Why does a child in a wagon seem to fall backwnh uwo(x-- :jg qdb0*mard when you give the wagon a sharp pull forward?*-bojx-:u n(dg qm0wh

A box rests on the (frictionless) b)znoak 1lv5wxpg8/ q2ed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws,v51/ lo2)xqkpnz aw8 g 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 zer bugi5+0 ifq1hpl d.3y dshw;0o, are no forces acting on it? Explain.

Only one force acts on an object. Can the o* (t62enjy2,77aidd) hlx i2criz nznbject have zero acceleration? Can it have zero veloc n6,dn2(y2c7hat in*dili)zxje 2 r7 zity? Explain.

When a golf ball is dropped to the pavement, w6nze5 d(vn h(it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, 5(h evnnzd6(w what exerts the force?

If you walk along a log floating on a lake, why does the log move in tho 5uuca2b+ y,ue opposite direu +5 2b,cyouauction?

Why might your foot hurt if you kick a heavy desk or a wall2uy w7 nj:1cor?

  When you are running and want to stop q boeru8u9,8 8qpushxr:+gt3 uuickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimat8o8+8x rutq epuh gr3b9us: ,ue (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the ff6 h4nr1u(;6 zctwmf same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the danglin1m ftzc un4 w6(ff;h6rg 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-kg1v)qo6bf njt)hgj 7u4g(h9ji rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavierbq 7ho1jv()t ug6h)jf49gijn rock fall faster?

Would a spring scale carried to the Moon gi/o go, o/h, qtif -5qkj;rbu(a ywm3*sve accurate results if the scale had been calibrated (aw*ko5(qo , i-g 3fj,/m;qhoyas b/rtu) in pounds, or (b) in kilograms?

You pull a box with a constk0liqxg)2h k2; 2p.d/hs jq3 qntan4pu q8n6rant force across a frictionless 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) increasn64j8.2qp3kx;lr/tdqu q a)niq 2p2 h 0hsnkg e, or (c) decrease? Explain.

When an object falls freelycjy; +z yozl-2sr0di; under the influence of gravity there is a net force mg exerted on it by the Earth. Yet b2i; sz c+z ;r0yy-ojdly 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 ltq6 5v3o8jwf0 3nnpxto lift a 10-kg object when you are on the Moon with the force needed to lift np3qt368 0xf5nj v wloit 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 tug of war (Fig. 4–37)yzpw8.k j99u d pulls with equal force on the other team. Whdp.w9 uy9j8zk at, then, determines which team will win?

A person exerts an upward force /juuficv)5 pftp,0mh z760ecsi )nr9of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its f p6 hc )ej0n,u0f5tri9m /)zv7scp uidirection, (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 g/r6wj.q (mr7j vr3gpn round exert on you? Why doesn’t this force make you rise up intor nmp qgv7/j6 (wrr3.j the air?

Whiplash sometimes results from an 7 **srvancit/dfog v2 g35fm (automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrownv 5gcfgr(*3nf a v7m/o2itd*s backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed tru6nb trpxo4 gqu/:a7f )ck. When the truck accelerates, the crate remains wh/xp :b6 f 7gr4nt)auoqere it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itsd1ek v1;y jwt6sr 4:ys highest point, it slides back down but the magnitude of its acceleration is lwys 6je4 k;:1vt1s rydess on the descent than on the ascent. Why?

What would your bathroom scale xjno08b.. p c xjm(cu0read if you weighed yourself on an inclined plane? Assume t.0j mno xj0u.xccb(p8 he mechanism functions properly, even at an angle.

  What force is needed to acce8 6h:d1cde (p aczh5z j/rax-blerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.x7b; x;5kiach k(ts1oo1uu(t w kr(z830$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand i,bqly)m+vf u 1p6dc 18 xzdg2if 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 ,snk5lhhrry -z whz 5j( k22+pa $76-\mathrm{kg}$ 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 8.0k* 8qnd 4jgnx9 s if the car is traveling at 9gn84nd *jxqk 95km/h? -  

  What average force is needed to accelerate a 7.00-gra:p jjgy0ld+a 41risphe:m , 2ym pellet from rest to 125m/s over a distance of 0.800 m along the ba:jp2lye psd,r+ j: 4iamyhg01 rrel of a rifle?   

