Why does a child in a wagon seem to fall backward when you give the wg 0tt3 g61ahe)mf )7m lgf 4oxk3;brwxagon a shar73tw03hk o6ab m ; x)m lg)f14fegrxtgp pull forward?

A box rests on the (frictionless) b wpy qf,et)7xg.o5mabfx*( ) wed of a truck. The truck driver starts the truck and accelerates forward. The)g t .5yfx,7e mxqawopwbf)*( 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 no forces actin5iy8 qxq ;c,iig on it? Explain.

Only one force acts on an object. Can the object have zero accelehgdgf:1 c2 u 4jy3f5zjration? Can it have zero v dzj h34fj5ggf2y:uc 1elocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is aqa.6zu 9fk 3irm:nw-a force needed to make it bounce back up? (b) If so, what i:awk-3z6. m9rf aqunexerts the force?

If you walk along a log floating on a lake, lvli9 ;pc0ff +t s;no5why does the log move in the opposite directs0o i c;59; +pllffnvtion?

Why might your foot hurt if you kick a heavy desk or a wabs-mw1 *iqv t/ll?

  When you are running.d/s vv u:cnv, and want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximcnv uvs vd:.,/um rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a 33vof6jng bxzh v85f(section of the same thread dangles from the hfvf8 bv5njx363g (ozbottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on;t)0i *chq essvv : fyj1t;e*e a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock faht) ;*ee0 ;1: fsjyicsvv*tqell faster?

Would a spring scale carri/o2*jhc/b hit o2d-kred to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kib hc/k/j2-o2rdt * oihlograms?

You pull a box with a constant force across a z *x(grnn/w 9tfrictionless table using an attached rope held horizontally. If you now pull the rope with the same /tnr x*9 ngzw(force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the in*zs:t*0ua .nu g mhe*tfluence 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 gu: tn0*ahs.u z**m tethe Earth. Why doesn’t the Earth move?

Compare the effort (ny -v1fvon uby- 6 *4dmngdt(1or force) 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 horizontally with a given speed on the Moon and on(f11uyvmov y-gdnt4d nb*6 n - Earth.

According to Newton’s third 7ek b0sjq0bt32q nk)l 2x.mynlaw, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team wiy0bjq02m bk2e. n )7lksntq3 xll win?

A person exerts an u;+xs/uqk qjk0w;lli7 rg a9v+pward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d)0 ;u/qsw rai 9+g+qklvl x;7jk by what object it is exerted.

When you stand still on the ground, 1rol7 gg:o77 s1f5bmapogu- chow large a force does the ground exert on you? Why doesn’t this force make you rise up into the 7ugro g171- s:lpoaf c7gmb5oair?

Whiplash sometimes results from a v 4w skkxr9xh+dom9s7dwv98 )+n y/vfpd p68on automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward i9d9xhkd )s+w4op 7 vownf/98s8p v+mvdyr k 6xn this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck+q kdb1s6l8zc accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force caus1kc z 6q+s8bdles the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block mgf,qp.us p(3 reaches its highest point,,f u.gm3ps(q p it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scalebyb;h3 llva sy:w:k-2hr2i f; read if you weighed yourself on an inclined plane? ;hvbf l-b:y wkhrs a2yl;2:i3Assume the mechanism functions properly, even at an angle.

  What force is needed to au;eh wux0/w4x;6rz a)(n-fclq8(v2zpd igj sccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at*u2,achpb s0a n1e tn zy-ib8q ++u6jg 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope with25h)ja5 bury,ap m1npxj1) zustand 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 4 p8qcox-(bk ta $76-\mathrm{kg}$ 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 stor ff/1-dnu jnueh oc74:v902ru yz5cd p an 1100-kg car in 8.0 s if the car is traverz chyv -d5j9uu4neu2c7n/o frd f10:ling at 95km/h? -  

  What average force is needed to acceleracw03zoib/ (o fte a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a ri i03oowbcf (z/fle?   

A fisherman yanks a fishpo gmu2pg5 (;cff+w,u vertically out of the water with an acceleration of 2.5f; +uop c,mu52gpfgw ( $\mathrm{~m} / \mathrm{s}^{2}$ 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-js2+kcqe35 bb mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) ie;q,8rhba-aj 6z : uqos 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 supportiu: a ;h6boq qearzj,8-ng 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. Whe3m15o *epbv kpn the elevator begins to move, the em31o* kvppb5 scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a mam1e3y2rvs+ fuj p 0q(lximum strength of 21,750 N. What maximes(upjvl r23q1 0f+myum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diver, 0gkm(vn2if js (mass 132 kg including parachutm,(0ijgvn 2kfe) 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 he strikes the ground b4asczx d.-y eb2;5 ) frcq/bvlelow, 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 bb2ls q.-xze/cyc ;)frv5 a4dkg, 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;-;ewno-nc o95dg d v+rbgl:z a table. A rope tied to the box runs vertically upward over a pu +nc;v5er; o9-g-odwn lgbz: dlley 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 am) dax8pm(e l:adc0z. basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dir8 h 98b-nboi l8grz1gagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward thb9 o-gi1z 8l bg8rnr8he outfield.

A 650-N force acts in a nor m wuw 7.970jxv0hz-)lzzz urxue- /gfthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer wig9ze0/w7xzhzfv)m ju.url zw7 ux--0th a vector diagram.

