Why does a child in a wagon seem to fall backward when you give the wagon a /jp 8kq1 sdtxv0vg9/ksharp put sg/k/9kp01jxvv d8q ll forward?

A box rests on the (frictionless) bed of a truhf k j(b-ows0(el5kgz /t, x)qck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the trucqsf)kl jwt/h e 5zx,-0gk(bo(k and (b) by Chris who is riding on the truck

If the acceleration of an objw/p pf:1c*r ksw)s7 3 nol)aiaect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? xade,3d+xex5 Can it have zero velocity? Expd,35dae+xx xelain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forct05d( f/l i 5kbgxit/te needed to5bift0/lk/ti5 x d (tg make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mo mk/ert4r+pz .f/dh.ove in the opposite dir.fdph .e/ mrrz+o t4k/ection?

Why might your foot hurt if you kick a heavy desk q;w )1z9 c/lw/fhts. zrpdp*c or a wall?

  When you are running and want to stop quickly, yoy:l ubs5d.c2ru must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estsy bc5du :r2l.imate (using your own experience) the maximum 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 secfrwxyb*c zl d/2a x21hcfr(56ax7 :agtion of the same thread dangles from the bottom of the stone (Fig. 4–36). If azwf gbd7cha(6r f 2ax/yl1 rx cx2:5a* 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 jkx+gjh/-v- dx; beu y* 10svotwice as great as that on a 1-kg rock. Why then doesn’t the heavier r-xvv1hey/; * kgdus+x 0j-jboock fall faster?

Would a spring scale carried to the Moon gi5 pupppbl)(b 5.7mvibg ,ddm:ve accurate results if the scale had been calibrated (a) in polp):pd (m 5bm dg5ipb7,pvub.unds, or (b) in kilograms?

You pull a box with a constant force acr5/ lqvzqm: ( 8zdz-vmyoss 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) deyz -/ :q(ld v58zzmmvqcrease? Explain.

When an object falls freelw)4ui;2whkwk jh/eagbt5) 7 c1gj w2jc3 we 8fy 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 Earthh24)ejwe3/ tki b8j );afgw uwcwh1 cj52gwk7. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when yy9.kmnz e5 rhkx1f i)qzwb.8 0ou are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a q kxz.wer z1bhfk)m0i85.n9ygiven speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls w91h fv ba0i6/q m3fqmdith equal force on the ot/f mm qh16qa0 dbv93fiher team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe h9lfso+ou t(gdp/(( lthe “r/(o9tghlud ol+((f pseaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force dofky7hln g h,j))qjmes6tg9wt:j,1u5 es the ground exert on you? Why doesn’t this force make you rise up into the aqn6 j1)fty7h,,et m5 9gwk)shj ulj:g ir?

Whiplash sometimes results from an automobile a ob:.cm9) r u7(gbgizul ezx10ccident when the victim’s car is struck violently from the rear.xge g:)o b97iu br 1z.czm(0ul 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 ktgo; b) god8p;o3mq ,qh5 )wfflatbed truck. When the truck accelerates, the crate remains where it is on tog qkwf5,d o;)3obt)g;h m8 qphe truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push scovs84g1l0q 8 mo ew97kgkqryos7c (1o that it slides up a ramp. After the block reaches its highest point, rqw7e8v 0cmloq1ok(k s9y7g4 c1sg8oit slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scalpj ela;e.6csgv a(7 4we read if you weighed yourself on an inclined plane? Assume the mechanism functie p evaa6c;gw7l (sj.4ons properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25mkwl-z5f 3qf a o /pd iv+;.8aaawgh:;m/s$^2$?   

  A net force of 265 Nn,g ls-ym6 (qg accelerates 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 withstand if it is used to accelerate a 96t*qpw ,zt8eg/ d 3+rgl0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of m5v)rd/ lye f4a $76-\mathrm{kg}$ 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 cc g0y 58x nz/xfq2g5 -tujl3nmar in 8.0 s if the car is traveling at 90nfxgl-5g2x5j nc3 8 zymu t/q5km/h? -  

  What average force is needed to accelerate a 7.i(8. jb8 fcfr l)icp1c00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a c(i 8 jc.1i)cf8prfbl rifle?   

