Why does a child in a wagon seem to fall backward when you give the wa(o u69gdshmj/5zw.g7 f gj5ww gon a sharpf h(ojw9 s wmu7 g6z5w/.gdj5g pull forward?

A box rests on the (frict 5u98qgxjvv,s ionless) bed 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, aqx 8 g5,v9ujsvs seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration 4tzd b0 rjo4fwjnf03+-l y,nqof an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can theft((o;f bcu3nulx)o , object have zero acceleration? Can it have zero velocity? n3 (ocxb(l u)ot;ffu, Explain.

When a golf ball is dros j9 ,n7f,g;tyhmw xn8pped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up?,xy8w;7tnmfh 9 s,jgn (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mz) zh/z1yuv-2 97 dc ksoggu2 6x.hxxzove in the opposite dih ug.ghk2y zxdvz -xz)72cx9sz/6uo 1rection?

Why might your foot hurt if you kick a heavy desk b.h(grfy j +c1or a wall?

  When you are running and want to stop quickly, you j: s;,lpq9xcs+ ok2(ojy:sdmmust decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum ras:p x,o mj( l9c:djq;2skys+o te 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 awfz.w cr zyt.56zj l,4r xqv., 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 threzyzf4c ,r 5.wqtz 6vr,.x lj.wad 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 iie 6h,di1us97ve lg-u s twice as great as that on a 1-kg rock. Wh7lv ,u19g6he iusie d-y then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale.u73f u 2mkj kcd3ox: i(nbx+e had been c jxxbfe. uk72co+ 3k u(3dm:inalibrated (a) in pounds, or (b) in kilograms?

You pull a box with ide7p6uf apa;.lozj/u o( u+/a constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining f/p.aoe7f adlj+u/ 6puizu ( ;olat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influe ev(bj.97ar4xld d;c znce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton 7(dzjlvb.er9c;axd 4’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 arant0-z /gd sdl:pe.-je on the Moon with the force needed to lift it on Earth. Compare the force needed to throwj ./-ldtdsap- n:ezg 0 a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug.uw+u(/nf b+h h(evafjvob7 8 of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team / a v hvjn((+bhu8.uowef+ fb7will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descrigp tf*ory1wh427d/l0 nas0f 5qa *hh ibe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it i f2nhdhys1qg p0fiwa5r0h7 **to 4/al s exerted.

When you stand still on the ground, how large a force does the ground stlj k3l0am9r 1q4 .84ig tuflexert on you? Why doesn’tljr4 .g1fk 4u3tlm0laqti8 s9 this force make you rise up into the air?

Whiplash sometimes results from an automobile accident whecf-h azq-7h;p n the victim’s car is struck violent za-fhh;7 cq-ply from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acy -wd2,h hsy-scelerates, the crate remains where it is on the truck, so it, too, accelerates.2swsh,-y-ydh What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reqe8 (,a5s-qe1 z)zhst 9vblm paches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on ,a19ehv8smq qszl)b( t e-5pz the ascent. Why?

What would your bathroom scale read if you weighed yourself on avbcpp7n8 yx)+db na(h; 1kil2 n inclined plane? Assume bnc)y1x7 apvd;+l (8ikbpnh 2the mechanism functions properly, even at an angle.

  What force is needed to accelertb*,j2wqr zc :4)xmd am fk8t6ate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike ae4ha 3pbqy t5(nd 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 is9.w-g-ndcupd umf :9 t 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 s82 ay* (du1/vq vamvsa $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car 7exgjxe cd2(19j8vl qin 8.0 s if the car is travelidxc1lx eqvj78 jg2(e9 ng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gr ;fn c:et th;lr.:j3jeam pellet from rest to 125m/s over a distance of 0.800 m along ft:l;j ee;j:t.rh c3 nthe barrel of a rifle?   

