Why does a child in a wagon seem to fall backward when you give th v;uvp ugonk: wq*-);g )g oppf0;2lrxe wagon a sharp pull forwrgk; ggv *;;lo-q0vn fowp :) pxuu2p)ard?

A box rests on the (frictionless) beqaqjt0ix1fr n6q*sj-j)cz,f/ x ktq,m1jh + 6d 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, as seen (a) by Mary standing q+6 s6qh)jinqkj0*ftaxq, r zc ,- 1jjxtm/1fon 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 yqk*7c l(bzm4 rny+e d818lakforces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it -vk9 f-v/or ktspur;d4ty+(ghave zero velocity? Exkuvpd -fr-; 4(r kgot+styv9 /plain.

When a golf ball is dr3v48kf saf 5zotm5wg-c qa w)9opped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fzqak34sg w -m8v w5)9 f5actoforce?

If you walk along a log floating on a lake, why does the log move2ksbpnhy 0.y: in the opposite dik:by0n.syp2 hrection?

Why might your foot hurt if you kick p6,t j) 292ny2wo v)pshacvjva heavy desk or a wall?

  When you are running and want to stop quickly, you must dech 3emk)ge5zn+po3 da0t19:g vub+u tyelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximuum3 0u+e )tda9eh 1tkvp:+z bg3o gy5nm 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 ty8 40 zef)* kvi9nfetihe ceiling, and a section 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 thread likely to break: below the stone or above it? What if the person gi4kiy f)89nev fte *zi0ves a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is vc cq 4-6vhoaj/x vj6f;+qi/qtwice as great as that on a 1-kg rock. Why t6qq ;-vohc qvv// i+x 6cf4jajhen doesn’t the heavier rock fall faster?

Would a spring scale carried to the -a- y/ vpdf)adMoon give accurate results if the scale had been calibrated p-/aa-f)yv d d(a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an y251 wwl rlg7-t 1a7lb-szkorattached 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) incre1asr7bwl 5kty r1-gzl7 lw-2oase, or (c) decrease? Explain.

When an object falls freely under the influence 1 h0o,wxr*qfsof gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerr1q*,xo 0hswfts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needeh5tpjv8ja3 (ed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the fajv 5(j8te 3hporce needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, r3im6 q8k;arnmnrk ( 0h6bq4beach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, detr6n6q k bi4b(qn 0m; makh8r3rermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe the1-aj 7yy bz oubw1i2qn9m55la “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) y1wq1my oaiu b2l-j5bz9n7a 5its 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 grotf +g lq 7a;vb3;ufdb6und exert on you? Why doesn’t thut;va6fg3 7db+fb ;qlis force make you rise up into the air?

Whiplash sometimes results from an automqf fy5mp*vs: 9/.d,ayudp ts9 obile accident when the victim’s car is struck violently from the rear. Explain why theqs:p vpyf.y*5 dut,9amf/s d 9 head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on therr m0ygrvct7m - h/82j bed of a flatbed truck. When the truck accelerates, the cra0 jm7r htg-rv/mcry82te 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 block reachen + vkc 6r,q5 xcm6na 6htl c2mku)7+agzp,ht3s its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. g,q62 ru7t+cmv,a+k5k3 h6chxlczntm 6pn)a Why?

What would your bathroom scale read if you ,bx -8ux h52fvr2f(wdmhv(xy+hq kn9 gue 8q)weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an hx u-)g eyqr+58vxh( x9n2hf8 qk(2wbf,md vu angle.

  What force is needed to acce6e+sh xp:z7y rlerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerat7 w j/,ikui(nlh2f 7dbes 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 withstand ifta, :o,xvm:zs 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 ofn qd;wid2r6 f+ 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 cc:q(a0ymwl +4ato ag* ar in 8.0 s if the car is travelingog 0w*y4(a+a: lqcat m at 95km/h? -  

  What average force is needed to accelerate a 7.0 9ijcjs j-u+8i0-gram pellet from rest to 125m/s over a distance of 0.8+i ju-9cij8 sj00 m along the barrel of a rifle?   