A fisherman yanks a fish vertically out b7 k-ixhr +z0;ezinq4of the water with an acceleration of 2.5i4-z n7 ix+qeh;r zk0b $\mathrm{~m} / \mathrm{s}^{2}$ 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 ca/v(znb:6usq0bp f3 ky r can 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 kg ) is to be desi*xmwh7wzc mz*w ,;v9hgned so that the maximum acceleration is 0.0680 g . What are the maximum awmwz ;vcz7h9 ,hw* m*xnd minimum 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 eza9;(xpnw r6 -sb)tu plevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, ;u xbpz 6nwt)-sa9(pr and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whdkbw ,jeq+))l at maximum upward acceleration can it give the elevatoql)e jd,k+w) br without breaking?    ( two decimal places)

  (a) What is the acceleration of two falliodhfk7)wk ac7r ,14eang sky divers (mass 132 kg including pa1kc)we4f 77aokdahr, rachute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he stri hf(gaa( ri;dk7wk-y+ kes the ground below, he bends his knees so that his torso decelerates over an approximate r-y(hk a+ad iw;gk(7fdistance 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 box runs vks 1ecedosg4n;l+ 9*vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of o1n 9ed;v4kssel gc *+the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbaanvzz-+6cp 9ms+w5q j ll player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momentq6x5h o(3wwiozb a- rxh h1 jounv4)1/ it is hit by the bat, and11ha j/)oqib3wno4xrh(u wo6 - zvhx5 again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly di*cvha)lkk:di;rxn4tp-c, b -yp te.1rection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrac p yebn,*-ikvk.-tx:tra4c1l d ; h)pte your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hor9t a40acsa5yxizontally between two buildings 10.0 m apart. The sag in the rope when she is at tytxa 95 4asca0he midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from anoth nfp29fmfp00df*d2il r 7qd0 oer 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 14.0g h7s5b60 )lfhx4-vhl,z w m,idjx :nk$-\mathrm{kg}$ 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 lk4/a:bgfh 5jmq4o .h McMurdo Base, Antarctica, as shown in Fih lg.hqa45/: f4mkobj g. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the sammsydz;6 v7.f le mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupli;lfmz .vys d67ng 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 upward using the bucket-pulley 0j9se6vt )kv tapparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise j 90vttk) 6esvherself 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 berkq:cuy41 f8kgan, 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 (masw8 e. voe zdyi1d-o5n7s $ 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 surfo1bv -wm6zy 5w, pfgzm c j9c(xh qb/(m,h3,udace are in contact with each other, as sho96z mjywm-xmb q(,,(ow,f cd1b h5v3gzch/u pwn in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 xv), xr..sv, vf dcs6fr. +ocrare each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height doef c6,.rx sv ,sdxvcr+r.) v.fos 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of9v4m5eidupofzwozs 4(e )):zfic3; p mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Ff 9i)3(uiz)e44:zp5moezfvdwoc;sp ig. 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 betwekaf*gnl/ dqe)2fowecule 4j(0- y9y:en 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 statff8m/q;t1cawz g7h4rt 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 accelerating at 0.20g. What minimu3h 7jn) ywaglka. gl*dgz o2:if7m8u*m coefficient of static friction must exist between your feet and the floor if you are not to slide? gi galyukzf. )hl j27:a **n 37womgd8  

  What is the maximum acceleration a car can undergo if the coefficien6 qq:av (6ou+.mqlejnd))s nds d9e+kt of static friction between the (uk eds:l6ndn6 qv9ao)+sej q.+dq m) tires and the ground is 0.80?   

  The coefficient of static friction between hard rzp6ti(ax 9+m5h .qcpfubber and normal street pavement is about 0(fppimc9a5.t xz q+6h.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 av4xu,zv un. u;t -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 h:kc kt t o0s)v.roz4(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 qxnh9p h*8ti(have a very high coefficient of static f(9*8 qnhipt xhriction.

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 fm50jy6 4jy6m 6j9c jqjlsep) vriction 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 4-20x86o 6rwpp4dr) how large a mass would box A have to have to prevent any w4pp6rd8rxo 6 motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How n3d/7t2r2sgru0 tra * bhpeo1far will it go, given that the coefficient of kitnob3*s h20 2g/ptrda1r7e urnetic friction 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 contact and at rest on a horiz v tamz, 8xuh/. xb1l wy8(g1lf7ea.etontal su .7l w8tfb8(e a.xaylge1/1 z,thxmv urface (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 heav e qdhirm ):tl6il:n.;y crate. The coefficient of static friction 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 having the crate slide against mli.hrn l::qi6d;et) the cab of the truck?   

