Why does a child in a wagon seem to f6co/j8:t z fieall backward when you give the wagon a sharp pull forwaezjtio6 cf8 :/rd?

A box rests on the (frictionless) bed of a truck. The truck dp9gk *v r0zp 9(kpq lrzk1-i:criver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Disz cgipq9pk*-1vk (rpr0 klz9:cuss 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 acting on it? Ex7p38mb.nkcigfi 9vs3 4qgy h; plain.

Only one force acts on an object. Can the object have zero amp)pp8u 1d ye-cceleration? Can it have zero velocity?-p mu1p8ype )d Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a)c7dko h1*ut iuvf.j./ct v 8t5a0r9hg Is a force nejt.5 f7aut/ihu8*c 0hkg9v1.rvto cdeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floatinqur/r/l r :,ge;nn*lcg on a lake, why does the log move in the opposite directio: q rr encl;*r/u/gl,nn?

Why might your foot hurt if you kick a 0dlqf15v aa:tw 4elh, heavy desk or a wall?

  When you are running an:syxnpn ae)xi/ t(1e mbta-m;au+t / znn,)l-d want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) th-nuzmnxl,nma sx;eya+t )nt b-i/1ae: t)/ (pe 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 ceill9t b45/wl clling, 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 gives a sbl5/c4l tllw9 low and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on7mlqc8q1,v) 2mx hf)ejpwiql 1:-ery a 1-kg rock. Why then doesn’t th)qev l182im1:lmq)-7 rxw,yjhf pceq e heavier rock fall faster?

Would a spring scale carried to the Moon give accurattl,i8he5 2t ree results if the scale had been calibrated (a) in poundt,eir 5 l82htes, or (b) in kilograms?

You pull a box with a constant force across a frictionless table urzh3(+ :bje*)srr8ip*rx xlasing an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on thz+biexlh)8rx p**raj( r3 sr :e table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the 1-p7z0 xoy1t*mw7k9z d r vquminfluence of gravity there is a net force mg exerted on it by the Earth. Yet by Newt*m70 t9zupzrk1qx ym-1w 7vodon’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-kg object when you arngj5;sg q0hslo h*3w: e on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizonta:s5* 3g; q0hojlghn swlly with a given speed on the Moon and on Earth.

According to Newton’s third law, each tea y)vy5-l8e 2vy(goddis/ 6uo tm in a tug of war (Fig. 4–37) pulls with equal force on th)8y6o iu/sy5vo ydt2 (dvl-ege other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thet1hp.9 l0 wgrz:hg y*k “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (dg wy 0hr.k1hpt*z:9lg ) by what object it is exerted.

When you stand still on the ground, how large aiuxwn: x 3n1*r force does the ground exert on you? Why doesn’t this force make you rise up inw r1:xi*nx3nu to the air?

Whiplash sometimes results from an automobile accident when th i(o mqp2u74plghz (x;, nepzt06x ;w9gwawg1e victim’s car is struck violently from the rear. Explain why the head of the victim seems to 7z0(gxen, zpam(hwi4 ;2 xgtl pugww1 q;o6p9be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed tru1l-oqd ;xz2o w lr;pod15) erzck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crazrz ;wq-dpd1;rel xl2 )15ooo te to accelerate?

A block is given a push so that it - +81rs z2cccll+yvstslides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration iysc c+t2r sll+vcz18-s less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pla iqd/ 0si4ktj/c u5d 7eekfczpqo:2,.b/0sllne?//li0i 52d0oe, cdlb.f4/7t q puqzs :kc eskj Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a :zp74im, r s,psicj6 :mezk) esled at 1.25m/s$^2$?   

