Why does a child in a wagon seem to fall backward when you give the wuerd z a3;k00cagon a sharp pull forwarka0 3ru0;cd zed?

A box rests on the (frictionless) x :r)wkc1 j4ssbed 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. Dis41s)c xjs wr:kcuss 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 f fw8+)eq2y u lmocp0w;orces acting on it? Explain.

Only one force acts o+;;vhde9us:o ln2h olmn;+p s n an object. Can the object have zero acceleration? Can it have zero velocity:2ldsp soheumnnl9 ov+h;;;+ ? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a ;8skh cb 7y/oljd7me5g d+d /jforce needed to make it bounce back up? (b) If so, what exerts the force?g8ded jjm /d77k 5l+/bsh cy;o

If you walk along a log floating on a g gr)j 2/fe4ckgkjp fz w6(3p(lake, why does the log move in the opposite direction?jk jcwppze(gg(2f6 ) rg3/f4k

Why might your foot hurt if you +oogj s5iwbx,4sr.6b 5khz(tkick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec )dgz s x:v89:4hmkvyoelerate quickly. (a) What is the origin of the force that causes you to)o:kysgx:h94 vvd8zm stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same 7r7r h+ asj*uythread dangles from the bottom of the stone (Fig. 4–36). If rjhu7y7+ar* s 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 r: zk7xm0n jlwoo,l -1fock. Why then doesn’t the heavier rock fall faster7o,z-o0wx n1lkmj l: f?

Would a spring scale carr, vt 4wb: q-lo( fe,l9pfak)gnied to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (4lk ( nbt)f-ewg,, ovp9alf:qb) in kilograms?

You pull a box with a constant force across a frictionless table using an l or2l +oy( c/k yu*r0fjdu. c5hec4lc+k73iz 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 sam7kc+4+c k oru rfzcye0(do/jlyll3 hu25*.ci e, (b) increase, or (c) decrease? Explain.

When an object falls freely under the 1ky+h1kku-jv63y 5fc;yo iwz4o.w xiinfluence of gravity there is a net force mg exerted on it by y +6 xyf3ikkw-ojk1z1ih ;45yu.wvcothe Earth. Yet by 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 to lift a 10-k,zvc1xncp:u4b2, ;n 5 dyk;vi) fyqg ng object when you are on the Moon with the v2zb;inxnvy,: 1) ,ydq5p uk c 4gcn;fforce needed to lift it 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 teamn s w1n(5htx+s in a tug of war (Fig. 4–37) pulls with equal force on the other team. Whas+tnsh( w5 n1xt, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe y,(p tbf8 -q*nl.kprxthe “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direc rqxky(,-*bp.ln 8f pttion, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on kn s8 ;f9q(xflzq yq +ir d,5yq;--ywcthe ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the an+q lr(yqf s8 ;kq;q dy 9zy--,cfwi5xir?

Whiplash sometimes results from an automobile accident when the victim’s cpklvbo .x1 uqeiz;fc5 --73bbar is struck violently from the rear. Explain why the head of the victim seems to be t3l up b5b ox-bfqk1 c.vi-;7ezhrown backward in this situation. Is it really?

A heavy crate rests on the bed gftrz v bbro*.5(8yz6of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it.ry6bgz8*otb 5( v zrf, too, accelerates. What force causes the crate to accelerate?

A block is given a push snz,h i86r) 5ye vwmnu3 zb4i.ggqwn.5o that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of .wnzu 4iz,n55gib8mv)ger.qn6w3 hyits acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on;4p(u phya d q)7wj 7ax/y/tvj an inclined plane? Assume the mechanism functions properly, even at an an qa/ 4v /(xd a7);jythywp7jpugle.

  What force is needed to accelerate a child on a sled at 1.2d1 z(( : ridnw0iskhji/y0k 6y5m/s$^2$?   

