Why does a child in a wagon seem to fall wdokgs88pd5,backward when you give the wagon a sharp pull f pkw8o 8g5dds,orward?

A box rests on the (frictionless) bed of a truck. The truck driver starj* /i54yeoqdc ts 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 t 5ie o4d/*cqjyhe truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no force7bh)lp-n , uqts acting on it? Explain.

Only one force acts on an object. Can the object have zero accelera8 ;mfmqgxon53 tion? Can it hoq 8xf;g53mmnave zero velocity? Explain.

When a golf ball is dropped to thn1. vj ek asw(;i*3vnge pavement, it bounces back up. (a) Is a force needed to make vge13si v;a. wjn(n*kit bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in 2c5esma 2)3oz 0wa4,dvu ea guthe opposite direct5,e3 )4mda2uv aogwaz e 0s2ucion?

Why might your foot hurt if you kick a *hvdb/b5lh,yb. yisp) 5x;wz heavy desk or a wall?

  When you are running and want to stop quickly, you2t4fdsnpt k;-qw 7 m3m must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of decelerationm tm3sf kpn w427d-t;q of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread ;b7f+xn5 opdnfrom the ceiling, and a section of the same thread dangles from the bottom of the stpn o;bf7 nxd+5one (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity o(ezc k3,ckl0 a 3wohb5n a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t cza (o h eb,k0k3c53wlthe heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the sz7+y0 ;v bhwmscale had been calibrated (a) in pounds, or (by7+vms h0 ;wzb) in kilograms?

You pull a box with a constant force across a frictionl8 3zdkjnco;*fq8ngf7x l 3 /gvess 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) decrease? Exd7 ncgvlxofj8;z 3 kq3*8 n/gfplain.

When an object falls freely underpgzt4bb spy r)p,0j(6 the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law thpgz s 04(t,pbpb)6 yjre 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 objn+ix(v mnu p0mxa 6 ; u7-jejv,zk2kz0ect when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-k0nik-xvm 2eu+p7 ;ju0m(z,v6janzxkg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in uef a8 :)c8y+3lxjgdca tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines8 3df8ac+jgue)ylx c: which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thei fns 4y 6lchq8ud513e “reaction” force (Newton’s third lah4cy u56d8s n3qefl i1w) 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 large a force does the ground exert ox)h .hs xu;p-tn you? Why doesn’t this force make you rishp) u ;s-x.thxe up into the air?

Whiplash sometimes results from an automobile accident when kzseu)1 ih j4:the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this shkjezui :)s14ituation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When theknt .lv 3(87*m9pfnfc ujcl z. truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to aul.zfpf(m9vckj *ctl 83n.n7ccelerate?

A block is given a push so that iif. n)*uq lfa2w/ xql)t slides up a ramp. After the block reaches its highest point, it sli2lu .)lqw*f ixa )n/fqdes back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read i:n33o u ou*erbf you weighed yourself on an inclined plane? Ass urub*o3o e3:nume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a cp)s(1sr2ufv;ohs9*a au(uj3pq hw m: hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at ,6-unk0qezt:kay1xmqoymhe 4y*, g+ 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 uss 5vt:z inbc8*ed 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 kd ,)yz4dtg1ya $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if tr*h rrv6+kts ;he car is traveling atv hrt+6r;rsk * 95km/h? -  

  What average force is need5xng1ee k -bt ;jy/j2ged to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alon/nt 2x-; jebyg1je g5kg the barrel of a rifle?   

