4vqtk kv ,l4ijl .er 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 seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is ri .4ik t,tv4)ve* llqkjding on the truck

If the acceleration of an object is zero, are no forces .-9iv3m o f16fpqjkmsu92h(n hedmgl ge- ) u,acting on it? Explain.

Only one force acts on an obj)w fbxxl; 5xo*ect. Can the object have zero acceleration? Can it have zero velocity? Explain.xl f) xo5xbw;*

When a golf ball is dropped to the pavement, it bounces back up. (a) Is f8)kr cikrqb -kaz0 83a force needed to make i-zcrbkk 8 8qi03a)rk ft bounce back up? (b) If so, what exerts the force?

If you walk along a log floa-cl qwmoa6w7 zv+nht9 * * om)/zyh:hoting on a lake, why does the log move in the opposite directionh6l9ozh7y no +qzch/-to):m*w *va mw ?

Why might your foot hurt if ,4mddz*t,f abln42j low/u8 syou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. rjz3udh w3q(a(fcn5,0lco7 e (a) What is the origin of th(7,new h dcaq35f0 3c(ljzoru e force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of tc7 yz(z(jd3myllk:;f09czi4p dsxd .he 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 person gives a slowsl(4d:c ddyj;zfk9 (.l z izmp 30c7xy and steady pull? Explain your answers.

The force of gravity on a 2-kgmn h0h7aws/1 o rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rso/n7 hma10wh ock fall faster?

Would a spring scale carried to the qy jvk4mf/tw8t(yf/ x p*de24Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilo2qyvf t*fem(/wpk844ytd x /jgrams?

You pull a box with a constant force across a z.(ncwl-d 1b/y a+hcefrictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box rclhz-n y .cw/ab( de+1emaining 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 6,- bst6h;avza-ih i bthe influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exer b6iha stv-a,bzhi-;6ts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) neede o48m.x(us hwdd to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on t8osdw h. mu(4xhe Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pu/j)0c nd o e6alk7lz5wlls with equal force on the other team. What, then, determines which teao 50/lj 7de)czawkln6m will win?

A person exerts an upward force of 40 N to hold a bag;jfh p;p. ub; )jobvn60plg6t of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it opf; jpjvu;n bltb66 0h;pg).is exerted, and (d) by what object it is exerted.

When you stand still on k 33w( ow zpx79szti1by;8cysw5) ldx the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up intolxd1 x w 5w)by8c3ki to ss;yz(39wz7p the air?

Whiplash sometimes results from an automobile accident whe8a h ;y*1rfaoaq 4.muyn the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thr*84o .aaamuq yr1f;hyown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. sapo3y:n tb huma(1uevr72* /When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the cra*aat y/eo(r1 m:s vhb3 p27nuute to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesxr9ippz - i7bsh98j3y its highest point, it slides back dow 99hr87pixi3p-jbszyn but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wo1jet9wuk ,gt m1+m8 ieighed yourself on an inclined plane? Assume the mechanism functions properly, even at an m 1ewg9tt,o8+ kuj1mi angle.

  What force is needed to accelerate a child on a sled at 1.25m/qal4( gxr6wi/jj 7 n)ls$^2$?   

  A net force of 265 N accelerates a bike and rn :iefh/o -wh0ider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension musq buc /5whi /pmckbj+o.ze(/+ j8a4lzt 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 of a u y3q:z 59blyv$76-\mathrm{kg}$ 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 oq ,p+hkq7ao 2to stop an 1100-kg car in 8.0 s if the car is traveph qq7o+k2o, aling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram p3 /vus4d v0fkpellet from rest to 125m/s over a distance of 0.800 m along the bark0u p3v /4fdvsrel of a rifle?   