  A net force of 265 N accef ( 4zjzi+)51f2iiyumcp:b :btaf hd;lerates 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 if it is usedix (an 5gh0j8(mu z41j p)nact 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 a t wb x0m7wmw ;9srd6/k$76-\mathrm{kg}$ 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 requi7i tx x+-*ttrqred to stop an 1100-kg car in 8.0 s if the car is travelingrt q+- itx*tx7 at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125m8envfedfy9 e: td mx 7akf1ppy85 x -3ok..ab9/s over a distance o.1nb9keme :af 3df t-kypv5d e8 x8fxa9poy7.f 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish yjh;ps*6nc)4*i:u qoloc-vz vertically out of the water with an acceleration of 2.p u yj *4h*os;)vcl-:onq6z ci5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarte ti;bt : x0yhv9xkcuou rt6*:/r-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 xh853kevpxngl6 7zy+ designed so that the maximum acceleration is 0.0680 g . What are the maximum and ml3gyh7 xkzvn e586px+inimum 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 elep6e n /;r :ovns)+nmtrvator begins to move, the scale briefly reads only 0.75 of the persv;stp mrn+no6r n)/:eon’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 of 21,750 N. W6ghrpof z -(,ii gr1z+hat maximum upward acceleration can it give the eleva6r-p+,zi rofhg1i( z gtor without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dadpmdk)3 j:x0ivers (mass 132 kg including parachute) when the upward force of air r:da3k) xp 0dmjesistance 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 strbiubi:ved a rr 7,3/mk5 m4y8rikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding lymk eii7r ubv48r :/3m5b,d raegs) 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 tab0r-/ehyjsaw 0 3uop1 cle. A rope tied to the box runs 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 the pu0-0ey cj how ra31s/uplley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball play+ tv( (,p v5dif+gghqber
(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 b lqreig(tad76/v 2 b1oaseball (a) at the moment it is hit by the bat, and again (b) after it hqe 6(a lv/2 1botigd7ras left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direelqd/kcls 83i1w jj iftz +370pni/7nction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vef0 jn/ li3tz7ckqin/wpis7831 j+ldector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildecxt pka1 *j0pw o+ze .u4m)4zings 10.0 m apart. The sag in the rope when she 41 ep+jzzt o* apxmcw.u e)4k0is 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 cord from .fu esooex e4bo:8imj1sa 9/4another 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 1knrr zqq4s9/b9+ .mzb 4.0$-\mathrm{kg}$ 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, Antarcqa2r1axeh u*b 68 rt-ntica, as shown xhb tq2-aauer 68*nr1in 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 two cars of the same mass behind it, Fig. / eud7z*bdu( z7j)rsmdp ov1( 4-47 . Determine the ratio of the pd*)mdz/o rbv(u zuj 71eds7(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 herself upwarngun-*yg8 p,wnj 5nolnj2(9s d using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must shensjj 8go(,n*gnp 92 n uwnyl5- 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 bega zj;q3)pbdzt it3,n9 +err hh8 9bwy-yn, 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 blockz9*kz )fl 2g nlxsm q()ii0il, (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface a3*jw bw i6yf*rre in contact with each other, as shown in F b3*f ji6w*ywrig. 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.+nunc pd zs;v9: lv;q2 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter ob+2pv dcnvu9 : n;;zlqsject 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 f0 a36(ykueigconnected by a heavy cord of mass 1.0 kg . Calculate the acceleration ofkfuyiag e 60(3 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 kineticepbc:d 81jc e; peh(-6sv xu3r 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 requir dh /5m4rcak6 (otqa5qts,qk3ed to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standmrqp 9byay.g i)w)+k0ing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not t +qab9.m ky) g0rp)iwyo slide?   

  What is the maximum acceleration a car can undergo6oen)icwh/h; j40 dli if the coefficient of static friction between the ioli04nhejd;6 )hc/w tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pave8)q(ntv dxytew5x/ ;sment is about 0.8. On how steep a hill (maximum angle) can you leave a car p vnewx8 t t/xs5dy(;)qarked?   $^{/circ}$

