Why does a child in a wagon seem to fall backward when you give the wagwf gy.6 (.5 8z;/gqkwqnwjqyb on a sharp pull forwa b(g/wkj qyywzn6fq.wg5.; 8q rd?

A box rests on the (frictionle0nk(t+hul nedb3jd8a5ih+)q 2o ppj-ss) 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, as seen (a) by Mary standing on the ground betpqd52u8oh-j 3i e+hdpbl)+ 0na (njk side the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zers 8;/qk4vn1xq fd6:gk4gbjl wo, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero l-o.c.hsl)xohv;bz . acceleration? Can it have -s )h hxbozl; ..clo.vzero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces brcr7 o7xf ht(h5bk2k+ ack up. (a) Is a force neb+kxorcf(k5 hr7 h7t2 eded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does nm hs ,p)in 32nnnnv.6the log move in the opposite direv26nh3.imn nnn)nsp,ction?

Why might your foot hurt if you kick a xferiu;e13 0 zo/w c)ppbrx2*,+ wwhwheavy desk or a wall?

  When you are running and want to stop q y+xr2j9w; h11wn f lqxml o4,8u)rsxzuickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come;f49 jlxmh,w81yz1uqs n)wx ol x r2+r to rest.    m/s$^2$

A stone hangs by a fine thread from thel- v1k9)bu. edulc ihod;:wtre-5t h 6 ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: belo)r- : 1h.i9dklc tdbtu 5ow6 -veeh;luw 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 ipj -8+2m-jwwws+f jrrock is twice as great as that on a 1-kg rock. Why then doesn’t thw2- jwij++ wrpj8s fm-e heavier rock fall faster?

Would a spring scale carried to the Moo .eut2ota:bdq7xq;m :n give accurate results if the scale had been calibrated (a)q ubmdt: .e:27xo;qa t in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an f bpop,kc:mqy169 xzayij22(zg8p/ r attached rope held horizontally. If you now pull the rope with the same force at an angm2oyp9ycrjp 2g, 6 /ziqa:z1xfk( pb 8le to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of tic kr44qf7 n7j*wd s)gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerjq77)k4s n fdic*wt4 rts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-jm3 z;zu/qbwy -70 huakg object when you are on the m7wa;/zyhjqu0-3u bzMoon with the force 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 team in a tug of wo.: *udr6n rmma l+g5sar (Fig. 4–37) pulls with equal force on the other team. Wha*6dm+r lo 5n:g sumar.t, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descri 2x 8t ddfsy/b;hfhf 99sgx).sbe the “reaction” forcedhs/g2fys);9 hxd ff 9bts8x. (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 is exerted.

When you stand still on the ground, how large a force does the gr 31r0lhshlqv 7+vhl7in f*)v wound exert on you? Why doesn’t this force make y +*h rvhl fliwlnv071 3shvq)7ou rise up into the air?

Whiplash sometimes results from yg8:-xk7t6if o cycv1an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it royxtc-6y 8kf:icg v1 7eally?

A heavy crate rests on the bed of a flatbed truck. When the truck ackvqai*tmvks4) -fr 3pr h63dm9) on5ecelerates, the crate remains where im6 )dvoefv m -rs)9435*pathk i 3nkqrt is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After t;b q1ccy -q/hfq ox)vh(0djd/he block reaches its highest poinq h1q()-dqocf0/h j b c/;xyvdt, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wearl4ik(wp)l9gs ulozy 06 wf2n 56 ;mbighed yourself on an inclined plane? Assume the mecha95l20r) lgu6;y ml4on6( w wzspfkaib nism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at ao5 l;n (mk)dt6teb 0l1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r-uixq o-q jb91e1/fik ider 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 used to accelerate a 1qbj7 nj (yhi*nw9uk +1 wnxctg6* zg .f,oqy- 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of azlbnkx+k 0(otuv8j1c *yu13 m $76-\mathrm{kg}$ 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(fts .o3zb;7:56k tzuuveiof 1100-kg car in 8.0 s if the car is traveling at 9 s t:5o;k7b6f ef(tu.z ozviu35km/h? -  