A fisherman yanks a fish v:de3k +sf(i.nt hmj,l ertically out of the water with an acceleration of 2.fh+id.,j3 : kn (selmt5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 c6 isd:q4u2bg /em dudu8or)1pover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is tofpa 3d :td9lh7jkbf8 3 be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable h3apdfk8 9:fd37b jlt? 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 e6(q4fr+ u iod2hkhav97wr3c wlevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Cac+ (9v rdrqahuw3o24hfk6iw7lculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has abe6)kxb*h)qoobp edy1e: 55g e. xr t; maximum strength of 21,750 N. What maximum upward acceleration etbbkep5 r:d6gybe)xx;.h oe*1 )5qo can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 13+45gbc) 5b/lxsxjt kc 2 kg including parachute) when the u+bjx x t5)lgs/5ckc4 bpward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3jch/6 vn7mt-c.9-m high. When he strikes the ground below, he bends his knees so that his torso c 6-/ct7vjhm ndecelerates 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 tied to the bo eu0sq7g1yfp .6g)a9qyejc d 0x 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 the weighdpugg eqej01. c)y609q7f sayt 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 diagra8z kf0u 1k33zgw9vg bnm for a basketball 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 thezl v t2;p0l9w-5rc zhe moment it is hit by the bat, and again (b)9zw0trc2v -l5 h pel;z 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 forct*n8 qprrv- y+e must be exerted in wha*q+8v-p rtynrt direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a -fsln - ,0hipuho2fv/jv,h;xsi: mq7"high wire" strung horizontally between two buildings 10.0 m aph,smfqv7p nh-v :;0 j2fo/ -hilsiux,art. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless co/suw ,ngjk2 x*glx-)d4uxg e.rd 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.*uu9rph lrx 8q8r /)eo0$-\mathrm{kg}$ 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 locatj5 ebxnni n)crx 4jwmh7q)5 *,ion at McMurdo Base, Antarctica, as nx7jw5xb qh ,cim*j))ne54 rn shown in 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 t4rwy9x ; rrp8 4.jazqlw0m0 ubhe same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the loa4 x w904rympzq. 8wbr; rju0lcomotive 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 i0st;klol02+yout -xupward using the bucket-pulley apparatus shown in Fig. 4-48. (a) oi+0k tlu2; os tlyx0-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, a 6x +m0n4 e5znyk::zoyp5$-\mathrm{kg}$ 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 (m-7rf3wajo h*2fh 0ywpass $ 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 hori0w3g ymq6 k/ose4lrk (zontal surface are in contact with each other, as shownsmlo4kq3 6kgy w/0(re in 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. 4-52mhcu i-66zj*b are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system6u zch6ib*jm- 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 pycj1k9 +jzd:5)j gat heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diag dcktp+ j15ga z:y9jj)rams 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 lsfh9 7 xp;4g(p g/+bl2an*gdyjf;bx kinetic 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 to start a x*bhmjh.4s-p 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 accelerating at 0.20g. What mi1mjgm5 zo+)tk nimum coefficient of static frictimk5j) 1tmz+og on must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if t beaggt;v,pg. 3jv/ u.,ad2ivhe coefficient of static friction between the tires and the gro vd/3tgjigav v,e up2,a gb.;.und is 0.80?   

  The coefficient of stw. ,n0fenuj.o9.c m pratic friction between hard rubber and normal street pavement is about 0.8. On how steepwn n.,.9e mrcf p0.oju 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 -4.8 ;4y8efhvrht 3t:y2k8az x tbt39dlr +0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 -l;bw p49 0ng(ha9+c,blt nudlu*rfprough 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 s:*sgqa l1 8wdhd9 azw9urface have a very high coefficient of static frictlw:w 9g9 hqaa1sd8z *dion.