A fisherman yanks a fish vertically ouk3mpi0ja 3q 0ka.e(r rt of the water with an acceleration of 2.5.eq( a0ip r3k0 3rjakm $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile th peh 0v (ar.0v8eipn6rack (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 b oc,i ,5v7iedqx3;lg pr re /0tp6-qg) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor shouli,gp ,;r p g6 0iq-x/5bo7rlvec et3dqd 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 euip- 27qf; p c5fot+ss0*mycflevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calcu im ouc y-qppfc*7s;0f+f t2s5late the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has ah-lw::n j y7eexk 3(xao /5hc (kbm,wd maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator withou :lxam7-,yhb3n:wd (kwhx ko/c (eej 5t breaking?    ( two decimal places)

  (a) What is the acceleration of two v -otu -qn(khvaxe9*f g83i3tx+b4kh falling sky divers (mass 132 kg including parachute) when the upward force of eig-4f8(axov nhbt +9v*uk3 xqt-k h3air 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 3.9-m high. When he strikes*q0 goljx f0o0 the ground below, he bends his knees so that his torso decelerates over an approximate dista gxq000j* loofnce 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 r +soreg(a- so2ests on a table. A rope tied to the box runs vertically upwardoe2a (s+-o sgr 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 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 bas -s-fcs;tpqu 7givco;8zfk +(ketball 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) atp7e y )t s,vek,u/;b67 fs c:pbjewp7t the moment it is hit by the bat, anub 76e w)7y,ppsb;jceev,:pf/t t7ksd again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly )mgsf(r( sol. direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points r sf(s.lmg()owestward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung h(m;fc /n())cqeo4 y;e fs wftoorizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoi(ft)me;f(e4nw yc o; )oqfs /cnt 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 cord from andn xg)fm1c.w-jxr.l7qfc-. f other 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 14.0qf cxyh6dblau,qdywj7* o6 2 4,t.tv.$-\mathrm{kg}$ 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, Antarctica,g.kjla a.0,d1(ld vtq* frqq5lmaw5 - as shown in Fig. 4-46. The sum oaa-f v w *15l.ad.gjll k(0t,qq5qd mrf 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 be5x9cvdvr9z8. u3wv aq hind it, Fig. 4-47 . Determine the ratio of the ten3 5wxqv9v8uzrdac. v9sion in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself h.,*wmjc;y : wzebja) )dpz-jupward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull hja) mdb-z;z) j:e,*wjcw. yp 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 begs .+aab-h(qeoq fr+zla 5e x0.an, 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 (m pcpj+789*l 4ww7xbxrp2p* ypi tmjj8ass $ 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 e*ox9vnlwbeuc .09c:d ach other, as shown in Fig. 4-5* 9wlc nvud9xeco: 0b.1. 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 1.8 lpvf92)hk,pydfq5(o 0 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the ligh) yv9o qp2dplf(kh5 f,ter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connec78ut/sws xzt2ted by a heavy cord of mass 1.0 kg . Calculate the accex7s8z w/t ts2uleration 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 fri*-mm1tzj2 z9w:qslnlh( r * nmction 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 r9n sq*4-bwmz lequired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a t a, lm v)0c1j*owvoqc,rain accelerating at 0.20g. What minimum coefficient ofv,ov1*a0q )l,jcw com static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a ca,,dst rh:lyl0so )l4lf m2 f/nr can undergo if the coefficient of static friction between the ti dym04n,/,lflhr 2f)tlo ssl:res and the ground is 0.80?   

  The coefficient of static fricgfn 7n wk1+*(lj xi)dzn+wlw1 tion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximu+ilw) 1z* d+fgw7jxl nk(wn1nm 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 decelerate5yjv-5t; o,a tote ld5 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 l3qghj .3z; 0o ezm9fmrough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very hig(chl61sbdg,t h coefficient of static frictionsh g16dbt l(,c.

