Why does a child in a wagon seem to fall backwx h40g*ze fip26 p)lazard when you give the wagon a sharp pulle2p ghl4i f6 *ap)x0zz forward?

A box rests on the (frictionless) bed of a truck. The truck driver le8:.t9;fp.l )t8bp dq mfiahstarts 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,lt9mtihb 8dae.)f8lp qf. p;: 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 iskil et t5 cuw1v9e;4m5 zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerat f 3)i0q2rhq)ubx e2rpd;ei9uion? Can it have zere32d0b)fei qhqi;rur9 )pu x2o velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forgfg/z;vhun4*qq1qr f+ jve(pe53 / sqce needed to make it bouns/j3qqpv5reh +eqv/ ;*q f n ggz14(ufce back up? (b) If so, what exerts the force?

If you walk along a log floagck. lz o4.6d83aflg uting on a lake, why does the log move in the opposite direzu..8o6flcdg k 4 gl3action?

Why might your foot hurt if you kick a heavy desk or a wall -u9;e eps7qmkj i*: kz)xde2yfk7.a m?

  When you are running and want to stop quickly, you must decelr6lukak+b))vn b2c sdjo 28w(erate 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 spee(da 8jbwu2rl) 2)k6knvcs +bod to come to rest.    m/s$^2$

A stone hangs by a fine thread from the cejoe-l;7he3)+jf sp oqiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a j); e 7 heoopjlsq-3+fslow and steady pull? Explain your answers.

The force of gravity on a 2-p*4snnjfb;0 gkg rock is twice as great as that on a 1-kg rock. Why then doj;n*b 4sg pfn0esn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the s gxv7y*)yaijtk/br(.j7c. xbcale had been calibrated (a) in pounds, or (b ycjv /a(y. xk7b)gx bi7*j.tr) in kilograms?

You pull a box with a constant forcf n6 t suk4z;u/tck3z;e across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Et kt ;sckuuzfz3;6 4n/xplain.

When an object falls freotq m)h1.1c hrely under the 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 Eh r.1)o tmcqh1arth move?

Compare the effort (or for nwtd2a+-y 7ib tlyj3/eo1v7nce) needed to 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 throw a 2-kg object hooav/2l7it 1yey nw+73 bt jn-drizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of wadgocx/+t ,:f slne 9h8r (Fig. 4–37) pulls with equal force on the other team. Whc9dn fl hxsg8o/ +et:,at, then, determines which team will win?

A person exerts an upward force of 40 N t7 mlxc 1c3wypb(da0;r o hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what oclr1a ;7xb(p yw3m0cdbject it is exerted, and (d) by what object it is exerted.

When you stand still on thx v+l1 vgl xq5x4igv:5,ol mi,e ground, how large a force does the ground exert on you? Why doesn ivm, gxq,+o: xlxv4vg5 1lli5’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident c,g fc),cxskv8 * hsq6when 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 really)h v 6c sks8gc,qxc,f*?

A heavy crate rests on the bed of a flatbed truck. When the truck aamtn a0br.3zdxg +nx:sci*;ttwqc 5(jl5f ,; ccelerates, the cr,nxd(n*;i0:g qbrsmctlz;f xw j5taa +.5t3 cate remains where 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 n 6o :j3x khbnxaiz.c(z60bk3 slides up a ramp. After the block reaches its highest point, it slides z0 (6kbc :abn.kijoxxn6hz33back 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 weighed yourself on an inaz xj9b1w; 9phclined plane? Assume the mechanismzjb 9w 9ha1px; functions properly, even at an angle.

  What force is needed to accelerate a child on a sl)a(4;.qkzp goe)h z mked at 1.25m/s$^2$?   

