Why does a child in a wagon seem to fall backward when you give the wag *u0jl-ipqp19dgyp g.on a sharp pull f9gj- *p ldyqgu0p i.1porward?

A box rests on the (frictionless) b :v8 ckw)*57jpz m qrbl8l)hbbed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starhj )zl57kq8bp br:)c*vmblw 8 ts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces ay:k) ecvcwb tckul +1bt37d*3cting on it? Explain.

Only one force acts on an object. Can the object hmh /2eb+ j(c1zf21dl8ivo 4+bnwnb sl ave zero acceleration? Can it h+vsij2nz mo2 b(41n l+/dcb e8fb1lwhave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force-j( gl xsm073zn ,f8/;cniynw*jswxr needed to make it bounce back up? (b) If so, what exertsni7 x,z*/jss mxg8(30j;nl c f-yw wrn the force?

If you walk along a log floating on a lake, why does the log move in nz9heu,nl 9k- the opposite direc-n 9,u 9zlknehtion?

Why might your foot hurt if you vya4.kw*h p o dbawy,h7;q ;,ykick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quick;7w* t)y /;nkr 8spoa9 r:7nfg wxjljyly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usx8laty:7 *7ysgowwk ;/p) rj nnrf;j9ing 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 ceili5,x 4-4kfnhu4hxtd +neky+ zmng, and a section of the same thread x4 4,mezdhnn+u 4kykt+5f hx-dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock6 teeidi72 uk3,sdu2y . Why then doesn’t t,62ii2u tsedye u7 kd3he heavier rock fall faster?

Would a spring scale carried to the Moon give accurat4wwwjjdo4l 9q) dh+6be results if the scale had bqlwb ow+)j j44w9hdd6een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionludei8 uyc1 7b uy+:en:ess table using an attached rope held horizontally. If you now p cnuy:1d eub7i8u+y :eull 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? Explain.

When an object falls freely under the influence of gravity there is a .7(l ayp.azaenet force mg exerted on it by the Earth. Yet by New( a aayp7zl..eton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kkuwd 3hbyp;hk 1+98fo g 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 doy9uk+hbk3f;8 pwh 1object 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.v/cx)4 zz t8zi 4–37) pulls with equal force on the other team. What, then, determines which team willx)8ciz/z v 4tz win?

A person exerts an upward force of 40 N to hol643 l)n/pz awto(.p,vcnqewphdy: n;d a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, acnaplnp 6oeq(d)h v/zpw t. n:y;w 43,nd (d) by what object it is exerted.

When you stand still on the grhu4-:l4louo5x5jq;x. nchyc w w m/ :oound, how large a force does the ground exert on you? Whxujluw:w-;4oq4.n5:cxy mo 5l ho/ chy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car is edazoa3fa,d,hc z::7 j 6qn4e struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it reaa,djz,cnqhdzo 6f7 eaa 3e::4lly?

A heavy crate rests on thz 43j6/7l 9kc;gvfj7rny qltne bed of a flatbed truck. When the truck accelerates, the crate 6ljn; vyqk4cg9f77nj r lzt3/remains where 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 ypkku wrj2 /5/+jb(0wjao ,rgblock reaches its highest poinguww+j , okkp/a/( rj2rj05b yt, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yom b3f.mc2gzjo(icj)1sx+:b eurself on an inclined plane? Assume the mechanism functions properlyo+z3bcjmc g b2).jism 1: xf(e, even at an angle.

  What force is needed to accelerate a child on dq( 0a -gxl8 75emwz)tfdo0 rda sled at 1.25m/s$^2$?   

  A net force of 265 Nw+l/ks lk:9o s accelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsh /i:.kwpge 0 ekgl9+ttand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oflb(y4p-rc4poqy ;pw w8q)0 zlfi0v 4 e 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-kg car in 8.0 s if the car hi 9mo)jg6y)v is traveling at hv gy)io9j6m )95km/h? -  