  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 wvvg b*3fj4l8 -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 rou2hg11 xj 5m4jij3jd*shn4 mlb3:gpx tgh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coe der83o7;91tf l 1(nr i(xrkqoiog-jwfficient of st1(eroo jw;kr 3f9tx di8( qnri7o1-g latic 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 g bs: kke(45- e )ia*rjx2xolca $ 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 would box A have toxmm ()xwd(31qn*nnt m have to prevent any motion from occurrim1x*tnn xmq dw)nm( (3ng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across thebojv-a 7):yisw2p 4pb floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an inisvi ywoa47-p2 : bjp)btial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contac,ns9b4gr; asyi-/hjp4v yy- k g-uc;pt and at rest on a horizontal surface (Fig. 4-54)pkbsgspy9-u;v-4ag;yj-4i rn/yh , c. 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 coj7k -mmb42 xchefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which thbk74m hc2mx-je driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cargls0(qhk, e.p in your driveway, which has an inkpsl0h(, e. qgcline 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 witkc sn 4z qegz+yb8(88jh a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies om+u gb ar)a ai3w)cz*pe16ja+ n a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3. 7 of/doa+lj (itbro430 $\mathrm{~m} / \mathrm{s}$ 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 obhqud2cr :m a0pi+38with 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 pushs3od xg. tjd 8ok4;b*ling on it with a fs.j ktxdl ;38obd*g4oorce directed 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 p moktg,5m v8o;h+j683mjb2 hfwyg5vkzc:d8l rojectiles as they melt. Consider a chunk of snovv5g3:,h jzko y+ 68h8bkdlm cmw8mj5 tfg; 2ow 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 automobile traveling at 4e s8l34utxvs speed v is equal to sv8t4 uslxe43$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 dash when 0urv-97rfx l nthe driver dec -rn0lu9fv7r xelerates 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 an in.hj0u9uud x mnqc233duk1 g 8kitial 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 wherjy;ux5 wg,e- xe they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if 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 i5-g,xx u;w ejys 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 of7x2 tgp (abnhp+1/ kmt 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 (:gskfs; 2eay 9 p9d50in1n/tu :lpk tcincluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each p-f0w(uxll/pnpi.u87 uogpl 0 )p s 2dkulse approximately 20 g of blood is accelerates xlupnlw(8 .0kfo0 pu uippl/g)2- d7d 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 s uuz.w6 0a1hl7e9 lpiof surviving an automobile crash if the decelerl97e6az.0lp1u sh iuwation is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earb /duf:akkgp +1w 6 4x.k0ovktthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with t:0 k.6gd1pok 4wv/ akuftx +bkhe 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, examinin1.x:/2y pz bd3o 7zay gc*negfg 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 of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car ga3fzc1e 7yd/b.ypz gxn:*2o assuming a level road.   

  A car starts rolling down a 1-inue ; 9 i+(cp1:iy-qp adiiu5zn-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change i d p5iiqciu:y-ena9;zp +( ui1s 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 P//bdalj 31dollbe7.ax m7p+- ndo1k bisa and falls 55 m before reaching the ground with a speed of l.al 3oo+1/d 7kb band-1/blxmdpe j7 What was the average force of air resistance?   

  A cyclist is coastingp/ ho6b v/lfc: at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. f/:ovbl6 hp/ cWill the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portiond ne8d; q)97gicsvhr 5 of a city. An important consideration is how vhd8 g) c9rn i5s7ed;qsteep 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 experiments, dangles her watch jnugdg1 8 1u ywp mqto4p+oc6q+i12x; from a thin piece of strinmyj41 gp g1uwqxqito1dop +uc;8 2+6ng while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there aihphzi ytnko8. ;j+g 97ch88yre to be several ramps connecting different parts oj8i g 8c9 78y;+nhki.ohyptz hf 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 (maswnpte2iq izp- +7(j/gs M ) using the pulley app+g2i 7wj n (q-z/teipparatus 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 acceler6 p b9z19gkryp8og ;ggating 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 considi t3- g1pta1gpers the following set of conditioip1t3g 1 tgp-ans:
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 mar qk0q vp-pv;)ss 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 pnjwrr:s 8(r94l 2txz pmx(,z ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretche92rrtn8 pzs4lpwmzx (:(r j,xs 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 i1fj j8mquy2o- -,r ko(xt7fy hs 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 building is allowed to reach a maximum speev.lfo ,in)q k-d 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 ann y2zu3/y e w z4mpw:bh*u9e4c ice field inclined a4pywcynwe3 9u4*zbe/um: hz 2t 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.