  A net force of 265 N acagchv8k*bt y687 skw3 celerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsaac9k axjix )a,m:2c3tand 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 rtzwm k+3ei1qig )87d $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the car is 3m.(absw vk.92 vqmhytravv3(.hmy vksqm.ba29w eling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram xq kp:ysmoq 5rv )1r-+8 loi/zpellet from rest to 125m/s over a distance of 0.800 m along the b: xq) loviz-r8+yrp5os1 m k/qarrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an ac2yi1 )k(0hdx6hoczbr9y:q k e celeration of 2.kzo61i)qc9: 2d( byrkye0hhx 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-mile track (402mpruluhv/ y4+ c4b7-p xq,x -v $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maf8jx:1gv 5hg oximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the shxj8v gog:1 5fupporting 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 c17.uwppw )x su-4jaagzn*8nelevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelerati*j7 c.-x1 wpu 8)spwngazna4 uon of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wha3di m7 6**od+1ps1sdh io /e+np2anmo wgsc 3vt maximum upward acceleration can it give the elevator without breakin i6o*cond1din2 /+sa+3p7w dsmegv3 msp*h1o g?    ( two decimal places)

  (a) What is the acceleration of two falling ;zdqcg2ecycr.d0 (hq ez924e sky divers (mass 132 kg including parachute) when the upward force of air4rh;ccgc2 z90.(ddy eqz eq2 e 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 high. When he strikes the.+n)2.i6wu:wjk u- fwqnm hdh 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 (exinq+:) ud.hw62kwufh mn jw-.cluding 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 vwd 1v4( sfzw37)zymal u-3 q8dat6dbtable. A rope tied to the box runs vertically upward over a pullewyavm 3d8zwqat7v-(b4 l1)z3 dds 6ufy 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 basketball playe mh02 e1a( yufvf:1vpwr
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the e*u9 zz71u(omfb ab-qmoment it is hit by the bat, and again (b) after it has left the bat and is f*u au9eb1ofq7z (z-m blying toward the outfield.

A 650-N force acts in a northwesterly direction. A l-ei xpkuu wx7yld. q7t3;:q 2second 650-N force must be exerted in what direction so that the resultant of the two fo3p;tx:q lu wy-qxu7kl .2i d7erces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two v4fe 4vmj;u8q buildings 10.0 m apart. The sag in the rope wvm4 fju4veq;8hen she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a ma :ivakq8zw 1-rssless 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 1o ,ux ;7a)ichu4.0$-\mathrm{kg}$ 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 f*8 wzawaefn 6am5xl4 h (ed599v)gcua new location at McMurdo Base, Antarctica, as shown in Fig. 4-5xvluzwm(f5d 6a*an8) f wce9g9ha e446. 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 pulliue9c5j*futjx+w- j u/ng two cars of the same mass behind it, Fig. 4-47 . Determine the ruju/ w9tcfu +ejj 5x*-atio 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 bucke70n:nh rbrx.53 z:gqeh3 xmmn t-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at consta3b:qn x30mzm5nhnh r:. re g7xnt 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 beh-yhg e ck-e, w-9sp(agan, 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 b fxzcopa69ti8 mw-w7q*,4m 5fj dpf l+lock (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 a c 0.zckb2)mrhre in contact with each other, am c0ch r.k)z2bs shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initial/bf:1loz xwa 8ly 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 acceleratiol:zb/fx 1a8wo n 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 ta4xq3tj 8zp zbk:m5hp+ ble are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cj+5:3kzxpbm8 h ztq4 pord, 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 fricis-;wgsowe0w ,fv+ uef5 nr-*9as .pyu (;g pttion 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 stab xwc+p/o1*y zumig6 5rt 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 wfe 5rfihr;8/accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if e rfhiw8f5/; ryou are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta hlw1cm+*y/8;vky5z.bwdievtic friction between the tires and the grounz;15y+ b lew*d8h ic.kvvwmy/d is 0.80?   

  The coefficient of static friction between4 8hj:iknvbtywjsk33 - z0 z)v hard rubber and normal street pavement is about 0.8. On how steep a hill (maxihzj :kvtyj0nz3ib)w4v8 -3k s mum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.*ecdx9 sf-.k-pvrd elk:s60r 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 r2eh.;t uo/krzough 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 surfyfp./rhkp6s o)8mp9 cace have a very high coefficient of static frico6ys9)/p8ppckrm.hf tion.