A fisherman yanks a fish vemqh 1itra9(cgz 12jhuvea1ge5 8t *0jrtically out of the water with an acceleration of 2.5 20z(hea1 1tcmgrjjui5a*1ghqe 9 t v8$\mathrm{~m} / \mathrm{s}^{2}$ 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 capbn2spemvwtu hy8-kmk4 o )yr 3b;;3/n 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 designed cin1o6io 7ez6mw5p:qb/(gabl m kz67 so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor showzmg (z : eb oo 676kic7n/5alpm16bqiuld 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 motioaunr4rx q/3or 15:s 0:hlvio ynless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accelr 3rnl/y 5o 4:x a01vsqiuho:reration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengtj zx5e yvr(;r)h of 21,750 N. What maximum upware zj;5)r xv(ryd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includinj *ulg:hp,jbn p;/5nu g parachute) when the upward force of air resistance is equal ,u nhj;u bg5lp:*/ pjnto 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 thew)1cpd plk1spy pau; c (s92xpio- e,0 ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.71iopx10)wcdpa(p 9kps 2 ;yps,-uec l0 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 vertijhkr3-f got,; cally upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exetok f,;-3rh gjrts 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 basketbaio) ns(v k3s1 en9t;pzll 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 moment it is hit by the ba8tsqwn,d2 ly u 9u,k7oxk27/ bddu:iyt, and dwd7d9n,: oyk ,isku buq82y u7/xl2tagain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterll*mrrm ci ;- e7zwxc;c1t7re4bcj:+ly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your anrzceb mwlicr;r 4 -l1:7+cce;7mjxt*swer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildingam( b)kn uo ;(exq;4aa :fhba5s 10.0 m apart. The sag in the rope when she is at tha4f(a (mb;x:huk5bqo; aa en)e 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 han+wd urt-l k)k8ging 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 14up4*q u/p(evy.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 to a new location at McMurdo Base, Antarcts.v1pyq: 9 -yp;m:e xz6nrm2uowsi sq(7p 3nkica, as shown in Fig. 4-46. my:prq:es k 1q6pmy3nvusizp9(-2s xo ;n.7wThe 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 th6 ok)dl v js-1pqwte7(e same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and 17sv lwd-p)e q(6jtkothe 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 thecyild+al+ap73p -nh 1 bucket-pulley apparatus shown in Fiaa l1y+h7 n-3 plcip+dg. 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 began,(jnw6deb9r f ) sfy6ig ;.9kurv.l y3f 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 (mpls ub,ovbm 129l/, 7i f:buucass $ 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 frictionop+6-9gkcyn6c (yj*e6z s jbxless horizontal surface are in contact with each other, as shown in Fig. 4-51. A forbj(ko9* 6j6zx- sng yc6+cy pece $\overrightarrow{\mathbf{F}}$ 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 the ground5b*n4 v- qyyw 0asf,1fq*njze, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assum0v-4s1f * zfeqay*q,bnnj wy5e it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table arepw. u 9-wru,dggzooqij9-7y 9 connected by a heavy cord of mass 1.0 kg . Calculate the ac9p9- 9w z 7.,ywdujouoqgg -irceleration 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 pn0a 6seh5 5evkinetic 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 required to start c jilm5n6r o(19 :mpbua 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 standinbidy3om82 o+: qds4, j qwga.lg on a train accelerating at 0.20g. What minimum coefficient of static frictila8 jd,:4qosqm 32yo.bdg+iwon must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of staticasa 9 4y;2ecas friction between9y; scsea42aa the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemeqm,lg;hf z 8h5g5 /xzxnt is about 5l;,m8g x x zhgh/zfq50.8. 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 -4.8*dtih8vlff 0;vbthz22b 9h/4iu bm q*tb o9l -0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 mxe 3kg ()62 cs/yzb*d hns.sm 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 an 3bn;1xre7tv e* 5bmk very high coefficient of static friction.n5x nk;e 31 bbev7mt*r