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 fricti kjw7-hk an1pxf7e9 i*f8 eys-on 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 Figu-eug* ;-q9: nhnmfkz. 4-32 (Example 4-20) how large a mass would box A have to have to prevent ae;kh:-nuuq9m* z fn g-ny motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How q6s7o4lc( :mlpewo2h far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiall274h( soploc:w qm6e speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest jdk+5+8u fqke on a horizontaqf8e+5 +jdk ukl 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 static fricr; tbwcdq*2idr7p 6, 8:njsdp tion 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 avoid872rd *:rbj wc,d6p s nqtpdi; having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has anf yg.nc7/ox)z z ar5djild,56 incline of c6/yr n5 .ji)f5,xloz dz7gda 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 yh4c.rpbqt)tb0 -x9cs+bfp+a 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 Fit.q4q p, co xn/0mm6dyg. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of mjs):z)k)x j b3.0 $\mathrm{~m} / \mathrm{s}$ 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 o5t m .pdn*k41o0uumhp f 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 somezb z* bd9a+wt2one pushing on it with a force dirz+zbb a w2d9*tected 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 slipperr1ez7m f.irh.wcv2tk4w o*0w 3-r dk3 or 2swty roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridg3 v3cmwot0k1 wkrowtz s . 7*iw.efhrr24-rd 2e 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 automobile travewp zf t7b(-7euling at speed v is equa7( fb-7zuet pwl 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 th,p5qgb+jppo 9e dash when the driver deceleratjb9 qp gpop5,+es 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 a()lshfl+i1fdx;8j5dt nuy4i9w59 k l0a hrben 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 belaqz41jbr aak/(ho1k6t from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what q41rhk1( zk6 joaba/ais 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 kinpca6/ a *kq-byetic 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 (infvi)*rs+* kn4q vf s5ss:y2*n 0p krpacluding 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 hsb6afyu,b7 3 w9o(jt neart, at each pulse approximately 20 g of blood is accelerated fromn6 9awf jtsy(b37oub , 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 automun b,nci)0stw s,hw1yok0p7z9 vi*6 lobile crash if the deceleratiksy ,u)np7l n0 *iw1z0bo s th9vw6,cion 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 produced by an earthquah nved/vd o(94d0yhj8ke is a , and if an object is going to "hold its place" on the ground, show thhd0n 8ovdhe/94j(d yv at 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 cg ;fd4zuh;xtly(cq r2)/2 wst q*z3qthe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assumisqr*(yzw; h;l z2uqtd2/c 4qgx) t3fcng a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for eachtu4) jobs7 hg/w+hj9s 4 m traveled along the road, the elevation gs) s74 9ho jwh+jb/tuchange 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 f7 n),;s azmeu9x1 dorfalls 55 m before reaching the ground with a speed of What waox)9d a1 s;fmer,z 7nus the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m0k3/ukbsny fcv1 7;vy/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 to pedal if the mud lasts for 11 m? If so0cfyn7 /s 3 1;kukyvvb, what will be the speed upon emerging?   

  A city planner is working on thedls 4i e2u):ennfgp 71 redesign of a hilly portion of a city. An important consideration is how stgu e1l fipe:72n4s) dneep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , 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 her watch from a thinj cw: ik+nno/p2xi 1v( fq78ht piece of string while the jetliner she is in takes off from JFK Airport (Fi wx(vi qt 1p+2 j/:8nnfioch7kg. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermark)ak2wpfanug v /e k(d0x6i;u)et, there are to be several ramps connecting different parts ofwf ivn60ukaxa dpk ;/ )ge2()u 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 tosr t0n lj:5l8s lift the piano (mass M ) using the pulle8ssrt:j 0n5ll y 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 3omu ,5m m*(dlrcu)e bkv-.ea+ :khba2.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 the (glf/ zfshef n2o5)a2following set h)2s( n zogfa 5lef/f2of 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 660 metric tons (660,p1xt y54o2cs sfv g;3u000 $\mathrm{~kg}$) . 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 wern5(ik-uu. '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 and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming tru -w(ue.5nk ihat 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 usingvcvl7p(ulk4 v(y9gfu (/16 yhvcwad. 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: .c kwb-7vtuak8 8kwx building 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 are roped togetheya53yren732ot jxbcgb6 i7 l5 r are ascending an ice field inclined at 7ctb3n oix 5ea75g6bl2 jr3 yy21.0$^{\circ}$ 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.