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

  The coefficient of kinetic friction for 8wnddxa rvw0g:euf /9/m6pl5a $ 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 mass would box A hawy.)/x8kzd b fve to have to prevent any y.wbkd8fxz )/motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How f (z,a)udlh;cp ar will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of ;)(pclhza, ud4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at o)fqis1pgly1 ( ,pjg( 6yywq:rest on a horizontal surface 6wj,if1g:y(p (1g )py sq qoyl(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 cratu*nrvxu;6s ccj(- /zs0 +sew ee. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the cratv/x+6-*cuwu z0srs( nje;e cse slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has anvw( q.jbz.)zmundc:i2c zsy33) r2 ql incline of c)q:.si yq(jrd. z)mbczn3z3wl22u v12$^{\circ}$ . 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 slivovix5 - na*6pde 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 d, . 0tjbg,nsnrt9w )oFig. 4-55 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 initiq6:p0*f2qg jx xsqe7sal 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 th)uvcg y 5m*.u48jnwxre top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wcg*ua:a.kl/h ga5um 3 all by someone pushing on it with a force c 5 .ak:3ahul/gug*amdirected 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 becop,612r,v 5s xu( r 2znyykhdnpme dangerous projectiles as they melt. Consider a chunk of snow at th1kv2 u6dshr( 2r,,zpn y p5yxne 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 fwym,30eb/il(oe183z.sqbwsa jg*v z or an automobile traveling at speed1 moi( vyl8ew0.ebq sz , *ws3j3gz/ab v 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/8uq1cd l85 j* gorxka car slides forward on the dash when the drivecld*ra51k8q/ guo 8jx r decelerates 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 mas)2e6 phe m 6 ;e4cc(fyv kaopru5nj10fs 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 con16tsaa(s za5tzz5o z 7veyor 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 thea765o1z tzs(a5atz sz 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 ooyw*p.p9e 7jvqgg 2s:f kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicy *ckv5w yi2a;ecle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse ) fhb8 m)n/tisapproximately 20 g of blood is accelerated f fs/) i)btmhn8rom 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 cr 2y1k91glqxyovv r4/ cash if the deceleration is no more than 30 "cqyog k1y21r/vxl 4v9 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 przklha 2pc 3.m-f;b bjqo; /czef/6w3 nm ,um2coduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must j nmauw2zq,k-63mlo f;3bch;mcbe f2/ z.pc /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. jom:b:ppw1 a the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before collm jowpb .:1:paiding. 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 ldo*-/+ wkdv qhill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is itqkdo* v/d+-w l 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 Tower of q3i602xgr09 y -zykj kb3jlb bPisa and falls 55 m before reaching the ground with a speed of What w096jr b3x0-bziq3 bky2g ylkj as the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but e 9(lfc)hnsfm ln8ulzt+0 /) punters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without ha80nl+m /zu)f c) h(9s llpftnuving to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is workigu.(* . mlrntwng on the redesign of a hilly portion of a city. An important consideration is how stln(wt..um* r geep 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 rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watchri rbs4rc4aizk i1bkn2 18 6a( from a thin piece of string while the jetliner she is in takes off from JFK Airp24aiaicrb i n 1r48(b61 szkkrort (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 ramps connectinj 2ood+cex1q 7 qp4p5oe 0lal4g different parts of the store. ooeapxlp1 o4+20l djq 7q e4c5
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 toq;j1.i vpzdt,t.gmva3r)- hm lift the piano (mass M ) using the pulley am.. th1gvid-rj3 )z ,v;tp mqapparatus 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 acceleqqr63e(xc)l )nn n23sr wc1ptrating 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 foa* 9 ljard.l*fr a child-restraint chair, an engineer considers the following set of cjdl**a fla9r .onditions:
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 3s-+abiu*4bsspk o42 +lx hlsItalian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of simit bfyjs 8ffgx2 n9*i.:lar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended foxbgj 28n:sti *y.ff9f r 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 boatu;f5qf 2a9 kxmt6rn; h is using 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 maxim14v upel7:p4vr7c ivpum 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 arelj v6 lydk7;e8 art7 :hmbq.w- ascending an ice field inclineddj.hql: k b l87mye-a7tvr;w 6 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.