On an icy day, you worry about parking youubtydtl1ld. :;6 ik2tkz5: xpr car in your driveway, which has an incli u 2kp.t1:d li:l;6ztxdkb5 tyne of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a +m+pq e rcte*bfg l4cim6xm5.)p) 3b o 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an aly/ gl); p6 rx2jn7eow;r/zy kngle $\theta=22.0^{\circ}$ 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 i r(yew)(i2in bnitial 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 top o4k8heb6k pm)3m)dcbz b6 m4zt f the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place n5ck/mt0w3gz vtl;( r against a rough wall by someone pushing on it with a force directed upwwk ;mzt t0r(5/3gcnvlard 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 slipper xp+jfhq+3* zry roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a rp f+z+j3qx* hroof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile travel9xfs:t,-um+m fh e8h5 0 btpvx :iwol5ing at speedfbt5 5m hieops, x0-h89mwv:ux + :flt v is equal 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 slidr/ (0tae-9cjz- it)xbno fc p3es forward on the dash when the driver decelerates from t3 z jcpci/nt0o(-exar9b-f) 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an init0v: gch dpgd21/qd1gzial 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 41; bd ssx-6uwuqz yt+3kpo5nc+ p4s gstation 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 bxopzpwb4 ut5n3;+s+c64sdy q u 1sg- ketween 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 coefficienr2d*e o(:nk8 o8y kimrt of 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) cab m:1 hlj kp,kn sj9ub9,)xx0in coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pul 2n-cvqo4hlv4a okm )4se approximately 20 oa4vv4hmoc -nk42 lq)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 automobq5vri7r r++pxile crash if the deceleration is no more than 30 " g 's." Calculate the force orp 7xriqr++v5 n 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 arbo.8 k1cruyz ct6q 0*n earthquake is a , and if an object is going tq *rz c0.b8r6ku1o ycto "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars,79 .bz.js;tl g e2gitr measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic frictg itrzesg.lj 9b.7 ;t2ion 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 fo,kcc:) i.zj bu3 u*kwrr each 4 m traveled along the road, the elevation change is 1 m). How fast is c 3rb w*i.:kcz), juukit going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leas5;-rp8k1iq fcauvnoc 5vvo;rco+8*ning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the averagavr sc 5v1r- 8pvucfon5 k8ioco*;+; qe force of air resistance?   

  A cyclist is coasting at a steady speed ocs. oa*94* j7tgjxwal -du4ob f 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge froodc4l*4t *ug 9wax-jas .j7obm 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 rede9a:ts, pfy*timv ;4b3 houph. sign 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. A particular small car, with a mass of 1100 kg , can accelerate on a level road from resp4a iy 3t;b*hv s9mf.:t,uhop t to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangler)u;cdu.o+m6u xp u3 ms her watch from a thin piece of string while the jetliner she is in takes off fro+pu. 6u3;o uc)rm mxdum 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 connect,g) y+s q.l ru)z.irn:h0yegftk3v o-ing differentnfql 0vh r-eoitkg,sy+yg:z. 3)r) u. parts 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 ) using the p*jj(+i6pifjw4usa s :ulley apparatus shown iwjsjusp f4a +:*ii(j 6n

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:fc w:.itqt2 mpx0ndbngn 23k+2 gjs1 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 thejr 1sp-xhu4z: 4+qy ig following se44xr-s1phz ujgiy+ q :t 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-car Italian train has a mass of 660 metric tons (660,00ag. ac1gs1mn y9 es4jo2tqe89 0 $\mathrm{~kg}$) . 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, ue9r jat5o uu242. wx/x1x sagb)s) spjse 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 (jsutxb xs 9je rw5o)ua14x/ a2.sg2) pFig. 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 boatni *4 w;x92of a1ykbee is using 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 builg+ capc2pj7 (eding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fieldz0n 64c6 dv6hsl2symhn5/wg w incline6s6z402 /wyvg6wnh m5 l chsdnd 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.