Why does a child in a wagon seem to fall backward when you give the wagon a sharke00 6mm cy5dufjn3k :p nked:mk5 0c3 jmf 0y6upull forward?

A box rests on the (( p5jskky 5d0nfrictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts 05(5pn yk jdksto 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 beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, a+3s164cpmahf rt 87i4 bztwacre no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero y/zbix wfb - p)0dcrfc7b9w. c. 0xwv5acceleration? Can it have zero velocity? Efw 7w9b wr- 0 bxydp.c/xv )zf5.icc0bxplain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a for -itxyt(4hapd 00:fb bce needed to make it bounce back up? (b) If so, what exaf00h itpytd- bb 4:x(erts the force?

If you walk along a log floating on ac,4kb jaihd5 0 lake, why does the log move in the opposite d0,d ic kah5b4jirection?

Why might your foot hurt ift ol.tnydi,su09ws drr6gp 8 3r24hs0 you kick a heavy desk or a wall?

  When you are running andzc :r,e3yeylhk )3r a4;r,jja want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top :c hry,eja4; e3jy,r l k)3azrspeed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, a5htwoa q1i 0it6hfi/0nd a section of the same thread danglf/oiwtt 1h q056ai0hies from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as 8eqmt92h l9 jmgreat as that on a 1-kg rock. Why theqlj9 m8mt2he 9n doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resu8zf( +vv(uf xalts if the scale had been calibrat( v(x v8zuf+faed (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using 7t 5e j:ew(roaan attached rjew7 ot:5rea( ope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls f gc2*rz k)oebewc5 (kz/5zb; yreely under the influence of gravity there is a net force mg exerted on r zw25ekbo5 e;cz( zb/ gyc*)kit by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed t6 nqc .cdch)iet4mx1u5 9+eado lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to th1u i h6cdx.mqa+c)etnd5e 4c9row 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 wa*cst;i8now-(j nio9isae 4s* o 4s9cdr (Fig. 4–37) pulls with equal force on the other team. What, then, determines whicj es i*isoo;in-wtc84(c *sosa49n d9h team will win?

A person exerts an upward force of 40 N to hold a ba(o qdu*d 7x 0yhvq9gc*0kch-ug of groceries. Describe the “reaction” force (N 0 vcq7q*(o gy9udxh0kuc *-dhewton’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 ground exery6b f/(bforg7 t on you? Why doesn’t this force make you rise up into/6fg7fr bb(oy the air?

Whiplash sometimes results from an automobile accidrmug 7k;hh2j(ent when the victim’s car is struck violently from the rer;gu( m jhk72har. 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 accelerates;f (o p;qmzew chvgs+dy;+07r ohg-;x, the crate remains where it is on the truck, so it, too, acceye7-+dv(rmh +;fh ; zqgoop; c; 0wxsglerates. What force causes the crate to accelerate?

A block is given a pay6zpo dua9memf02,j /g :p7 qush so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration isygf,6 p2 jq/zdum:m9o0a a7 ep less on the descent than on the ascent. Why?

What would your bathr zb19uce/a5bhoom scale read if you weighed yourself on an inclined plane? Assume the mechanism 9 b 5ac1hu/bzefunctions properly, even at an angle.

