Why does a child in a wagon seem to fall backward when yo,u)az09 rkyx qu give the wagon a sharp pull forw9krz a,qy0u)xard?

A box rests on the (frictionless) bed of a truck. The truck driver starts thzhjn:4na i r +*,yc/q6l4vrhl e truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion rr:naz hv, 4hlq6/ cji*4n +lyof 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 ;la*+te+ .g opb0o ruczero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati1y+3t: 8jvw0eotkc i c)r38s0aykiv ion? Can it have zero vel38)i+w tcci v80j 3yi:ea10kr ksytvo ocity? Explain.

When a golf ball is dropped to the pavement, it bounces back twu-s;.9pdf2 mgky3 pup. (a) Is a force needed y-293wm;dpp gt.f u ksto make it 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 the opposith lvm czw;74wj,vtn7*fn6t w:e dirt z,w 7 ;7wjwv6lvchf4n mn:*tection?

Why might your foot hurt if you kick a heavy desk or a vv1c52v5 3n:5sdcbmp kez tk,wall?

  When you are running and want to stop quickly, you must decelerate ws+fp (2z 8u 4chk90zopkn/ q5uj.mpkquickly. (a) Wha.ck/qnpk58+mwf(p9 zkszu420 j hpuot is the origin of the 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 ,sr/ a )rrpy:ksection of the 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 thre/) ,kryr rpa:sad likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a o/t9v2rr n ;uh1-kg rock. Why then doe9/ nrt 2r;vhuosn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accur8 a:9h2kp3kj xrg 3meoate results if the scale had been calibrated (a) in poundsh 3ogjp 8xr:39kka em2, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an a0qi i1 x haagy-*n-df(ttached 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) i i0d(aan1 qi -x-f*yhgncrease, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there -td/l1zp jd2auw (rz;8vzi0u a9nl/m is a net force mg exerted on it by the Earth. Yet by Newton’s third law the mlu9wuv a(di;/-/pd1r nzl08az tz2j object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forci cvuxv6q/spg)6vshztm9m4td4 .+s o7 o9l+xe) needed 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 horizontallyv+t /mq 6omvgo4t z.cls4+ss9)x97vuixp h6d with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (u(qsa x7v ico)h.ah)l;t.*auFig. 4–37) pulls with equal force on the7 at ai;(vhcuo)u*.h s.la)xq other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold s)ktby. zj v3zt f+0*ba bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude,y)*fb bt.0 tzvjs3+kz (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 eo xszoae85 kt eoru2oxy-,jx 7xbo1w*)( 2o.kxert on you? Why doesn’t this force make you rise up in eu1be*2joo.zo7oy(x 8)o, koa xs 5xr-wtxk2to the air?

Whiplash sometimes results from an automobile accident 8g2it1s 2yejowhen the victim’s car is struck violently from the rear. Explain why the head 1o jigs822 teyof the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whvtprbau gv+g 1-qm/h9z-k*lc /g+j . pen the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to mg/*qt19b/ vgz-p-g h+pv cr ajk .ul+accelerate?

A block is given a push so that it sl)+hv6(ehvxpjwf xpn.-r 6*w cides up a ramp. After the block reaches its highest point, it slides back down but the mae- xw. *n+c6j)r fx(ppvvhh6w gnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself oh (3rfobr0*; 5 n+sxfholo7x9 8ev ppxn an inclined plane? Assumeoo( vxs+lr 9;hf7oxb8px* 0hp3fn5 re the mechanism functions properly, even at an angle.

  What force is neededp*t r0uj+hz1e:.bk c) zgd d6m to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike anx) e2r.dgd(at s*y:eh d rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is us: t 2fqmdh/ p6k;p6yzbed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofu73)2 at ycr. yol9.outb2 ,bm9oqsxv a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100 v6( ge5x)rimr-kg car in 8.0 s if the car is travexvmig 5()rr6 eling at 95km/h? -  

