Why does a child in a wagon seem to fall backward whb jro1 zcpug7z4/a5( p7-ccy jen you give the wagon a sharp pull cpz1rcgb7jyp(j7au-4c o5 /zforward?

A box rests on the (frictionless) bed of a truck. Thrv9eq0 nmz)egvowm1 (pph .w)2x n23je 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 Nerezwnpm219xg(vnpo0q3 w hem.v j2) )wton’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 objecwt6h+ 7j;rj- ke3qb;u )qjbju t is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati b-+rynr: v8ae ;m/pkton? Can it have zero vel r/-:n; v8ptak+eb myrocity? Explain.

When a golf ball is droppet,.grbd 9j-thd to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, w .rt-hdb ,j9tghat exerts the force?

If you walk along a log floating on a lake, why does the c)rewwq:o yax:2j 13alog move in the opposite e r:y:1 )3wq2oxca wjadirection?

Why might your foot hurt if you kick a heavy desk oritd254d,pjzisfg5 l)r9 ziw d58q 3ikrds s0: a wall?

  When you are running and want to stop quickly, you must decelerat z*312 8 svwnjs8pbhhle quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximn hzhw3vpb8*l1sj2 8s um rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sec/5amqf*,sm 5cdllnlxg o 4: f(tion 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 i fa5q4lxcl: *lm/sd,5omgnf (t? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as8q4swpw., mi tdw/f8w great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasterww8d/q,8f4wp t.w mis?

Would a spring scale carri nuph8fb)on r/i64 1swed to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogri 8f1nhpsnr )ou6wb4/ ams?

You pull a box with a constant force across a friction o3t)3:ph h sny/;qmyjless 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 remh 3toy )psyjhn;q3m/ :aining 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 thezh9j9uw ,la m:qs7-xn influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earuq z7-9 hj,n:w9lxsma th move?

Compare the effort (or force) needed to lift a 10-kg lf hjho85/+ia,an6oa object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-o6af n5 +ah8l,hoaj/ ikg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig.n k*pa/: fa+sd 4–37) pulls with equal force on the other team. What, then, determines which team will winkdnaa+ */:fsp?

A person exerts an upward force of 40 N to hold a bag of grocey 7-3t 9 i8 ful3yjy,huoym2jsries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (o3 fyiuy u3l82 7h-, tmyyjsj9b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground.jry1esp,5s3asug 0u , how large a force does the ground exert on you? Why doesn’t this force make you rise up into the ar1us5sgs j,yp .e30au ir?

Whiplash sometimes results from an automobile accident when t3v (r7x5xdz aghe victim’s car is struck violently from the rear. Explain why the head of the victim sr(53 dx vzgx7aeems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed tru//ctw032j++o zn qenth;eco( wfw4p mck. When the truck accelerates, the crate remains wher cjwhn4t0 wc2+qt;z o 3fe(/p/ +mnoewe it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block qi:s(d.8yk9o omfn, wreaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the as(mf. :8dwyni ko o9q,scent. Why?

What would your bathroom scale rykexi1/w0q3x *pxd b/ead if you weighed yourself on an inclined plane? Assume the e3 / xiyp/xd*k0qbwx1mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled atgm*jht24uree 7ppb8 / 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikfrwt 0sg6alphy9 hnx1 :km 2.6e and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960 :.bhe8v; d 1g;z1mbrrrfoll0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of * dx.hnyys.a19m7vxnm 8ss; na $76-\mathrm{kg}$ 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 care;d 4 0oav3pax in 8.0 s if the car is traveling at 95km03ox 4;pvad ea/h? -  