  What force is needed to acc al6p qr.006fggaam5zelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bi 5irb y-9qx nk48na,q 7;pg;e,7:r tpbhduzak ke and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must byq r,o- 8di)e7aqy1wpdh ;-btcb6 6ma rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a vksd+ris7j ) qx-wi xv7g/)v+$76-\mathrm{kg}$ 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 requxb*z kj+fp9+y fe 0sw4ired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? k wp y*xzf4+s+0jefb9 -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 1255g0tzbx *+t q mc5gx4v41 d/ot)zxxzj m/s over a distance of 0.80055d)bt z x14tmqzxgv0jczt/+ gx*4xo m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the e (ltu zn5gp/skv u-,)k5irw:water with an acceleration of 2.5 : ,gstkln(u)i / vuekz5rpw-5$\mathrm{~m} / \mathrm{s}^{2}$ 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-milk,m)lu ojv66y w,5 (kw ewzc2ce 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 desfxqm**g ( ltu,xvb0-z igned so that the maximum acceleration is 0.0680 g . What are the mz** 0ub- (ftxlv x,gmqaximum 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 th,njnpht uoz 12 i77m/ee elevator ,ji2nz on7meu1/t7hp begins to move, the scale briefly reads only 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 212z kv3(uvsy 6)k,/yh cg5-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevato)z63/k vgksyy cuh,(vr without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (tg5(7 qvj2lo tmass 132 kg including parachute) when the upward force of air resisot2v5jt q(gl7 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 houawkne 1:fvjr 3/6o we z;1cgnxv:-x3ese 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distan 1 vxe j;13agxo wv::r-wc6fk3en/zence of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically uhjq896 vs q3fepward 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 qvsq8f69 jh3eon 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 ku6 mks 2ouk7)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 baseball (a4h dqgwa36 m5gt-xf z)) at the moment it is hit by the bat, and again (b) after it has left th 5f mgwaq-x3t46)g zhde bat and is flying toward the outfield.

A 650-N force acts in a northwesterly di rk 25 d:u9i4ngficzz7rection. A second 650-N force must be exerted in what direction so th 425dzu 7:niifzc9g rkat the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" ;//lia st 8jgljwy,5ostrung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midptwl/y8/ sga il,j5o;joint 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 abz/waj z y a66dgxti*7 h7,ue, massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14*: nn y2j fqmh,c 5nydxu2tg*8.0$-\mathrm{kg}$ 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 Bas)i;k-zdyb6 )oza r a9xe, Antarctica, as shown in Fig. 4-46. The sum of the forces ax6ao 9;zdk)y)-rz ib $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 ised bhp3bw+,r4hq s22g pulling two cars of the same mass behind it, Fig. 4-47 . Determine tde2b hg q+,h43wprb s2he 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 pulls herself upward using the bucket-om9 k *-eu *,xnreiu59n3eaonpulley apparatus shown in Fig. oxenen 9*eau im3n,59ur*-k o 4-48. (a) 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 race begah 7cbparz 8ihq7a8fc0:x,*lx n, 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 ( o0 4r i2clqpq/vic3dn w3ouur21 l,h4q1gbg .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 othp gf, cd-p*zrsf0 ;0-lqosyw0 8 0qcqger, as shown in Fig. 4-5q; scgf*-8ozw0 dp0qq-f0s0cgy ,lrp 1. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 mrmlr *7.n,l yo 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. This is its "launch" speed. Assume it doesn't hit the p7*r nrl lom,y.ulley.]   

Suppose two boxes on a frictionless tc*zc a4t1bz j5able are connected by a heavy cord of mass 1.0 kg . Calculate the acacz 5t14jz b*cceleration 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 between a 35 zyffh /1*p7cq$-\mathrm{kg}$ 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 towfzy 9wf qlc5,1(.ij p 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 standing on a train accele8ygc *z8qwmp, 1v165xg ixchlrating at 0.20g. What minimum coefficient of static friction must exist between your feet and thecp5zw 6vyx li1c8q,g*gxm1 8h floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stat 3sno/ww+1ua2ah tne4ic friction between the tires and the groundawhn +ues 4/tn3wao 12 is 0.80?   