  What average force is needed to accele vy .fb 0e 4.+dn)ae4 hf.eul6px6aeqcrate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m a6.evbl+yaq6xcf4 4 eeu0a .hndfe p).long the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ow:(mlxdi (gmzp m3..q6z dg;bf 2.5 lzmmg(; .z : d3mdxqg (i6b.wp$\mathrm{~m} / \mathrm{s}^{2}$ 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 track (4dq*+)a jz xi:e02 $\mathrm{~m}$) 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 j0rv 6y xl0in4to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor shijlr6yn0x v 40ould 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 scal 9an5xptr, 3do()s+n jr yic oz1.2ztve in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Cc rz3(j,snvp1 zxdo+iay .n ott2)5r9alculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength o22 hu,w0j fih frcwv58f 21,750 N. What maximum upward acceleration can it give the elevator u,rh wjcw0vff2hi 528without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dias+5tw iftb), ,i 8iebvers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of w+t ,tiibf8bi),a 5estheir 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. Whenx xlpe+fp4;ka g7h3)84 sdob v he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kgo4x)4d7xvflhp+sp3a eg;b 8k , 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 box runs ve2g 8sylu, og5//hb1o cr hzgrei,p z9-rtically upe5/r 8g-phz sh9/il,ub c 2z,roy1g ogward 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 qg.sfm/+8o*ed d e t.u iv1ed/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 base2g9m bkssxlhi: t r+2(t,uly,n / vh)eball (a) at the moment it is hit by the bat, and again (b) after it has left thm)kle ( l x2v +,gttis,yhn:9bruh 2s/e bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direcmuq8jqsv0n 2zma8 l ;(tion. A second 650-N force must be exertesq0mun 88 a;mjz l(qv2d in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "higho60fif;kwt s5 sp/ xf0ci;1bfub9 t )x wire" strung horizontally between two buildings 10.0 m apart. The sag incx6 f9;ftow /issf tix 0k;0upb1bf)5 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 ish- +h9 dgc98ofe twk)s hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1o+:p(jy/)/f6k dofx mrok me94.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit tc 9xsiau;rv* c/a0lx1o a new location at McMurdo Base, Antarctica, as shown ;axcl/vcrsu*09 ia1 xin 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 ti8xavp*iz7g :9-h jnpulling two cars of the same mass behind it, Fig. 4-47 . Det*zi 98j:nvagi xht7p-ermine the ratio of the tension 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 pulls1 lg-r pjx6i(l4qw7c w herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cocgw(6 j xi74qp 1-lwrlnstant 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 6ee /g vr y7r:*mvr8zk2j f8fo:5$-\mathrm{kg}$ 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 1+kmk2wwn f1rg5g )q gblock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in cow7xb in i:7am 0 bh7nww4b02le5uf 2gcntact with each other, as shown in Fig. 4-51. A forg bf7w:u an202 hwc0bn wieb xlmi7574ce $\overrightarrow{\mathbf{F}}$ 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 Fih.)*a5il-gn 4(c-ualk8 5s zaenw jtfg. 4-52 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 system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hitsluaf5(- enkna8thsl *w5) .c4 zjiag- the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a fil1csdcryu 20o7iy5 6rjd,f )rictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the accelerai)icsor0yul1y f6d7rcd,5j2tion 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 kinae714;h-l /mqcdxoiv etic 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 r w2p n(yj1;yy w,(+bv -f(gttdczo;irequired 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 train acceler d:/ 3dd.d vu;ausq tv/(e3 3mtwtlji)ating at 0.20g. What minimum coefficient of static friction must exist between your feet and the fljtvvtde/ 3d ) 3um. addu/qi;tw:(3 sloor if you are not to slide?   

  What is the maximum acceleration a car cayss8 ;hfv 0sz70gjfa+ , .3jpnv uu-qnn undergo if the coefficient of static friction between the tires and ts ,-3.7gu+ avfj008s;zsnhj n upyqvfhe ground is 0.80?   

  The coefficient of static friction bete4o:/op-w )qfrbfy oe9n ;qc1ween hard rubber and normal street pavement is about 0.8. On how noqfyepc;oer4 /b 9: 1-o wf)qsteep 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 -4tb;juk- asxrj: zk7r(ics :20.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 aknn9uu)f;+ulspd*vpm0 lx 05w ycd*9 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 with an asphalt surface have a verfdx 3j3q4nkg1by 06p sy high coefficient of static frictiops4 y3b n0qkj6xfg3d1 n.