  What average force is needed to accelerate a 7.00-rxsijn* 0g5i3h0cn5 p gram pellet from rest to 125m/s over a distance of 0.s5jn0 i *i05gcpr3x nh800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically 4 0atlnrz;9qeout of the water with an acceleration of 2.t4 9 erl0n;qaz5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 covesgtk3i 3* hn 0pzzp./gr 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 designed so that the maximum accelerationz8 1b6fy-iqa e is 0.0680 g . What are the8-qeyai1 zfb6 maximum and 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 scale4egr7(.na cccxk4 r;u in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the pe( cn4cca4 x7gr.er; ukrson’s regular weight. Calculate 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 ;zs aq;yec 8bf 45im-t-b*fl+jru1on of 21,750 N. What maximum uz;au mbsb+4ie j-;n -cyt lrfoqf 81*5pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of tw(t x(1hhdz(w5*zgajjh3+e d so falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equah5wtjg z (ae1(d*hdj s (zxh+3l 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 t8 csc8/ p;lltehe ground below, he bends his knec; /t 8slp8elces so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs ve3jd tpyc(-h tve(6 ;aprtically upwayt dc ;h(j-pe(36 tpvard 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 diagramvlcdn5y ) fl,3 for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at th tgwog1m,p 0k1-+-qh +onp d0zsy+lnce moment it is hit by the bat, and again (b) after it has left the bat and is fly1 lnyhmo ktzg0pn0q +-,sdo-g++pwc1ing toward the outfield.

A 650-N force acts in a northwesterly direction. A st th3k14.qiwmu+1 epsecond 650-N force must be exerted in what direction so that the resultant ofm4uq is1pht.1 t+k 3we the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acro q57;s4 r-9aynmrcj+ yu) lborss a "high wire" strung horizontally between two buildings 10.0 m apr4b 5+j u)sr;qn rmy7 cl-o9ayart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless coejm4jw d ;h+q4- o :rkujq3u3xrd from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.ux*e il6g:2j jnkm3ph8h)3c y0$-\mathrm{kg}$ 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 locaml-if6 ny+ 6d5puh8m f4ltj 0dtion at McMurdo Base, Antarctica, as showld6 l 4y-8ffim+nt jd6u0p m5hn in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling twvwp 7dm pa4-ma 1iyw.*o cars of the same mass behind it, Fig. 4-47 . Dete41wmpdvm -ai*7p aw.yrmine 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 pulls herselfpyd 6 eqr4 gs,r+kj5;d upward using the bucket-pulley apparatus shown in Fig. 4drpegqkyr;5d j6+,s 4 -48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race bkay ugsbg2n1e0 g7s zww260 k9egan, 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 (jn3jr g qx8xe v b3gb(o)y7d+dnk178 wmass $ 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 frictionlesd h4172ukue;q nsba8k/4(i 7eo wupjws horizontal surface are in contact with each other, as shown in Fig. 4-51h1bp7w48su kuuk j( a /idoqn47;ee2w. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above ynruo.n*vw z)t 6yok /49tej 9the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter)nur9yt6z4* y k9vw/jeootn. 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 cor e zf.;us :qwh6fsve23d of mass 1.0 kg . Calczf: sfe;3q6 .vueh2wsulate the acceleration 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 friction 0 w c: 36q.xhb+ rbk2kiaehf-pbetween 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 start6p6bus h2pjtl:a*a)vcq q(k 6e hkw83 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 0.2rhj,o qn2w3k93 lv.uj0g. What minimum coefficient of static friction mustjnqujr wko . 923,l3vh exist between your feet and the floor if you are not to slide?   

  What is the maximum accex.a57p rvv*6a xvxd ;h r29wwileration a car can undergo if the coefficient of static friction between the tiri9;*pxvr5w 7d2w.x ahrvx va 6es and the ground is 0.80?   