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 frictnalh2pv9ejp/gc,w.ayi2r3v)7 l 0 rq ion 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 wofnpa bjp09bi)ew l/ oh3)lm8 1w4sq+i uld box A have to have to prevent any motion from occ/bml+l) 9jfqpown 8 1i04b e3 aw)hipsurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesy/9c+t sj9)/pc e; zq5y ixxselobr38 across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparc ey38 zts/;exio/r+)bq5lxyp99 jcsts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and /2z *lkf;mles 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A lze ;s/f*2kml 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 friction b/yi( y/5crkpjb2nr7 h etween the crate and the bed of the truck is 0.75. What is the ma r/hb2/y75jcr npk iy(ximum 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 wo/.te0s ux xkh. 1sf7usrry about parking your car in your driveway, which has an incline of sf./u.07s e1uhxs x kt12$^{\circ}$ . 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 slid i+uy) iku5iitj2 cxxn:ba+ ;+e 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 liaad8)r y s2tzp6wx( 4ues 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 vic1)4hhg bm (3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wiblj( b t6.37tnkbf6gp th 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 rough7u) ey/vg;cgm5 occ/u wall by someone pushing on it with a force directed upward at y) u;gmcv/o e5g7u c/c 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 projectiles as theid6ws /x 2/vbmy melt. Consider /bw 6 /2xsivdma chunk of 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 autbgipj:+yl q 7/v i2-giomobile traveling at speed v is y /qbigj+gpv27l:i -iequal 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 onz j+0z sx+if3p the dash when the driver decelerates + jszz+x03p iffrom 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 xykz* cj+ aku ml62;ne) f2(ll m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt gct:y) a: gjk q9i)igk17 qz*xfrom 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 thjqg1g7* g)xik: ak qit) 9cy:ze belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic f7+ bsr *pj5p nkwkn85wriction 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 593 vt 9u8c6iqkt bbxv(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 mammaliyd vgc2+jr4zm4u,w 7 hop.v6n an heart, at each pulse approximately 20 g of bloo+ w cdj4yu vrnvz. ,h2g74p6mod is accelerated 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 of surviving an authe lfcnw*(q6 2 zv4ow*xo*rx ;omobile crash if the deceleration is no o*xlfce qh6zv24w; *(r*x wnomore 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 earthquake is a , and if an ob2dri8:2nkh )v/xhq x vject is going to "hold its place" on the ground, show that the coeffic2hvxnk)q:8 i/d2rh x vient 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 involvinhnjiu 2jgi f6) h0b2a5 k5hdt-g two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetak hij fi6 -0)d52h5hgb2utjn ic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m tbh1h/)v n5t c9t wq-qyzv b9v3tr-f *braveled along the road, the elevation change is 1 m). How fast is it g- hvqf-qn5cv/t* 1vwbb hztbyt 3r)99oing 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 0 6cmgzjnve p-l+bgsfe37 g+/Tower of Pisa and falls 55 m before reachg/lf gze+c es3m7 jn-pb+ 60vging the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but 4 /fvg;xlqv 9denters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist em/xv ; lgqv9fd4erge 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 o,)z027tedy 9xjy xnq(b,.ab o :nebo redesign of a hilly portion of a city. An important consideration is how steep the roads can be onxx no 2t,)a7b:y zdbjebeoy(q.0, 9so 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 80t /ct9 kqoxt8wm5iw :lqxqm(9fx5yphysics experiments, dangles her watch from a thin piece of string while 9qtttwfml5w95y k8ix /q : c8x0omq(xthe jetliner she is in takes off from JFK Airport (Fig. 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 supermarket, there are to be several ramps xg* 5m;/,ue mxu7iqnoconnecting different parts of the u ;/qx ,5oxi memu7*gnstore.
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 ) usi g+u,pn ;y:aey:sl,ahng the pulley apparatus s pngyeul s;a,:,h+y:ahown 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 acceleratingr*xrlsekxr .je(2rkipz 6/7h ( xl u8yd3m(b0 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 child-restraint chair, an engineer considers the fold h0,a 9p7cq( rq:ndm wc3bxx4lowing set of conditi0cqdxbc 9d( 4h: xp r7,qnwma3ons:
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,i2:pd5ym4 tkmj nz*x,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 nuztkt3 m3pp6e26 n1g Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuekt63g3pu2p1z 6ntnm ming 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 " 0 ao7mh d5q5xuv(*a n1l7cfsu10-1 $\mathrm{~b}$ 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 speftrdfpwp*2 j505(8s vq/mu ht- besy5 ed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field h3qvmp -oars//l 7 .cza/z owxsa(+n2inclined -/zx.n /3 7s+lva ca(2/aphos wzmoqr 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.