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 forf 3z7*rsls9gret 1bvkm cnz:0f3,p / o a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass wh9; t,d 3:e r*yxd* u(opwysoxould box A have to have to prevent any motion from occurrix* e; dw u*3oh(xd ytr:ps,o9yng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fz, s8gbw 6m)juar will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts anbgwj s,6u zm8) initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass vo s,5rl;j v-t)cz,nc75 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A c) ,vz-t5crnvl jo;, s 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static friction/+eujx hu ,5gs8 wwm0q f-8hwq 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 th ww -uemxhh5 wqj0q+ 8,fsgu8/e crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your;a p-*w4f74gs nfbg nse8n- xs driveway, which has an incli-f 4en sx*pw4-s g8a; bnns7gfne 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 2:q 0mxav* okx/8$^{\circ}$ 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 ktw o)w2 +oqw*on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed 6cs cm2wpra(+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 reachbbr16.pzzz7w es the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone push,. ws cay/ 2pdjn78mku/ lh3jxing on it with a force direc.lhs2pnxday7j /mw /8,ck3 u jted 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 dange .uibgu0 g.0 ohm2c(xqrous projectiles as they melt. Consider a chunku2gb ..xgim 0oq h(0cu 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 vk r6i-1navg2x(h3rg(s 2w,ly h6lnk stopping distance for an automobile traveling at speed v is equayl(gvxr k1s-kg6w3(6 2nhvrih 2 n ,lal 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 forwad 3onrxk2t-nc lweiz :s56s0s2g;r p,rd on the dash when the driver dece: rz,2x ssgk2or3tpdcs5 iw60 nn-l; elerates 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 ac d:ovq +xd ) p+rrqoyer.982fn 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 cokb3 q0 it1 9z5 ulbe)ak:8meh avz.k+dnveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationar8ez3i+mbv a kz a05dql)ktk19b:ue.h y 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 frict8s+hjf z)i9g p.v3taxion 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 64c1b;2bvdjb(wrf fz;0 ;wmjb .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 m: ljy mj:lxdov;0 m0-sodel of a mammalian heart, at each pulse approximately 20 g of s0m-j0;vodl yx:l :jm 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 reasonabl bvl4-5bbiku+e13f9xo,f.o m xd s4 hke chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force o5hfbf4ki91-eb xk+uob .oxl,s 4vdm3 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 acc)x sb.yz o em6wh)8pr. x3wh0ametz/rb5t9n2 eleration 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 the grourw/2m mze.r. y p)0ntzs9b3 5bxtx8o6wa) hhend 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 scn. aduocv4 a31*rkmp: ene 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 of kinetic frictd:k cr .aum3*a no4p1vion 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- xqd,p0wkt q65u,yndrwt6*:f in-4 means that for each 4 m traveled along the road, the elevation change i tk6w6*wn 0,p:xudr tq,dy5 qfs 1 m). How fast is it 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 Leaning Tower of Pisa and falls 55 *mteac nz lf-f3ffq//,vu 24q m before reaching the ground with a speed a* flqf3 m/euftz-c24qnf ,/vof What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enterscd-q,3w24 tadz( dwrs 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 wt,s dr-wqc432 za(ddbe the speed upon emerging?   

  A city planner is working on the redesign of a7 3if. ,j/zhkn-dwazv hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars canwz a3d7kj/ z.hvn f-i, 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 physn8+ oc.qb3:gr lxpf. iics experiments, 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 anglcqo+lf.3 p:.rbxg8 nie 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 sh* f w8aoh*s0f4 pti- s+8bkrkupermarket, there are to be several ramps connecting different parts of the st tsf*4s8kf-+8i h0kabph o*wrore.
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 ) k;5kcw8; 6q(chaleisusing the pulley apparatu;whc ;ki68a cqs5kel( s 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 3.5gc8:j ( 5c0,poflq )o tu/xsxv $\mathrm{~m} / \mathrm{s}^{2}$ 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 conx)20* kc jngztdvcj/6o -r/cz siders the following set of c) /6jt gz/vck- *2j zxocnc0dronditions:
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 man u(+5 5;xxt3+lc e ihcqgw+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,so0w; rdgfz*, use safety ropes of similar length. Karen's rope is more elastic, cas,*dow g;f 0rzlled 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 climber is more likely to be hurt?

A fisherman in a boat is usin5s pcl -;hbzwkv*+ uqg9,p(i ug 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 speed of 3.5yfz-ok+yi+8fz 9/ ypf $\mathrm{~m} / \mathrm{s}$ 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 ron ieo0-rzg04/r1 az bkped together are ascending an ice field inclined at 21.zbkg1i z0e/ r-4ona0r0$^{\circ}$ 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.