Why does a child in a wagon seem tsgi/pl573o b77gwnjco *k7iho fall backward when you give the wagon a sharp pull for h*scb/3j7gwlipg57o nko7i7ward?

A box rests on the (frictionless) bed of a truck. The truck driver startsbx/z(laou .k x/ ;o)fa the truckl fz .(o)oa /kxuxb/;a 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 riding on the truck

If the acceleration of an object is ewo z1nzg2 )qcm rjh(;/6i(rf zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can e,e jfda352u3 8fm prjit have zero velo d2m j,feeajp5r3u83 fcity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a f m+hnpa4* rz7y)nldc4orce needed to malm y7 nz dpc+*4n4h)rake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does94.add 0d(e+isiksp a dh+4 f eh i:pyui6-*bl the log move in the opposite direction?iyd .0e:da+p afidsuih9k+( 4ids *-bhl46pe

Why might your foot hurt if you kick a heavy desk or a wallny7hktg( )2qcu(on3+.*udi ayg 1orn?

  When you are running and want to stop quickly, you must decelerate quickly. (a) jx. n17atyjt 4o8*ftd What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum ratetj84tafntd7j1yxo . * 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 : arq+o0 +*iq4ikmbryceiling, and a section of the same thread dangles from the bottom of the stone (Fig.q*i rybq4 kioa +m:0+r 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 ij:cx4l -e; jj6kgc,zw- qg3r is twice as great as that on a 1-kg rock. Why then doesn’t thcg6 ,-4:3 r i-cjklx gqwzejj;e heavier rock fall faster?

Would a spring scale carried to the Moon give accurate ezstnz;nd8;19cv 0x t7uybl 2a+)a niresults if the scale had been calibrated (a) in pln;z e;d)t92zat nciy8bau0 1ns7 xv+ounds, or (b) in kilograms?

You pull a box with a constant force across a frictionleatf5e +-3+ ofoy3sj txss 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 remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decretayx fje5-ot3+s f3+o ase? Explain.

When an object falls freely under the ink2*5h h; uddb 3w1ghn*8xuh xkfluence of gravity there is a net force mg exerted on it by the Earth. Yet k2xk*h h*bwdnuh;h u3g5d1x8 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 force) needed to lift a 10-kg object k*w +f/k3nnd7yf cz il.1 isp:k 9d9ulwhen you are on the Moon with the force nezkn1 .nf: ki ki/lwf*yls+upd 93cd97 eded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tushnx g6/o o ;14moi,u lfx;cy3g of war (Fig. 4–37) pulls with equal force on the other team. What, then, determih,ooxm x3n6c;ufos y/lg4 ;i1nes which team will win?

A person exerts an upward force of 40 N to hold a bag of groceriet2:46a 9jpcode/2io w snifmlub u) 9;s. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exertj6e9 9suo) i:4duc nl of/22 itabpw;med.

When you stand still on th5 ygf vbkv46d8e ground, how large a force does the ground exert on you? Why doesn’t this force make you vgf6vd54 k y8brise up into the air?

Whiplash sometimes r;oq/kw j n0cr/ (dzw+besults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be n0( wc ;/b/ zdro+qjwkthrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck qekavrdfq (*x1c/b48/ ue:ehaccelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acceleratee*8e bq /:k(1/cvfrhax 4uqde ?

A block is given a push so that it slides up a ramp. After the block rek1nob+d 9 ;vwkx+p9 ln)da0ftj 6 iw4uaches its highest point, it slides back down butk9okdbu6) v;xln + + 0a4n wijd9ftpw1 the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bath987x;w badvsqroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functs dwa8xv;qb 97ions properly, even at an angle.

  What force is needed to accelerate a child on a sled at muyleb78s a4 0njz9o/ 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik,fsraurq g y+dov8 ;-,))7 bwnamjhs4e 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 rop4 i1k4;c ( z duz5j0t(twmjfdte 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 e ;+-qikysjp4m.s;ga $76-\mathrm{kg}$ 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 sto4:a91j cyb z)1ejhvyow4 y01 1dkuttgp an 1100-kg car in 8.0 s if the car is travj14ahy1:vb u te01wytcgo4z)y 9k1jdeling at 95km/h? -  

  What average force is exufr8i wm 2/.needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alou .ifm e28wrx/ng the barrel of a rifle?   