  A net force of 265 N aced:v-4st n7 dp9qsf8wj8c6xi celerates 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 wn-vr 1ae2, euiithstand 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 of a;rb*v0a* ti/b k pxqo4 $76-\mathrm{kg}$ 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 required6ll/1u f(p5 2gksv klgrfw-8k to stop an 1100-kg car in 8.0 s if the car is traveling ap /-fvl r2 k lu8fks5wg1kg(6lt 95km/h? -  

  What average force is needed to acceler;xffc9/i rkl)oi :b, vate a 7.00-gram pellet from rest to 125m/s over a distance of 0.80ivlf:c;,ofx/ ) ki b9r0 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the watj4q/th cyy2n1er with an acceleration of 2. /ycqyt 12n4hj5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 canj6pmr+f of ).e 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 so that the maximum ac 2)g4sehkz 3dmt4l6xgf1ymqn- .uq3 tceleration is 0.0680 g . What are the maximum and minimum forces gknlft yhm-q21q.t3 6gsx)4 md3uez4 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 ) o9z4lgd f; cxn5fmx:a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculatdxmfoz4x; c n f5:9g)le the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a max5mh/h.rw(6s.m4whmgy 8 vcgrimum strength of 21,750 N. What maximum upward acceleration can it give the elevator with.w(5v m 64rh 8h.mywc hr/mgsgout breaking?    ( two decimal places)

  (a) What is the acceleration of tw:uy oti+-njp/fxn2n+;s- uceo falling sky divers (mass 132 kg including parachute) when the upward force of air res+ c/onisny2u:ft;- p +xej -unistance 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 roofr7k qqhsg ( j7k:+zn4tu6dud2 of a house 3.9-m high. When he strikes the ground below, he bends his knees so tsr u h7q2q7gt6(udd:jkn4 k+zhat 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 vertically3eecqyb9je iw2g:jf0 3 o. 7ys upward over a pulley and a weight is hung from the other end (Fig. 4-40). Det:2o yi30eqj.3 ew 7y9ebgf jscermine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player h58 z .lvqcspe2qp:3 y
(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 22 f)fig 7fuxsis hit by the bat, and again (b) after it has left2i ufff7 )g2sx the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly z-1wwg (j3qpgn *7g godirection. 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 vector diagra jnz1g(gg7*opw3wg-qm.

  Arlene is to walk across a "high wire" strun9fv/r 1cz udl1g horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint iszc d11f lvu/9r 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 lja x*7(7h, bjut:au sis hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.s95yjsacy75 w:2e. nzdk vnj00$-\mathrm{kg}$ 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 McMurdlkv guheznk t5d;()92o Base, Antarctica, as shown in Fig. 4-46. The sum of the fozn2)d gv; luet59k h(krces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 tmy :: )/dgtoonwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the c to:y:)go/ ndmoupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using thed. .og:5l np nrlwlpb4-+11bux l 7fmv bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward t:7r u-gpn. blo1 l+5wn4.xmv1flb ldp o 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 racez nuxijhf,q)bv .t7., began, 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 blol xi-sha;rb wu: 6t42tck (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 k r6 re;o7og+bsurface are in contact with each other, as shown in Fig. 4-51.+ro7 kbreg; o6 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 the ground, ankcxysb/3w94, mhdaqg7dn gr8n9*1 w sd the massless frqsbwdkc8 xwsad3mn/4y7g * h1grn99,ictionless 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table aho0gd 4.2c9.kjs gmp1k t7duhre connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams c gkd .d k097uj. po2sgtm14hhshown 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 between clq m*vp b62c7a 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 starth5oul4ug ;rcd*5j5sp 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 acceler7*hh805eblc /tv hv6k kthiw/ating at 0.20g. What minimum coefficient of static friction must exist between your feet and the flk6/hh8 0h5t ltc7kwv/ vebih*oor if you are not to slide?   

  What is the maximum acceleration a car canarfo/jzu 3(j / undergo if the coefficient of static friction between the tires and the ground is 0.80?jajf( /3/zoru   

  The coefficient of static friction betn*im)lwnsf t)) 9g daqi6:tbit: .i:tween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car pa) 9.ngbnastid6w* ) t ) qmli::ftit:irked?   $^{/circ}$