  The coefficient of static f 9 ch//jojxnyh .sr6m2riction between hard rubber and normal street pavement is about 0c2sr6 hh xn. jj9y/o/m.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4/)k z4eqo,nfx .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 rough 303y1o-htaua cq2t zjm g* qf8; q1gx7b)$^{\circ}$ 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 wit/g (wzposc -,zh an asphalt surface have a very high coefficient of staticz, (-c/spowzg friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction for 6/q2yfrc) x 0msl4 e 7-vyusofa $ 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 2ovd,ywd jkoh 3c:d* + r(xz+ra mass would box A have to have to prevent any motion from oc z (*:ch2ko+ddjrdr+v w3yox,curring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so tpcc-e nh(b:pl / rfl +vxqc393hat it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiavnqxr+/l:- 3c ecph3(f9c bp ll 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 y z8li9avt,)vabyx)7fr/e. o:2 bkl a3 vd:f jhorizontal surface (Fig. 4-57 akbe,il)vz2j3/.y:v9l:otf yr)vda 8 afbx 4). 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 coefficno9+- 91h+z ldu-k q.g,jxo inaqhh0gient 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 xj zhhai-d+uo,q 9-91qk0ngl.h o+gnavoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has annun, )uafxr74auyy :0 incline oun04a:,x) au7ynfyurf 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 awhzd(17a ,02pki h, yivkkh+b)2bi gn slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-:uy,a3n luvo0 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 smkw wt:cg m1iz0:,o2t8 tn /qypeed 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 steepest hill with a speed o*io6kbtd /1 p:ckh h3qf 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 someonaz,2h4 j7p q za66iymae pushing on it with a force di yah,paa 26z4q6zmj7irected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous proj,hl*ws 1* b;rqtzhjo ;nj44 u*3zc xlfectiles as they melt. Consider a chunk o**lu ;zz jh*chot ,l4;rj4nqs 1f3wxbf 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 automobkw p; vu 8rbo25/lmyoicok(,/ile traveling at speed v is 8m /vkl52,rbc(/iky w;o uo poequal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dv9 n e21j0isugash when the driver decn2e01v g si9juelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given a p28ke tpvza;,n 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 tm4nhk4x+ bwzo4t 0assgx 2 u2*hey are filled to the packing station 11.0 m away. The belt is initially stationary and must f04 n2b2h4askouxt w4s+*gxm zinish 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 f;wy66r2rp pg+hv* p( txurnv*riction 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 a 6.ed 30m+kqkt7 b0$^{\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 pulse apnwkdy 7 thu,dsmb6 ;q1aa*5 -uproximately 20 g of blood is accele5h *6 qy1 sb;tadd -u,7mnkawurated 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 au,l5y8*e qux47 io beeltomobile crash if the deceleration is no more than 30 " g 's."oyq 5eeb7 ilx8e 4u*l, 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 ,mg (gz5cwi2( k and if an object is going to "hold its place" on the ground, show that the coeffici gickm5(2 (zwgent 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, examin.4i /kx3hkaddi:. ,t fx2ucddm7n/n oing the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient tn dd,ddm oii4unh./f3.a /2xk:xk c7of 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 (ijuurzgp(/ pr 24p4zcp m.t+down a 1-in-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 when it reaches the bottom after traveling 5u um/iz j2(p4rp(p gz4rp. +ct5 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower ofm +ark*xmao beg3tvjvo6f/ 873+ iq9w Pisa and falls 55 m bef g+r7wevo*a3 i kmvbf6 qa/ot+xj83m9 ore reaching 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 ed ,jc6sn/w*krk/ *ov8/ dhnj1j1lkln nters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddv1jo d8r*k cjjd*1nwsk n6 /l//nkh,ly 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 redesign of a hilly portion of a.z ;ulg,o- u4kxsy5qn city. An important consideration ;z-snyl. guq45 ux, okis 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 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 experimentlr o50lyn lw.w.bfv3 6s, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an ll0n ybww.v5 3f.lr6oangle 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 co 33px9e ;ucb3 wp8mb*s(cqy ;wpdf j7bnnecting different parts of the sw*bfsj(y 7c;dbpb p8e 3 3wqpx;cm 9u3tore.
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 i.wpjhil 1s j: k(nfv;;(f n4xls needed to lift the piano (mass M ) using the pulley n:nlpj1;;xv(w4ksjlfi (hf.apparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at r4mf9b8 i *2miro k+fh3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-restrainz7dfdms 3 -n.nct.v8 dt chair, an engineer considers the followin.d8 vdctds.nf - 37zmng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car I(qvjks:b 4)ugixy)f 8talian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar lhsu g p1g6cuf8x/vdfv5e /a /(ength. 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) E/svf5ge1hpcx auf6/u dv8(g/ stimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1d+)p+vz t8elme0 kv5 s0-1 $\mathrm{~b}$ 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-tvq6;vduy4 v0 nclj6 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 togethdwq9oci8h a,re91fc.o xm2s (er are ascending an ice field inclin.8f dcacxhr 2e19qowi mo,( 9sed 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.