Why does a child in a wagonf(7*g1jja xce u)s c2w seem to fall backward when you give the wagon a sharp pull fox(c u 1ce*js7)gjwaf2 rward?

A box rests on the (frictionless) bed of a truck. The truck drivebx-0juso+z ziljg 1r6tm/b.9kj-n p 4r starts the truck and accelerates forward. The g9xnrt+b0 js/u4 kpm6-zzj- l1.ijbo 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 truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are,qx7d)1nh8q8 q m+y1:nllky v ocyiqq1/la)m no forces acting on it? Explain.

Only one force acts on an object. Can the objk +r*dk1zh5lject have zero acceleration? Can it have z1* jkh+dz5rl kero velocity? Explain.

When a golf ball is dropped to thek:r6*g 7 izy8jx,xtsk pavement, it bounces back up. (a) Is a force needed to make it bounce back ,j:*kxt i rskzy68x7gup? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposieza6grcq*j -7 te direrqa- 6c 7g*zejction?

Why might your foot hurt if you kick a heavy den0jzn6a6m*cz0;v z arsk or a wall?

  When you are running and want to stop wn5va3spc.;xr x a8.cquickly, 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 spx5 par;csa3ncw x..v 8eed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of th nry)(ol 0 d3.khx;;a ujlmg3re same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling ;l 3kdgr;o nr0ayhm()ju.x 3lthread, 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 grea7w uy-za b;1n op)m;yht as that on a 1-kg rock. Why then doesn’t the heavier rock ma7h;- y nbp)ozyu;1w fall faster?

Would a spring scale carried to the Moon give accurate results if thsd1p 9wb+a bv0x9 /hdcnl,my:e scale had been calibrated (a) in p sd+ywdx/p lvm 1cn 9:h,9bab0ounds, or (b) in kilograms?

You pull a box with a constant fo3dv bxc2n tcu*j+.+ ntnonly:6o, 4bsrce 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 (. nuc+6dxntnb3j ys c2*o:lo t 4,n+bva) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravi rmisxv2 m6yjkg)(t/(ty 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 Earth mov2 xjsgym(6m(rk/ivt)e?

Compare the effort (or force) needed to lift a 10-kg object when you are on the t7g/-efkxt 47m k an/eMoon with the force needed to lift it on tke 7x /- g7amt/fenk4Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pullsqup0 xdyi;*tir- m5i. 7oixt* with equal force on the other team. What, then, determines which team wirt iqoiyd .*m5u7 tii0x;*-p xll win?

A person exerts an upward for zmv 7pwr:7kq0ce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by : 07vpzw7rk qmstating (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 9knuw,7b-yf p exert on you? Why doesn’t this force make you risen7u-,p9fkw by up into the air?

Whiplash sometimes results from an automobile ae-/3ii/ucvuto if *l. ccident when the victim’s car is struck violently from the rear. Explain why the head of- ci3/i/.tf ovuelui * the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck.tvzai /bl,g5j -eqes /,71 2sdlo4cux When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accel4duxel 5gs-/2l,osi e7jbz/ c1vqta ,erate?

A block is given a push so that it slides u+l1( 9j2w hv eqpzk9tnp a ramp. After the block reaches its highest point, it slides back down bukn jqp219 +htwezv9l(t the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourselfm5)m3vh;/z0 sgetkyc p fi0ujz9 p*q( on an inclined plane? Assume the mechanism functions properly, even at an angq s3t h90*ejfvkg;c /zm5 (z iu)pmp0yle.