  What average force is needed to accelerate a 7.0dauy6pq ox4*y4(y o q,0-gram pellet from rest to 125m/s over a distance ofqyoy (u *dx4q ypa4o6, 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.;nl/d . 3o 7b;7ymmnxx0t ywha1do 3dp5dlty;n7d03xd1.x h3yp7 ma oo;/bwmn $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarter-mile tr ier pn1a;n2o4l vket3 2jdgagi,+/n19ij8 pfack (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 desig (ap e8zyet+qt czhqqw 655(4gned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportingqg(z+qt qz6ea4yc5( tw e5 p8h 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 motionles (u+nmo/qb84r(d kv:j ixr i+es elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the8mirj(i+: +e(u4 vbkoxdrn/q acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum st9zzjh5 h me 19t(/f))wart-rqh4 il wmrength of 21,750 N. What maximum upward acceleration can it give the elevator without breahz hz tt a)w9lh1jwf)mr r9 5m/ieq4-(king?    ( two decimal places)

  (a) What is the acceleratsz.tmljp9t-u h:*ui0 )n(5 (le ;h+fbxjdcb jion of two falling sky divers (mass 132 kg including parachutml5j(*u)bs bpf c+tnhj0(ejhx. ;tz-9d :l i ue) when the 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 the roof of a house 3.9-m highhtt /dy 3vk8psos4b (s u*(nc2. When he strikes 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 (v(c / no(ud3ssytk4bsh 28 pt*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 okwfj5q5r- t( qn a table. A rope tied to the box runs vertically upw-qk5qwrtf 5(jard over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbalw)ki*wj/g./b6 :t mywxuh+ m*qa8 be9vvk ;ip l player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at t.vo6-j of-g6d1uiogbhe moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the ouog.1- g jo6-o6if vbudtfield.

A 650-N force acts in a northwesterly direction. A second 6e6 oq8 x; :eze:bunk3g50-N force must be exerted in what direction so that the resultant of the two fngk; e 6b:u :xeo8qe3zorces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between-(9gp:q baclq1i4w,loo t f dod gd18 q)3qbj2 two buildings 10.0 m apart. The sag in the rope when she 4(1q1 jiw9bd2ol)a,g d3 c-:q pt ooglqfd8qbis 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 fro(gdyx23;l,4amci u3 ojmup + sm 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 1acj2 lwqf 9. mchn52q/ ibl1.a4.0$-\mathrm{kg}$ 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, 1+pp9 xxfyow *as shown in Fig. 4-46. The sum of the forces owp+ xx*f y9p1$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 n;d:mhjuooyvpq .609 behind it, Fig. 4-47 . Determine the ratio of the ;o:9du v0 hp ymqn6.ojtension 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 upward using the bucket-pulley apparatus sho ,lcntk9hhvml;9ekmf,o 1h+4y/ fvy7 wn in Fig. 4-48. (a) How hard must she pull downward to raimn9lhkv,ohyh vt,7 1c9k mf/4yf; +le se 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 racsv4mmttj ny+3:bq*1g e 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 block (masspo cie; j :/ezj*ga(m3 $ 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 a4t-d 1q1jaix kre in contact with each other, as s1- qj xk1iad4thown 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 Fighg3*60x(iuuc 1s) q0f/ se glsl1shne. 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 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. Thslu31 uc0e1/l0 n6( hesx)gssfg*iq his is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connecteb 3v4(iu 3mexkd 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 shok3u3xvm 4b( eiwn 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 frike8d. s)f mes/ction 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 8)x :qbtp ;r)od +jcrmrequired 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 s87t/z mn4ffi/utpz95 oykg t ;tanding on a train accelerating at 0.20g. What minimum coefficient of static frictigti9t5 m fzfn74tk;u8/zyp /oon must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the cyzjwc+9fzv; ed5u ,c ,oefficient of static friction between the tires and the ground is 0.80 9yjdcw;z5 ,,fez+vcu?   