  What average force is needed to accelerate a 7.00-gram pellet 00r 2wcjyv- 3hh9pweufrom rest to 125m/s over a distanc9huy-h03cew p 20rjvwe of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceler0t-dn 7r. nq*k fcru6vation of 2.5 k0n drq f*t7.nuc vr-6$\mathrm{~m} / \mathrm{s}^{2}$ 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 qute 31xf;n ,sgw*1/ch 5 jvjblmarter-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 km 8o,locub3g5d 2:x dig ) is to be designed so that the maximum acceleration is 0.06gcildo8xd :,mu352b o80 g . What are the maximum 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. When the elx1ah, lho/jgvwb1s+ 7evator begins to move, the scale briefly reads only 0.1,7s/1lohvxbjhw +ga 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 a maxim ;dest(+xx:x)(8*lxvot u i mfum strength of 21,750 N. What maximum upward acceleration can it give the elevator wixx)o;x: se(fi(t*vxlumtd 8+thout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (ma3bbou(k;/ i vwss 132 kg including parachute) when the upward force of air resisb;o b(wiu3kv /tance 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.- odcu j (*lp;aug)vv99-m high. When he strikes the ground below, he bends his knees so that his tgcvj; pv*9ao( ud-ul) orso 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 rdevb is .(3,sN rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pull ,rve(ds.bs i3ey weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagrv; bmf-* nb32z5 dplmram for 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 bawo6(:z e1qe 7;i eckhmseball (a) at the moment it is hit by the bat, and again (b) after it has7w kihmo ze ;ce6e:q(1 left the bat and is flying toward the outfield.

A 650-N force acts in a northwester tju6+ar;cy *oly direction. 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 v6uaoc+ j*ty;r ector diagram.

  Arlene is to walk across a "high wire" strung 7ebzx*-i6mcp)i9 ks thorizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mie7 ix-csm *)tbpz9k6idpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another 3q2jyqd s11u 6 nh jmh.(zge5,bhs.7(z, qhoac.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 12 kg6i0epwn;s 4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at Mc4zs10wnng5a p Murdo Base, Antarctica, as shown in Fig. 4-46.g51pnan 0w z4s 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 sam(kyz. avjfzi3 vh 2(- hb08wdse mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the f(kbsjhw8a(yd3-z 0ifv h 2 .zvirst 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 tgb : odw+ s0 cso.mob463/z:ongyr9qmhe bucket-pulley apparatus shown in Fig. 4-48. (a)4 /drg6c0+:o.o zyong9wqm sm:obs b3 How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a racv0-va5n 6td jg :(ymble 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 q3on3+5hw hxgblock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each o f 80suk7q)ertther, as shown in Fig. 4-51. A force et7 qkrsfu 8)0$\overrightarrow{\mathbf{F}}$ 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. - j- ha-fg1muwmm3d8f4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter ob -fmu1g-mj-fawd8h3m ject reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are cony54*5o cgqwgqnected by a heavy cord of mass 1.0 kg . Calculacy *w5goqqg54te 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 fridt 0i4jphv:pr* ml6r52q 2tr .zga f6tnuu*v5 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 required to sy,7lw()o-h+bgl4pyi1 rj sy btart 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 accelerating at 0.20g. W8gtf +(du 0zevoo rcppk, 7.t1hat minimum coefficient of static friction must exist between your feet81fpk,ru.pgcv0+t(ootd e 7z and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo ifpz*4drtge8 s);dc +b w the coefficient of static friction between the tires and 8d st)cdpeg4*zb; +rwthe ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemen4rdy6f3zywq 4 m)o9adt is about 0.8. On how steep a hill (maximum angle) c49azdy)w3fmyo4 6rq d an 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 -4.80 lw6 yn.6kj 3yw-0xr zf$\mathrm{~m} / \mathrm{s}^{2}$ 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 roufixu-zsm 3:(; pikdq ,gh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficient .hh1ts* 9,u( 70jr lfcv0ihrb r)erlfg2z0 ocof static friction. bje s7r g0*t.,2rl 901ifc0u hhcor(hlv f)rz