A fisherman yanks a fish vertically out of t)j38mmy yn o jfiofufl6)4resw98;7b he water with an acceleration of 2.5 9oslymr jjefy8))u o64m;fwf8b7n i3$\mathrm{~m} / \mathrm{s}^{2}$ 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 (402 2:8rg/ f vos6jn dp;cefv*ru *$\mathrm{~m}$) 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 thvhjua6a7p wx5;lqy6 0 e maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppor;0qa6ha6uy 7w vx5lpj ting 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 ele+nid * /j8q7nmgy 8btxvator begins to move, the scale briefly reads onlyt 8 d+7/q ijg*myx8bnn 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-jbwal 4.ow52tjw)4vi s)b zr8;loy0g kg elevator has a maximum strength of 21,750 N. What maximumva2 y)8lz 4w4 ;ol)bwjbt5s.0o rgij w upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two ;x *eh1cpirq5tz 3:iw falling sky divers (mass 132 kg including parach1;t3z*wqe 5h :iipx crute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When gn me3255ki qtzk8(kc he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 ect i(5k8m kkq32zgn 5kg, 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 tb:urwn03 p;s upward over a pulley and a weight is hung from the other end (Fig. 4-40).wt3ups0; n rb: 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 b ((*uvii,hx3vo2 nlu,q6kthd n1jqv8 kbq2y-asketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment *wtmsj7jr 17xn.mc(uit is hit by the bat, and again (b) after it has left the bat and is flying toward the outfield* c7(wjurj sxm17 nm.t.

A 650-N force acts in a northwesterly direction. A secooej5l:mo v-c:go. l* snd 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate yc:l*.eog 5 sjmlv :-ooour answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontces 12suhs; 8lip o-u9ally between two buildings 10.0 m apart. The sag ins 29ssi8 ;u 1hpuo-lec the rope when 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 massle)hf 4v6,bevncss 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 14.0 ),5z m was*7istua9bj$-\mathrm{kg}$ 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 Bab3/c vg(b:dvx6(u2 u/guj bayse, Antarctica, as shown in Fig. 4-46. The sx(32dvu/b(6yacvujbb u / :ggum 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 pullin2vkxx0fuis9 . g two cars of the same mass behind it, Fig. 4-47 . Determine the ratio xf0u92vsk.i x 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 upw0f3we6 u 1zlnalx *t.jard using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mustul10jl3 6*fzawx. nte 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 began, a m;;pg r5hjl:e v8zxv265$-\mathrm{kg}$ 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 bloc ajran vu22lg-g.9r p8k (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 ; q vo lj8kjy y:)yn:eg53emk8other,nk:y3em qy 8jj:o8v;gl5)eky as 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 iniqlw/dsei94 y )tially 1.80 m above the ground, and the massless frictio4q)e/9i sdw ylnless 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of map6n gn:yyddn/n a23/ vss 1.0 kg . Calculate the acce: 2g/ dp6ynyd nnva3/nleration 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 frictsfd-gbn:: 3v.bhuzc2 ion 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 star.nit:( * inx h,4civsit 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 accele8saf1 ;bdxul j0 r)-ap1bx rb3/jjp*prating at 0.20g. What minimum coefficient of static f/b)a 0ldj1x*sr jp; 8u b ppfb3a1rjx-riction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo *h ueu1.a z6ehklz* c(if the coefficient of static friction between the1 u(e*kle*zz ah .h6cu tires and the ground is 0.80?   

  The coefficient of static friyx )7svkp 7ly7p :8rcpction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leav srpp7xyc8: 7kpy 7lv)e 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.qa: 22ep h)yas80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 r;0 , dee9 h5/m/1hdcjlipebxlzng /q(ough 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 a9 6-g0nbb:vx7 1 lbuka1 : aqr+ mf,q2dqpwctdsphalt surface have a very high coefficient of static frmk0t quabn 2q9,bwa d-l7q6dv :f 1 :x1+brgpciction.

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 kinpo*)ll3(zeov ,7 e-8cabha gh -yt et.b qsl9:etic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A rck rivd 7(5sxb+e (6ahave to have to prevent any motion from occurring? Assume r(x7(ar6dveb+ic5sk $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so thdty4ii1n x +m)c:m4i s8hvk *qat it slides across the floor. How far will it go, given tcvk*qi+ imyim txn)48 1ds h:4hat the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in cofd( qbtp7w b.6ntact and at rest on a horizontal s67 p.bqb(dtfw urface (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 coefficienjl0rf :e lyr 1 2a)iid0fr5,tut 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 crate slide against the cartd )alu,:i1 5l0fye20rr ijfb of the truck?   