A fisherman yanks a fish vertically (vr2svys8iu)- r s )jazm:i:rout of the water with an acceleration of 2.5isv)rv):muzs:j2riar -sy 8 ( $\mathrm{~m} / \mathrm{s}^{2}$ 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/ik)0 l ;quuwq cover 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 wpmdj-du1)e)qj c c 1(kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and micu q e-dw1d(jp m1)jc)nimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevatokr+ pqs.x -9mue/wf it) 9so+mr begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the dire.mi-u+x/o e+ps 9qr)9kmtswfction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of p4ku8g+z yg4t 21,750 N. What maximum upwargtyzu g84+4 kpd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including p254r w w uop8u8,i(4ss yddxjzarachute) when the upward force of air resistance i,44 rspu5oj8w 2wsdu y8x(id zs 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 vns(aw 0reu5 6uy0s 7nroof of a house 3.9-m high. When he strikes the ground below, he bends hisyu(au00 w65se7snv n r knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the bo yd*8xf yl(:fqx runs vertically upward ovf(x:fyy8*qd l er 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 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 diagrawzg(t hq rp8cavj/n (zy:+25zefqm7 + m 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 diagrusu m9fd017e jam of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying towaru1 jdm 09fe7sud the outfield.

A 650-N force acts in a northwesterly direct(s luo*9 *bsn6b;zp ow+xf f.0l8ltx eion. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Ils.obfz+ *n *uxo (blltxlf6pws0e9; 8lustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizonamoy kmo3 ( +bsec21uze9:k:etally between two buildings 10.0 m apart. The sag in the rope when she is at the :oeaekcms3:9 zem2( +1oub kymidpoint 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 byo,-* ky)*1qsxwo wvbm 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.h 8 i8vandz3p h-*n 8)vm6ldhh0$-\mathrm{kg}$ 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 location at McMurdo Base, Antarcticaim69y 5(detg ncel a)6wjdy:; , as shown in Fig. 4-46. The sum of thedyy(jg;):c nw6lda95 6m it ee forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-4zs/n7fxsb )u q9 cpg3,w m0h0s7 . Determine the ratio of the tension in the coupling between the locomotivm)upb 9zxh wsq0/c7,gns3f0se 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 buckem kj pl- alk 8pan;d-0m:kc*3ot-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herse-lcnl- 0;*a: kmd kpm3poka8jlf 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 bega wt44vsrcd:(jn, 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 (mass ts 2w.2s c)7:n orjnwb$ 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 contact with eacs: ny2+ydvxd3h other, as shown in Fig. 4-5v :sdynx23 +dy1. 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 abov64b9:tn ta)a tek0bd ve the ground, 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 ground. This is its "launch" speed. Assu:9v dbnta4e)kt at6 0bme it doesn't hit the pulley.]   

Suppose two boxes on a frt*m :gfs (-bv bu,hj x469cjefictionless table are connected by a 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 diagra6: (tc*4x mfbf9hb jjgsvu e,-ms shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between akg-y 8n37gq5fh ecn1 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 guazeoj/ +u: .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 stfv-8a/eo xjbe 6xs.ge9uw),yanding on a train accelerating at 0.20g. What minimum coefficient of stay a-j)8x 6,veoxfgu.ese b9w/tic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffwt6 n(xh2a+,d gssd:hy -tja.icient of static friction between the tira6 2t, nhhds:.(w t+xs gjdya-es and the ground is 0.80?   