  The coefficient of static fricq(2s*rn;wcmhg 8t.zc tion between hard rubber and normal street pavement is rm.g ;zh2twn cq(c8* sabout 0.8. On how steep a hill (maximum 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 decelerate5z 0 ,s:xr uhr2 r+7t4scujltp 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 rougdk e)8x g53d-( f3h ksmujce.hh 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 surfaggdjw*w r 9vcn pkr5i (-5g,m8ce have a very high coefficient of static frictioimn55c d9vjp r w(8gw-* gg,rkn.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction 40 6og 8irlbp.dp7vbb 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 4-2+q chust6d8 y89;kiha.,clmg 0) how large a mass would box A have to have to prevent any motion lcc.g d8y8h hk+ 9sai,;uqmt6from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it ss .:q ( 9e( 2ef.tmwz5lp0rkwwemh9islides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impart2e e9wss0z kw ..:r 9qpw(h(5mite mfls an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75*zgm 3h7/g ej)-l xso40 yxbgk kg and 110 kg , are in contact and at rest on a horizontal surface (Fis7ox bg0g3g4ykljx-/)z hme*g. 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 hz8. c g q )x;z)mftzq6y3u.7f5aznq bceavy crate. The coefficient of static friction between the crate and the bed of amy68x)3.;z u)t qqfz7qbcg 5n.fzzcthe 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 hpk,n ;dmkw .6d+d4fiyour car in your driveway, which has an incline oddhfkmn.kp;w6 +i d,4f 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 sl 8k;cru9ial,w(t iy6yide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane1vmu 21 :f-hikc(eln gr3 je1o tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.jai salmwe 8;,hrfvuw2ge1 58 x.2n 9d0 $\mathrm{~m} / \mathrm{s}$ 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 spgo6x,m9:l:a kbn ;6 s; wnvmaxeed 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 rous4q5 0xjal1nxo ek5;agh wall by someone pushing on it with a force dire5soq50xx4;j1 aklean cted 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 probgi z*z59d l bfgsf1:8nw /6xsjectiles as they melt. Consider a ci b8gfs/gzn59s * dxzbf:l61whunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automob yc, s 8rbku4)zyc3,yxile traveling at speed v is equal ts )x,k8ryccuyb 3z4,yo $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 dashboarmj3kquv 065rb/1jrm6kdc j b *d of a car slides forward on the dash when the driver decbr0 m/k6u 1vj m3kcj6drqjb5*elerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial spx3kyv, a h7ix8.qpv; keed $ 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 convew+0qdy.(*po ohigq,by .pr3o yor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zh.dgqb(q,iproyo*3 o 0p.+wyero 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 kineticn o 1e3dj 1krha.ne(,y 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 6pbx;mfu / p flt44,wy+5 kg (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 mop t (x:x8b9incdel of a mammalian heart, at each pulse approximately 20 g b(8x :t cn9pxiof blood 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 ch )jxr)( k6b(yioov) meance of surviving an automobile crash if the deceleration is no more t) (b6 yv)eoomj k(rix)han 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and gnjzn )e4p-z *7yas 7dif an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground muss7* ye dnza 7j)-pg4nzt 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 scenw)xv ihqr,x9 *e 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 kineticx, r)v*qw9ixh 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-inv/;oyx q /n9yea2lve5 -4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m?yqoy9 avne;el/x /5v2 (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppea q8khs;7b/6o6n wkk fd from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground w /hq6a;78 6fknkb kowsith a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 1mv84- jd0pm ,yqrpv,d2m/s but enters a muddy stretch where the effective coefficient of p,md-,py0 rvq 4md8vjfriction 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 speed upon emerging?   

  A city planner is working on the redesign of a hilly pobib r9.t* c;gyrtion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can;irt .*b9bg cy 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, dangle7xykone9/uos *.*l64iqo qmrxf -7xh:t2 b mzs her watch from a thin piece of string while the jetliney7qmtn9 i4.rmlx7zx6f: s/2oo-q h**obe ukx r she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarnnmep-d; o 2km6 ;0jvhket, there are to be several ramps connecting different partsn6 emjp; - ;vnhd20kom 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 forceb1r..ra wp;b7 irm :qv F is needed to lift the piano (mass M ) using the pulley apparat.prr; im bbwraq.v:71us 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 accelera5g6 vs .*( ccn3sfinwxting 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 engineekb , z2*pb26ohkmz6w8ct +hinr considers the following set of conditions+6c2,h 6z2piwb hzt* 8 kmbkno:
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 tonigq 2 dr*fzi)xw)2:p ns (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, usxh ;5l7ko hdewia eqx) 4rf3ae(4-sk .e safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. ;awask4dxel r(x4 f qh)i o.ke3he57- 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 using a " : gzh(jdsh,(k 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(n3z gcwms(yku .jf flc+ 5f64 is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fi2jho;w4yewq s/xcubb777z3a u3cb5meld inclineda7c7 wmwxub5e2h37jbzs c/b;yq 4u3 o at 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.