A fisherman yanks a fin-fm:8:roy x/b 4jy pcsh vertically out of the water with an acceleration of 2.5 c :by: -8ofjp m4xynr/$\mathrm{~m} / \mathrm{s}^{2}$ 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 cargnkjy8t g85n6 can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum acqez q9vq6n94d2 vxt .uceleration is 0.0680 g . What are the mat ve46 2qq.xundq9 vz9ximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. Wheo3)3 wd1diszyn the elevator begins to move, the scale briefly reads dz3wi3) d1o ysonly 0.75 of the person’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)4esv; bu2erb s57d nt a maximum strength of 21,750 N. What maximum upward acceleration can it5b ;es )2rbevsn4du 7t give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132obxx2 i w9;/oq kg including parachute) when bxx 9;2oi/ wqothe upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from tie jd 93v5sep:he roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m.: 9jsdev3e5pi 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 bbji,9uc0id j26 i uu2nox runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that ti6jci2u b i, 9j2nud0uhe 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 f (qywc+ok6uczve5w (dw3 vm34or a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball7b aygq) 6pqu4 (a) at the moment it is hit by the bat, and again (b) afte yqb6g4ap7qu) r it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-Ni88x.y6n: ejpmn1mvl force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a ve: .ni8mvp1n j6elm8yxctor diagram.

  Arlene is to walk across a "high wire" strung horizontal1g6 f03,sb-vk )whw hf nhnj m6qum194b0lwf rly between two buildings 10.0 m apart. The sag in the rope when svs0 kmg rjmnfnb4b0)6w w whuf361q9f1hl -h,he is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is 6bf qb law1o-6hanging 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 14pgt2 lmypx:nub)mm; l6my7*:h28 wtt.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, Antarctica, quqt)z0r :t s( ccx/r1:9vwesas: 9essr(1wztv/cq uqxr t:) c0 shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 39tv wsu p6(mx4-47 . D(6tws3 vu 9mpxetermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pull*zpy5 ly2 igi/s herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constang2 yiy i/5lpz*t 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, +;fpcim 5mf0xivu)8c( *h lhx 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 (ma2vh,civ .8nby ss $ 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 are in contgx +x plw4v*0tact with each other, xg0 +*xw4l ptvas shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are eaczco+vb.xrf 6 d g.80yhh 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 object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at th.zdr. 80cgbv+6of yx he moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord k ttq tr8 ueu*7e b.5v78tcyr9of mass 1.0 kg . Calculteku7b8 uc8tq7* v.yt9e rrt5ate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction betwi+(wk ykh g/t-een 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 ie,ilhfb542;rpsp 5o 04qecv required 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 stm8t9kxu e. l nz..5kxmanding on a train accelerating at 0.20g. What minimum coefficient of static friction mm9 xk t.ul.8knxe z.5must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a p.n x+my6,usfy5*lri: 2adda car can undergo if the coefficient of static friction betwdf.r2da y,56lsm p iyna:+u *xeen the tires and the ground is 0.80?   