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 friction for avk-vf ta9gkfs 7q0/0q $ 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 lw u(e8 4nzzab n,l+ .-r/iqmg7ebdlv+arge a mass would box A have to hav78 ge n mv+lqre/w4+z.(, ab ibzdnl-ue to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it y)ovi l*5b. t+e0bq +jb lw9nid13xxoslides across the floor. How far will it go, given that the coefficient of kinetic fr9w5ovoi b0 qn)i.e1+txlb 3+y d j*lbxiction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in co2w,b :b)s5 b1udmeo g0sym1bn ntact and at rest on a horizontal surfacdw ,e:bm yo0b1bm2sb sg5nu )1e (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 nrs*)q 72xdm bfriction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid hq rnm*x) s72bdaving the crate slide against the cab of the truck?   

On an icy day, you worry about parking your -v8xk3;xpjdpfxc aejz2 q sk3. 0cf;3car in your driveway, which has an incline of v-03sfq;k cafz; 383p2xx kjxc.d jp e 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with eq/t b/ a2yq0/dr)g joa 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. l;s+8em ywq6g4-55 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 s)vl zjlcm.e ig1i/pas 5 qkb7zc914*ho )y *empeed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the st6 l tle;ee26uleepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by eb4oh-bi h*;i someone pushing on it with a force directed upward a b;-o4ib hhei*t 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous proj8a6ukd 9t+ fsdectiles as they melt. Consider a chut + af9sdkdu86nk 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 automobilexzeu uh0yy3wuq; +*vl;*yyr* traveling at speed v is equ3uwh * *0;yvu* zu +yrelx;yyqal 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 fo u(qcm (sjf 4j8jk8pc4rward on the dash when the driver c8 8jcpuq m4fj k(j(4sdecelerates 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 gi/wfv)6f(e exru )ly.iven 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 the9cnaar yyht /*k7-;j i rp;-goy are filled to the packing station 11.0 m away. T- 9i-cnryg7j*payo h/rt;k a;he 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 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 frict4 fla9ji;t: mrion 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 down az*q: qy jo:ss7 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 simplifeb6e 08miq:gp ied model of a mammalian heart, at each pulse approximately 2e 6egi:q0mp b80 g of blood 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 automobile crash if the de+6r i702wa3rfddpk vsceleration is no more than 30 " g2drkwp f 6v307rs da+i '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 accelerars+m xhf46 uo8tion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with s46fuo h +rxm8the 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 ouu c4d.b+8 p-wd+vr7jybffp, f an accident involving two cars, measure 72-m-loncwuup +bjb dfd 7p8rf 4v,-.y+g skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-q fybvf4 ds,4: aen+5win-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going wh44a bfw5 +yvs,fned: qen 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 th uzc04;vj.l2s4swolo4 jvabc8j 6na *e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a s jbj*2ao u8;0lacjn4 . zsvc64s wv4lopeed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters q+mdpupp/y xt/qjv* ( (rxk) )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 so, what will be the spep)(kmy)d*p j txqqx/p u(/r+ved upon emerging?   

  A city planner is working on th26, 8hnd kq q74 6yqcmaeojlc8e redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. Akn d8oq l6mq6hc 8aec4q7jy2, 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 elj5kx x e(t;*f7izxe. xperiments, dangles her watch from a thin piece of stringxelkjix* ;e(tf7.x5 z while the 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 connecting differe 2r2iqdub:5 1o(k wlstnt iosw:u (2kq1rdbl 2 5tparts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) us 0u *: p7eluucho:;x:uvb9e zsing the pulley apparatus sho7eh*lbvu:e c u:z0x;:9upu oswn 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 3b i8*u o2 ve70wxapv*o.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 chiyrc /a*g*xhp/go,b hwn7nt omc,19 m9ld-restraint chair, an engineer considers the following set of conditi,/c *,m hp 7/91ygtxmnbco roh*w n9gaons:
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 har v/y/9tei8vet vq1b9s 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, Bill and Karen, usee j gzvmj;h r*nou. ec/zr)8*z2s3lk8 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, 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 cz/gu2r. khclj j8*v3 ne)ro;*zez sm8limber is more likely to be hurt?

A fisherman in a boat is usingg2g0mvy/cz (d2z kn3 u 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 speed7 3bbzxd3pn+c 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 ro/f c* k5ai+zqtped together are ascending an ice field inclined at 21.0 /itzcq+5* fka$^{\circ}$ 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.