  The coefficient of static freu++e2 x m1jlucg3bs+ 6 y f1bi,dn0gfiction between hard rubber and normal street pavement isgs e3 ufm j1l,++2xfcei 6byd0b1g nu+ about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80t;; qxo0iid)d $\mathrm{~m} / \mathrm{s}^{2}$ 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 yiaop2d;v cuj9/ z1w,m 5u+qna rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact w4bu7ea6z lx/i-k wy t59/q gfhith an asphalt surface have a very high coefficient of /feky6w u59l/7b-iqhgaz4 xt static 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 bwauol,s99 o:s4 wyz1ckrr+7yb kv: 1 friction 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 mass would box A havebg(;x4c;fs io to have to prevent any motion frf4x sc(i;ogb ;om occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it 5 idqtot7u: w7j6m6 1k njy1mp,ah2h nslides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initi 1hat o1mnn62pj7mkuh5t i67 , yqdj:wal speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and a v /2k(ekvz80 dm*7wim f+ujvut rest on a horizontal surface (Fig. 4-54). A (dvv+ uu0z/m*wk78 fikemvj2 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 coefficzhj d4gm3r-7 pient of static friction between the crate and the bed of the truck i43z7gjr dph-m s 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry abog-myo j-a2kr 3d7 8morut parking your car in your driveway, which has an incline of 1y okam 2j7d r8-3m-gro2$^{\circ}$ . 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 0st* n.wf -x2ya edn/o 5smd3n g+vzq, 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. 4rld1zrq *-5vmji* *pt-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 is0.7 uwy*jhle nitial 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 n ;*; fi6ir4g+g3klp-s muwb5yo86cr is3nbptop 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 s/y+,xw x2mrmv) gix8place against a rough wall by someone pushing on it with a force directed/vry 8xg2 wsi+mxx ,m) 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 datw.a*ousrup,g -xfqyu )z,pu2. j1:k ngerous projectiles as they melt. Consider a chunk of snow at thepuworz :ja,y2 ftu)-kuxsq1.pg*u , . 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 a tut t*ev-2yhj/ d1xe9utomobile traveling at speed v is equal tott1*y9tv/u 2he ed-jx $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 wh;(sa:s of6qv1 zl0 kh7*n/(f 9e kz1rcnwk ifwen the driver dece(9a1z wfkorn6 l0*k/nfkc:7qfw( hs is;ze1vlerates 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 giv. f;p 9mo lowwe5gg:zvhsc( 5:j46vv7qh rje7 en 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 the packing fu6bz4 dq8d0e station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time forfuz dd 86q0be4 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 omw iq gp258 mqc02a /6rxtitt;f kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast downv r vpxjz- h7i+vh,.,j/z vgc4 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 y(33 9f:gmq - kw s.9imvjwnhfheart, at each pulse approximately 20 g of blood is acw3mqfw:(fvj-9 k.y9 ghi3 n smcelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance oxu;9bfoe -* mpf surviving an automobile crash if the deceler p*;9om x-bfeuation 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 pro t)hw5qr)gpryf7- (hbduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficiq( )rfghphr7ywb-)5 tent 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 invu .6h i-te jaerz3n3i8d;u5zuolving 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 inte-;3d6uur.e35 i8 j azzhu 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 9u,ng.i ,vftkg39m pl means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bo,ufmg,.3ik9pln9g tv ttom 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 tzmx: b:olb)f m*c/tq0lb5p/zhe Leaning Tower of Pisa and falls 55 m befor:c* zbzpl btl5m //mf)xb :0oqe reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting co ngw/k3ftd8 .je+-t,9a lvzat a steady 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 to pedal if the tk,vf3tg-/wj 9o8ed c+l z.anmud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is wornbg r6cwlh.p 29el* 9yking on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered car26h*nwpeby9 9c. rgl ls 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 experi rtfvcy,aa)g*m 09ur3ments, 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 stringv90uy, ftrr) a gm*3ca makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be uc,up1 c(my)o e,: k* ns1d )pvy7wf9w(skqcr several ramps connecting different parts we19d y k1()(qrscwpoc,nk m7*s, ycf ):uvpuof the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the puli*k ae vftrr9p2*tg4 (lb9,h bley apparatus shown in 4g,t(her **bt9fka9rv i pbl2

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 3.5( :)u6m(ls3ovqqlxh4ln:rfk $\mathrm{~m} / \mathrm{s}^{2}$ 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 eng -v0cwwsuh, .gf6*xeg ineer considers the followi 0wx fe*cg-vhg. ws6u,ng 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-/z0 f jyg.85*kbn fvh1 wu3euwt(zgs5car Italian train has a mass 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, Bil7a2 w nmh,avb,f s2fhv5*ws8ij2)uo rl and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climv27sah2j f u),ihno wmb*v,8as2r5wfbers. 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 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 usi:ep(t g,x tyw8,sv8pl:y fyr(ng a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum s y,1rmemjuddl54 2q t2n (enk s*dxn-2peed 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 ascendiv 0,+g atpxl/ong an ice field inclined at 20p gavx /l,t+o1.0$^{\circ}$ 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.