  The coefficient of static friction between hard rubber and norz6kt3 gwjnzjx*b9ihba3/1a9 -2 ju2 uy2f hlymal street pavement is about 0.8. On how steep a hill (maximum angle) afz6hj /9t 3-l3u y1wynj2kbbzgju2 ix29*ah 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 deceleratel6.uji i9).ms(d3,r xwiav q l at -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 roughyk 39,yjsx2f, gs f.z/u2udhw, z -wak 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 h)yat7qf+tk04/dq0vmpoy-s:h00so xm c n.u b ave a very high coefficient of staym+t xn.0vc/0b p7q4qts o-h: 0)ky adm uso0ftic 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 frici ipejrruj 8er-q4a n,p/2qt 3w +n:s:tion 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 large a maj;z1nooqh u.v i gmi9-o9-t(vss would box A have to have to prevent any motion frvh -z1q i; no.uo oivmg99t-j(om occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push kv+z u0t3 vu3, -exn,dvoad,pso that it slides across the floor. How far will it go, given that the coefficient opd+0v-n,u3 vuv t,kza x,3edof 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 re.u*i8+adtmru7kwm 5bawo5 .qst on a horizontal surface (Fig. 4-54). A 62ud .5+a5kmq*a 8.mow rib7wut0$-\mathrm{N}$ 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 aes ,gevo7oqyl99w4 0a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the m7lsg 9e49ov0qeay ,ow aximum 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 in youpbikij 5n7p313qx0 *hnxe 9vur driveway, which has an in b3eu15n9*jh x0qxpikp7i 3v ncline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with ag0az.-ul ;bga 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 pla-m ncpg/vkq 5k h1/b*nne 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 ini9 vc9: ot;xeqqtial 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 the top of the steepest hill with*b)p(;j8lyh/b0pfyi+yzt* u :px6 xlrm /snt 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 bc b4(dadk9ix 1szsg/ x - c09nm2sff.uy someone pushing on it with a fogdi(f.usns 9x9x2c/ d4-f 0 ca1k zbsmrce 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 as qk.ym .pe.tk,2(x- *imbldf m they melt. Consider a chunk of snow at the ridge of a roof with a pitcmi-mx,yq.k( . e pkl*m2td.bfh 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 sc61yvs/b3ovw *gz11a pes j+t peed v is equal toj v6oswb/ gy+s 1c1*pe31zt av $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 dxaom8 b7 -g7uqriver decelerates frbx 7 o7-au8gqmom 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 ikn4578 /y4 .ola1hkq1 3mugvdb alt b is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conv-g- ph68x4 he* a +qruxe8ir dj1sebc3eyor belt from where 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 is 0.60, wha r3 egq 6+-dshe *baep1xix-u8ch jr84t 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 friction betx+n0)rghw3t mween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a:rneu/3v vo phn(5b)i 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 oa6oe ;y*xo5c-5tba-w ciyu.5(e lfveach pulse approximately 20 g of blw; uovx 5act oe(-iy5e ocayfbl*6 -5.ood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile cr6m(k-p66 k gnw4eebwgash if the deceleration is no more tw6gke6we46k-(p ngm bhan 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 earthqu1cv ,.f uxov 4zobs :sop+,ktu*efj:/ake is a , and if an object is going to "hold its place" on the ground, show that the coefficvb o4tcv*+sf,1:p/u o jksuxo:fe .,zient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an;) 9waymmo b8t accident involving two cars, measure 72-m tmb;w8ay)o m9-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 assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means thar3, h6x9z/orgtk5e y ht for each 4 m traveled along the road, the elevation change is 1 m). t9rhr 63/gey 5 h,kxozHow 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 Toy7+xs9kvzn a dup8)2f x6cnx.wer of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistancy n +)6d.pxuf kxc872n zv9axse?   

  A cyclist is coasting at ay .9cy+s*xw5f n.pero steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the spee5psn.er*xf9yy.o+cw d upon emerging?   

  A city planner is working on the redesign of a hilly porte3zta hj4,08 .x fsalqion of a city. An important consideration is how steep the roads can bje0azqf3 thalx8.s4,e 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 physibvpko 6ct+fobv84) 3bcs experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string v4b3p+)fck68tbboov 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,mnat:c hie*) differe :mcianhte*,) nt parts 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 i ks4, k67ug(u65our :g h) 1wxovcpnyws needed to lift the piano (mass M ) using the pulley apparatu :5 7ho1ukg,)osuugywck4v6r6w( nxps shown in

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

  A jet aircraft is accelerating ah+rwp 7q:loqe fzin4 dsh)61y 3j,g d+t 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 consjua(ahz+/sljh,6yut( 0 2athsn 7c 6eiders the following set of conditio+ uc7( e a(,ytsu0/h2ljtj6n hz 6asahns:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 66kv pg7 ux -:/ 9:jkxq:vapl8vm0 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 g-d3f5 fcr(8 phvau7x*prt 1ay q xkr1ud -.5ilength. 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 stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is moht-x 1(*i71rdgrd 5-.xq a8yp uvp af3rukf5c re likely to be hurt?

A fisherman in a boat is using fy 9t.z6q7d jna " 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 allowr(wgnw y: ya*s:yb).)re 7zkw ed 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 fiep 67-u: p3 rcge) gqaf/* nixzpr2eq0hld inclined at 21.0z6q/ x3pi0u2p7 : fq*cpgg-rn he )ear$^{\circ}$ 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.