On an icy day, you worry about pars8 7e. e6t yat 2r;gdyf:l.bqoking your car in your driveway, which has an incline tstl:.qryy 2e86 de ;afo7gb. 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 wit*+tk:z3ml:k ;r wit10 bdzbo eyj ,ed:h 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 pl 0l (kal0al s7c*ca h. y)vt*fypg5z,lane 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 sp3yg, rk/ 0hbaneed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of 1ji jk pm/w0-wo)p;ap-zvqe0the 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 wall by someonevt sf tw0o97a7 pushing on it with a force directed upwa9ttwv 7ofa07srd 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;9w fh7nxrfk 0 d45sdt/:ff gz projectiles as they melt. Consider a c9z: hrfff 7 tg/w;n4k dxd05sfhunk 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 minim7dvv0z n: oo-2 kqf9sxum stopping distance for an automobile traveling at speed v is equal tvo97qv0:2 kf -dzso xno $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 slid+xb 1ae 073d litj.ydves forward on the dash when the driver decd7el yv 0tja.i3b1dx+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 q 4z- v: afuo.k442 xhjwi4guv 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 where they are filled to the packing stab6e7mp5(n cb ation 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt ac (75ncp a6bmbecelerates 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 frictyv1x5. aq7)ts70wlctzzra n)ion 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 bicycle8tlatb qa +;.h) 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 0r md3vzc.ql4yw3l5z each pulse approximately 20 g of blood is 5l3y 4vz3m0czdq .rlwaccelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the decele2:w k qllhma/ qjjhu+)7l;u4vratiqvh 4mk) +l/:ajj huql;u2lw7on is no more than 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 acceleratiovh)l:sl- k8 ada 0x.d:n7r gbzn produced by an earthquake is a , and if an object is going to "hold its place"bs:r l vdl:z.ghk0d a-xn)a87 on the ground, 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, examining the scene of an accident involving two lpdf)kd*c )ajjy ;v6-cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction betweencv -;jyl af)k*j)p6dd 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-4t6/mobm 8n cn3 means that for each 4 m traveled along the road, the elevatioo c/mb8nmt3 6nn 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 from the top of the Leaning Tower of Pisa aaniqv c:eh(k;/p3;x .p/ p lcxnd falls 55 m before reaching the ground with a speed of What was the avehn3 ;(ipv c/. ;/:qpxl epcaxkrage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but en-d)yhx gauylnkv6)j,mev(z+ ,t b*; q ters a muddy stretch where the effective coefficient of frictu () 6kv y,a yq)+jxven bh*,d;-mgtzlion 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 portio:iu ojm sg9c2 6jvyw5fi,ue4.d5b -i mn 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 acy mjwj96es5,ig oviu: di-ucf .24bm5 celerate 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/ocqulj p grk;+y 4(a4 watch from a thin piece of string while the jetliner she is op(;c+qka y4l /r4 gujin 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 supermarket, there are to be severrjkw409tk19xf ydic3 al ramps connecting different parts of t1f490jcwy ik dkt 93rxhe store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to d a,aq9 8idj1vlift the piano (mass M ) using the pulley apdaj q,a di18v9paratus shown in

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

  A jet aircraft is accelerating at 3pi-9izw zj0rxi2 gx)5.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rx5 j3wm2iu xm.j yqg-r9u1w 9d hbr7/a child-restraint chair, an engineer considers the following set of cojm5u/q3 7j 129ig.h myrbd9 - wwuxxrrnditions:
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 tons (660yg*d)ff-kal :/: zp60 dojbhf ,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 safetyxrod)5q(5xjv5eqfln 3n5: c g 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. 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 tim: cr55qxqo j nfe)gx(3n55vldes his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1thf1:/w; 4z kr)9,u lilfdlaw $\mathrm{~b}$ 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 maximum spc ouolj+f aq4qb)2 76weed 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 field inclz;* q)gqg,o;q1 pph ucined at o*;p qqpz q1cggu;),h 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.