  What force is needed to accelera 70vmz7suu0fnp6iqax :)v+j nte a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceler6rig0r96sk 9 m(t ip*g3fotbx o8*q+zfh;ldoates 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 uiiio9g0butp/ 8 2nkj -sed 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 abv,x v484gk ,8uk wbzp 8c2f uom+3)/h kuwoty $76-\mathrm{kg}$ 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 e(au)h,ia l b5*n)5z yxn0rnqin 8.0 s if the car is travelinr b)lx5ei( qzahn yu5)na0 *n,g at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram .e0xeq4 jnp6ipet; g2.rol4 i pellet from rest to 125m/s over a distan.ieetiq464 0. pn g;j2xe polrce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerationpttegd*s1p 1v z- k::x of 2.*:kv:t t-zgxed s 11pp5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-miq3fwxp4 2 + v0km5mqc reuq08jle 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 485 7zkn. lxp 5cj2m6(hwt0 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max = x .7plhct (j nmw56z2k   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 m9j r nx/8 )*-.iq1d e eascdolag6r imn2/jbk-otionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s roke12 c)dignn.9e8*-li rab qja m dr/-xs6/jegular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 9 :swu)m:exk)lfijap. d8er8N. What maximum upward rw 9jxaef8:):lesud )ikp8. m acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration )fw3 ktrq-g qous;l4x2u3 u3. 4jkbx*u n 3xqmof two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is -.ub3golr k k;x2 tj43unq4 u3m)wxxusq*3qfequal 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 hoa.tlfe8rdss 38c s/2muse 3.9-m high. When he strikes the ground below, he bends his knees 2stc/8d.ame sf3l8srso that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box rmdi lflo 9 )dtqo6.,1ur/lu( funs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulleo) utffl1moqud,l( l.r / id69y weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a b ;c1g rtpxja3 m/zsf45asketball 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 mkb+tb+ nm1ul) v97 ea2z2jrmdoment it is hit by the bat, and again (b) after itvzmla 97d +2u2jer 1+bnbm)kt has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dief2k3g s3. 9(bn0:dsv martry rection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwtd:b92 y3essfmg a r3vnr.(0kard? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire"wpb4mlkk c29e 0x+8lkpu5fq+ strung horizontally between two buildings 10.0 m apart. The sag l m80klk +eu5 w4bxk9ppfcq2+in 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 buc51/ ie7.0amaqyox;+cawo3el - psop j ket is hanging by a 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 sqjy ped 206j(fofe43.0$-\mathrm{kg}$ 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 Blk;pj nhzto3v 1qj61 0ase, Antarctica, as shown in31p;10 l h6z jovqkjnt Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fiya5s9u ew9du rlz n8.:g. 4-47 . Determine the ratio of the tension in the coupling between the locomow dsur9ay:.l8z9ue n5 tive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatb uf5n;9n3mx: ;p3qz qhwep -pus shown in Fig. 4-48. (a) How hard musen3p; qq hz;p95pf-:xu3wm nb t 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 u4(,s kkki0r h.y0aois z2.l mbegan, 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 blocq-;hziax mez1y/;e g1 k (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 surface1yo3 xr:elh 1yowh-p, are in contact with each other, as shyp 1, holeh3yxr1:o w-own 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 g)x7qli1qp+x d14 7hcqros/veach initially 1.80 m above the ground, and the qvg h1 qrd747c)/x l1q x+sipomassless 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 pulley.]   

Suppose two boxes on a frictionless table arecm(etw1t8 v0w connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. A8 0(ewcw 1vttmssume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 frictionqp9uh0z /7svs9rsrc02r v(vy 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 start3in41iwy 1 h5m/vo) e0 n*tccbus-lbp 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 accelera3 hez y+tvqimk ,c-b ,l9hnh7+ting at 0.20g. What minimum coefficient of static friction must exist between your7-i+zn h, b3+y,mc9 qlet vkhh feet and the floor if you are not to slide?   

  What is the maximum ac b* jkz7 306hnzpcw7zpz2.i upceleration a car can undergo if the coefficient of static friction between the tires and the ground is 7z6*j0pik32znz p pwbc7 hz.u0.80?   

  The coefficient of static friction between hard rubber and normal street paeg6*s1 qvt r01al 6hnwvement is abo0hl66 1twe*vgsr qna1ut 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 decelerate at -4.80 owrga62 .zwt: $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough 3s(l 1ub2jmmw -0$^{\circ}$ 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 asphabkrgabgxx iu 8)qu;; +:5g 7kmlt surface have a very high coefficient of static frr biqx a7b;k;ug:8k5um+ )ggx iction.