  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 qt ct5p a avv9n. :s/ c2/;xq*ofunzt; -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 ro 19qg4zqm7he vugh 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 s(tcge gq7pt-y )s5*m(pk6x ncurface have a very high coefficient of staticxpptgc(5e qn 6s)m ty-*(c gk7 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 a 7 (l xiohb*zr8p*+ 2gt7waelf $ 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 a2 u (y9l5aa9qcvgb pxayc1*my.h8x0m mass would box A have to have to umhcv x 9 8*paq(.yy2mglb0xca51 9ayprevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides itc q0dl716(aj 2uwzi across the floor. How far will it go, give wz juci6qi7 1(0ltda2n that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horih2zze3nqax 5h g; t7ytxe e)-(zontal surface (Fiz(;7gn)-3hxyt5e axtz 2 hqeeg. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. 9jm6d-: juju); a6,irvbtvpw The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate a6 6iv9um:wj )but, vdajj- rp;nd still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car4b,: lef0a- x y.75aqpqkd l/ytpf5f h in your driveway, which has an incline of 1qa ,eyp5xlf-d:f0 tkaylhq4 7fp b. 5/2$^{\circ}$ . 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 sli7 mj k4yjr, 0 tp:tmo2wwn/fw,de 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. 4-55 lies on a planetvjxxp ,b7w0+x4 (u1 c/ubc50 mvge p4w ;zorx 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 ans yfiqtb4y ,e)6 oq2)a initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches t zyakdswo8g,- zwnm++ 0m6.ulhe 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 pushin hj5rn9m2wfvh :g g8l-g on it with a force29- 8n:m whvhf5glrgj 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 7*)pbjv z220n+e1 rqwc yp blgroofs can become dangerous projectiles as they melt. Consider a c*q0 1lzyp) 7gw+ erp n2b2vjbchunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distair:a(9pny kr ufpi46.nce for an automobile traveling at speed v6pur4kary9 : ni .fp(i is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the dr prjn4)b 47wudiver dec4db )n7jwup4r 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 an initial n32aig i) lubvhyp/ el(b2v;8speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to5z*w 7rvaalf0ox hx, k+sa9 x/ the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplishedxfls05aka zw/v,+r79o*ax h x 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 fricych( tj (7 zmzk.rcr6uj-t ltf:/.2v otion 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 ,xy up1/u tc/kdown 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 mode r.. 3hjvhpv)38ajbvjchek 8/ l of a mammalian heart, at each pulse approximately 20 g of blood is accebk3/v3p jcj) vj h ah88eh..vrlerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if ,:ia,knv2c 08vy he hpthe deceleration is no morc08 khvi p,h2yea:vn ,e 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 earthquake is acpl38zb* 3 rri , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictp3 * r83birzlcion with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accvx6zx -zkj8-4jj4i. m-qk6zmwt8 ou sident 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 0.80t8v o4- 8-kuxw4z zq6jim6sxj jk.-mz. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for eacfw yng -h3g60 a*5di /8dqnjprbdw;n)h 4 m traveled along the road, the elevation change a5 /0-gbnpyd)wfg;i8r qn3jh6w*dd n is 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 Ttodwf pr.*; f7ower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resis dt opf.7f*;wrtance?   

  A cyclist is coasting at a steady speed of 12m/s8mybf8o wlu bb,3cb* ( but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy *w8cly8u, f3bo(mbbb 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 t-a0 w9ed snucjm(s6jbeq. 1 onfn-w07he redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass do9j0 semfuc0aw1nnb -sej6 q(n .w7-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 waq);nc5c9 z (w,u dnrkctch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She z9ck 5d) ,rnwcun;c(qnotices 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,kt+,p b ok7s4y there are to be several ramps connecting different pabt+4, po kyks7rts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift yv 7l*or1 .wljthe piano (mass M ) using the pulley apparatus shown i 7y .j*vow1rlln

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 acceleratinz0y bjp(5(kgqljz k- kv6vdc468 kbt) ,ur y+hg 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, c gse g yz)-dt1p+ds41an engineer considers the following set d)+dspct1ggz e -y4s1of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has l;ogbo 3l *9fka 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 ropesu 8*omajp fwqw;(4**if) fig u 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*pi mgf*u;u)i4o8w w*a j fq(f 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 " 10-wp/g o+/9fag4md noz )yf5p*r1 $\mathrm{~b}$ 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 iirs b4 .i;vwyu3(xr8p s 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 togethe)a2,3hy// h8lxal m)e g a(b zalyyql7r are ascending an ice field inclined at 2aaey8,qla )/ h bl7a2lg(lxzh3/)y ym 1.0$^{\circ}$ 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.