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 frw 8o ac7k4egr k o*5yo85z/srliction 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 (w ;,+u/ jb:x6e +hvvssb (djwv4vkr/pExample 4-20) how large a mass would box A have to have to prevent any mo pw/ wb;evs+sjj vv,k ub4+rdx/:h( v6tion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fars8bo -q t7jw)e will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an w-q)tb soje87initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg:-tdzc+ k-gu*cng dxak7 d95z , are in contact and at rest on a horizontal gdkz-7 9xgn cauc- d*tdz5+k :surface (Fig. 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. The coefficient j t,ycpkhq0x rc2o5r::5x *gaof static friction between the crate and the bed of the truck is 0.75. What is tkaqxpjt,cy5 gr 0 :r h5co2:x*he 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 in your driveway, which has an i,) ue7.n uprhcn7.cph)e ru nu,cline 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 wi+e ,ie+s bp md00 7ibjt0dp*hh m+ozk*th 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. 2)o.w;f+8zykg qz;+t tnqkho4-55 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 yqw mekm9 ar)z2g(-;wk6sj l . t09tvcspeed 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 reache5 k ts;4tpbbuhyy h,3ew p50m8s the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rougi:p;knpcu0h dmf ;(y suc*s5 :h wall by someone pushing on it with a force directed upward at :p u*nspmd ;5:(y0iuf cshkc; 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 rxtf lr6mh.k;5oofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pi 5fl6mx hk;rt.tch 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 stoppinc49(ol4 c:flg0ojrf dg distance for an automobile traveling at speed co: (09 jf44ld rcfoglv 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 wh rzu l1oe2 a1w.3i(8ol 1gamkken the driver decelerates from 45 1 kzll a2e1a3w r.kg(8omoui1 $\mathrm{~km} / \mathrm{h}$ 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 ct0 /t0j2s pjkb3in6pc1az u3 m 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 conveyor belt from whenjptqumx7:i 3m2 e,b3re they are filled to the packing station 11.0 m away. Th23 bmmei :p7qxn t,3uje 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, 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 frictiosjxjfq5 :1 ,m6 mhk1hyn 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 u9x jad+c,+uik+p5ejn) wc7p down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse app8 ty:;aucc+bp /cud 1aroximately 20 g of blood is acceleryc ;:c1+c p8dbat/ua uated 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 survivingx+3;4n bqmbukw sba ohi+c,*) an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force o+,hmbnx q+kius;a*b)o b 4cw3n 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 produced9is4jqaef9: sfh54us by an earthquake is a , and if an object is going to "hold its place" on the groun59sjis sq9 :heff4ua 4d, show that the coefficient 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, examiuvm ccwc;2ibc 2n4: z4ning the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a ucnc zw:vc2 cbi2m;44 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( f:s0pm81boz 5a ohuh(kkef5 that for each 4 m traveled along the road,bkm5(( 8h15sozo0ku p fe :afh the elevation change 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 fromfk9 s ds fqr/:89yx)kc the top of the Leaning Tower of Pisa and falls 55 m before cd8/kkfrx:9 yf9qs)s reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speew6/m4p w4 40qeusfmfqd 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 q emq6 0uwm4w/p4sff4will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a*1 n*8fm hmbiy 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 of 1100 kg , can accelerate on a level road from resf*1*ih 8nymbm t 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, dangls .t ,kpz )y(emmwrb1/es her watch from a thin piece of string while the jetliner she is in takes off from JFK Ai(mpybmr)kz .e ,s/wt1rport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several .y(by8 a+klmc ( rrn4cwfh x+nhqxfpg,79* y5 ramps connecting different parts of the store+q fhwg(7 r8fy,*.phrck( c l+ n9ayyxm4b5xn.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using tqg/wqd/8/rq o he pulley appa8rqo/w q /gq/dratus 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 accelerqd ;)i 9mf4lktating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an e7q+ jp 4xv0zn td +(npqe:0 tlqjtn-6engineer considers the following set of condiv+qq pxe40l tq0ptnnz+jn td:e6 ( -j7tions:
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 660 metric ton7j.-vd hc*s zrs (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 simic9n6s;e-+nr p x+y0bz lqyyv6 lar length. Karen's rope is more elp+l0z +b;vyn 6x9r6qycs ny-e astic, 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 more likely to be hurt?

A fisherman in a boat is usi4w onia),ni1zj03kih ng a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a ma;pkja3azagi u:b6c9y 9;qs+zximum 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 wyx(5 )imlo b5nho are roped together are ascending an ice field inclined at mb)olnx 5iy5(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.