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 b ul**hhv/0hca $ 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 awvev;3ik a-2knt-q )s u.g 4gu mass would box A have to have to prevent any motion from occurring? k3 )gi 2-4quegwsn.va;kv-ut Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it sl9;6z0mc bodgabz 5e1g sot30gides across the floor. How far will it go, given that the coefficisz0bb 3 ooa5gt91 ;6ggmz0ecdent 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 contact and at rest onvt 9zl2k4h* 1hf3xa*sx .e) sy56rjtoje1obe a horizontay3sob j5jte6* 1*r9.)ltvaoz1 xsk xh 2fhe4el surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coh o1c.nd4cdq5 efficient of static friction betweed1dc5oc hnq.4n 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 cab of the truck?   

On an icy day, you worry about parking your car ixav-u c32g+gz n your driveway, which has an incline of c vz+gxga3u2 - 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 s ,avv02 s1empwir.s2j0 kwrbvz99m 0with 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 2b6i5y h bq*luxkl53w 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 anfdyqx556 u ka0k4h1xa initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill withr yp4ah(mb+9csun : /e 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 wal4(wd( e8 x r3rivlok.zl by someone pushing on it with a force directed upward at 3e(4o (kvrrz.8dxw li28$^{\circ}$ 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 pjl c4*ps*0llrzw r9n 1rojectiles as they melt. Consider a chunk of snow 1jwrzl spl *90l *4cnrat 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 min ma8 ybn,;co:oimum stopping distance for an automobile traveling at speed v is equal to,n:aymo;c8b o $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash kk( tw*qn ckd4oy0qt6,; vpz3when the driver decelerates vp0toz ,k qy 3d6(cnwq; kt4k*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 a,w1tv- ds )ifyj:qe h6w0(fm 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 t5qu19ibhbf r28o10hr w ho 4dchey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 59o boq rch 1w 2u10hhf84dbir0.60, 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 friction between o t v.nqgx9m8f+t d.,f $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down,;kv*zrr 3s/l roy l:g 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 simplifi l;; arww.fv8ked model of a mammalian heart, at each pulse approximately 20 g of bloalf 8;vwrk ;.wod is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the dece 63svdf 9 l2kx0af4kllleration is no more than 30 " g 's." Calculate the force on a 7a f0lvkfl392 4x6dskl 0$-\mathrm{kg}$ 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 acfwr uhd3d n)k*5s,pt:celeration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static d3d nwkput):h,*r 5fs 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 yo*m xqq/2 b e6czea57the 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 colliding. The coefficient of kinetic friction between c zo ex/72q6*5b eqmayrubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m8trn11,ncm c vn h9y*q traveled along the road, the elevation change is 1 m). How fast is it goingnrh ty vc8n9*c,11qnm 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 To:h2x-p:fc,d 9ydtr hn99ub dg wer of Pisa and falls 55 m before reaching the ground with a speed of :9 :pngu,9h9ddhxfdc- 2tb yrWhat was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch whed.ob18(tf 7y87kp7 fd nysczz(yh;mqre the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if z. y7p7n h doykbyd fm(;cq81z78(tsf the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is wo3dxkzn(, my4tum7:z urking on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up theky : zu7 u3nm(mz,d4xt 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, dangc0yv+o e w em2ne78m0qles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airpomqw27me eo8 y+nvec00rt (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 supermzor+(p r)0 aglfv ri:6jkw y)0cv.so(arket, there are to be several ramps connecting different parts of the sto(j rp:o vf0a+y.vrlswkg))c6o(rzi 0 re.
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 too )+d0r2g( qj xbdvee)gyek/ 6 lift the piano (mass M ) using the pulley apparatusvegrd gdyx/)be(6k 2)qoj e+0 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 accelkg:z:j(vgr.e:2i8oo t)rx2 j+w vo bwerating 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 engf 8jq, jm7):d80ycth p2cv ujvineer considers the follow,v:u tm)pqdfj y 88h7v2cc0jjing set of conditions:
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 ru.rh9,j cfb .0;snoc 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 ms;s2u8 3n,ttf3 og yfropes 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 simimoftn 2g 8s,y3f s3;utlar 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 isq:f f1 :5xbyb6+f eurb 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 qcz9poshdv-r n+ .)r7is 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 toc8aqg v0 f,;xdgether are ascending an ice field incline;d8v,g0fqx acd 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.