  The coefficient of static frictu*4msbl qi u/r oy(a*,ion between hard rubber and normal street pavement is about 0.8. On how steep a hill (max,*ls o/q*yr buau (4miimum 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.a we)u:fs6n 8edj5cg 080 $\mathrm{~m} / \mathrm{s}^{2}$ 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+en qw u:8f 64q6x(bxyvdf nv7 a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an9x)uahf wk7 f;a g7th z5,k2ou asphalt surface have a very high coefficient of ,u77tokx;kah 5 z ff9ahu2) gwstatic 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 exdr5 o,ho6e649hr kffriction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how lxxh9y dt1 c(.x**bnv aarge a mass would box A have to have to prevbd*xxh9(.*v txa cyn 1ent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will itmohyhsf .8 :ps)ge3vp+2 l/xw go, given that the coefficient of kinetic friction is 0.20 and the push imp)e:hop 8 gmswvf/ +xyh2l.p3sarts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and an8rn 1gb* le5vt rest on a horizontal surface (Fig. 4-54). A 620ven5*nr8 l1gb$-\mathrm{N}$ 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 stai.f2aw bz ;jp(tic friction betwja. wpfbz;i2 (een the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car ina4, ;2v j)*ctbarrhx6kj;7mxzxj x 0h your driveway, which has an incline x0kct* 2j)jrxx ,z7 ;avx4;a hh6 rbmjof 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 sly*mi5xedtr 3i:eb1 u5ide 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. 4-5/k(n; .mgs8y )l5j-x sme/sr 6aoohqn5 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial sp3tr c o+ 2,afb/mobo9deed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 632wxb dw j d:o nofa):9vbv l2,3e*puc.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 walli th048wm9 bhv by someone pushing on it with a forc hm9ih84bw 0vte 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 projectiles ase;tnn 9-s1b, hva)kfo they melt. Consider a chunk of1n)teo a nsb9h-vkf;, snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance fsm6jn8uw9k6e/q /n4 9sxwng yl m6:w5x/ sjnfor an automobile traveling at speed n6/ 6n w m5mgnls/jsxnu/:q 4ewkf6s9 9xj8ywv 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 o/upj; d/3e wjo1elpp,f a car slides forward on the dash when the driver decelerat eped;j/wu jlpp1o/3,es 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 initialu03 a/)o6c; m haomsgl 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 fro5+pwu)6s gxl vp,y q csy99e3lm where they are filled to the packing station 11.0 m away. The belt is initially stap9u s3+s5)qg,ewl 9ylcy x 6vptionary 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 kineti.mgk3o vlp /q36+bnc cc 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 dusiydtwl;l8 7/((jokg (including 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 mancx:/4c6 (u ax2qdbfgmmalian heart, at each pulse approximately 20 g of blood is accelerated f(du qcbx :axfg2/4 cn6rom 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 (wrkcr il:u.* i:;v uucrash if the deceleration is no more than*:uu:. vi i ur;clw(kr 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 i-bw a,,zdv7 h)5ndfal s a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mufh, a5-dv7) ,bdnwl zast 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, examinisz vgcda6e7n1cn1( z) ng 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 kineti 7z11ndz(n6sgce) ca vc friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveledva(cq -xu:cmmsugl,h/ h:ipy+3 ) o7d along the road, the elevation change is 1 m). How fast is it going when it reaches the b hu luagy3m hd/ vs7qip:cmo:( +x-,)cottom 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 fro0o3-5, .1f nceus;pgmrke 3xwi yevz +m the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force ofez;e +i,5 eyku.1m3for3-nvx c0w ps g air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but en4f0x crznj -k3.+6ka:t nw7f9u s/e0 ropnavfters 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 lauje-n9 n : .ak3kzwxs/6+r 0c70naf rovtff4p sts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign o5mc h76qi rj9df 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 pard6 j5i79hqr cmticular 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 from a thin piece ovky x*t sv:1x5f string while the jetliner she is in takes off from JFK Airport (Fig. 4xs5v x*:ktvy1-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting dixrd ), p :u*ntyfaerv k1g936rc+2v irfferent pa*rit rne +cv3:2rxpk 9 agvfr)1u6y,drts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (m4vm)o ;6nioo;n*5cjr 8zstis ass M ) using the pulley apparatus shown 5ms6;ivn*ciz;4 onoot s )8rj 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 accelerati 6+vp 6bp9te5 ,g3widmrw)yfs ng 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 hqaci4z)hz( rp, 0ftz ld(p).for a child-restraint chair, an engineer considers the following set of conditions: p (hi)( fa.cdzp0z,q)hzt4 rl
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 t( c3ympay0/6sqp1ot f :xvt(mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Kareg rwy g*:ewf6r/:a(u o*ps3 ntk*zvn)(b (xx tn'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 falt:xe*z* g r( rw63abn:( ouyt*pgnx/f(vw sk) ls 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 using a " 10qyd1 rxgaaf(8ae 1 /rmj e:21j-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 gn:ot9*b;a lipru*7: b qamr/to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fiw 2ud4 3sdyv2rw5c9ukeld inclined a dy93usu kc54w2d2w rvt 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.