  Arlene is to walk across a "high wire" so6tw , jrg1qt(trung horizontally between two buildings 1(jr1 t,qow6gt0.0 m apart. The sag 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 bucket is hanging by a massless cord from i3o65fe 27jsrkpxq b 6another 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)fk.dyufij8,a tjc.k c. 3 j3f.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 uni/x62sg5+ kbvbvehy ++kd gxe ..0o1f*l ubdoqt to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. T k +6h1dfxesgb.5.gkqby lvo */ xo2ved ub+0+he 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, Fig. ap*p/ud87 l6gx t8y xq4-47 . Determine the ratio of the tension in the coupling between the lu x/axtqp8 pdyg 78l6*ocomotive 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 appazn p1icyy) 58)nux;zk ratus shown in Fig. 4-48. (a) How hard mu ni5);8 uypk)yz1 nzxcst 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 tu +vae rc;1ab 9i8,uq65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block qn528; ows scj2by0frj qb ./v(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 frictio0j s w/.gmpvx;nless horizontal surface are in contact with each other, as sxg 0;.wpjs vm/hown 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 ini i;.ks pa/wi5*,cwd18f,mnnnmt dlp ,tially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m pil1/cpnf5kantwmw8;,*, d m,s dn.i 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 fr hyn6i o 4(fb7ug/ c,d3lwbu +v/suw*bictionless table 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 cord, using the free-body diagrams shown ico/ ubhblugw(+3 6in/dvu 4*s7 fwy,bn 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 frictiok90s z8jv2dgxu a b,;nn 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 start n 9yv8bi;o6d;e jgq.s a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating a/5;(omojc, xg*1rimf 6h nvt xoyx:b+t 0.20g. What minimum coefficient of staticx o j;gvmmh 6 n1(/o,itx:y*of+bcr5x friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of staticar5jqf dhs* h25mrf6 bo91/l*u-uryu friction between the tires and the ground is 0.d2hq16 h/5ja m9rby uos*f r-u5*lruf 80?   

  The coefficient of static frikp1cqfn/ da/1 ction between hard rubber and normal street pavement is abk /1a1d/cp nqfout 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 -41iu d2qgf4t/ l ),kklu.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 rough 30bc.f p(+p+d0x uf2h vaqvr:*m$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high oe-u5pr 1qdzd g9fb op.0(p0es,n8 vr coefficient of static friction. b( o,d51rzv.g -sepf 9eordq8p00unp

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 f.l;,pw ,w; lqkb mgpm2or 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) 1g5f iiz7cu :j*(vcc5zl /dbghow large a mass would box A have to have to prevent any motion from occurrin gjifzc* ic:z dub5/1g 7cv(5lg? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor37 vj8v;b owza. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an w v;j8aoz37bv initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hodgo-: k;b ai9xzddf5:rizontal surf:do9dbxdg -;5i fk: zaace (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of stclq9y3l7 (u sjatic 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 sl l3u(9 c7sjqylide against the cab of the truck?   

On an icy day, you worry about parking your car in your d/(n, ddu/ +cao2 in)i:gbefiv riveway, which has an incline o,) /:d dgicenbaii2 fvuno /(+f 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 aag s7z9 td eaz*mto3.218clzt slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane d, k,mmkzmw6, u5y wv yjd**.ltilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed l17(kirf qe6 vj:glc/ 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 w5jgbxj+/6z upith 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 rought;v jv80m q,pj wall by someone pushing on it with a force dire,j;t8qm vjvp0 cted upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippe.m ve6 embrk7e2)j hhydxe(vxvz3j5fw 2). s7ry roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a p(kxme7j h3seb6vwe f)5.yvzhre.v) j22d7mxitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveli r pstdy37ba)7ctslo,:8 0ghyng at speed v is eqypbtgt0r 7:os h l,c7yad 83s)ual to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides foreg-ob8h//b0 few + eegward on the dash when the driver dece0hog- +wbe/ge e8f e/blerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is gh /9myvibl-t4nx3o 0-0m jake iven 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 fr3kq.88pm lbk;8 ce.+wywfn bf om where they are filled to the packing station 11lf y kk.ewcp .;+bnf38 q8m8wb.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 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 friction between 24bs0qq7uu0 :mq efui $m_{1}$ 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 (inclut:k;2y; pl g3 6w( thgdthpp.jyd3rj8 ding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplif*kr jnvl.yf(e ,coi;4 ph6on0 ied model of a mammalian heart, at each pulse approximately 20 g of blood is acceleracyrje. nhiv(lop;,*4k 60n ofted 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 auj,xmhecx8w 1bi/,7tt/ i 0 oxchh 7ol4tomobile crash if the deceleration is no more than 30 " g 's." Calculate the force on 77 t,x h,oo810ex/hci4xlmtijh /cwb a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthq,qt5,zj :m6em9sk3zuwmn . bd uake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static mnmk3t: dz,u .6m ew,9bqjzs5friction 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 two1i .os4 ltv:jl cars, measure 72-m-long skid marks of j l4it.l:s1voone of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that f.a0m;oak9l9cuvxy 89 t5xuop or each 4 m traveled along the road, the eleva;ukx 99o. cmul59v ta8y0apoxtion 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 ow/ on vc(p7cgl6i0 lp-2.u ippjc*us7f the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average fogc2plw iv-jcul.uipo7 pn6/s07* pc( rce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy strec (lac /0piq-jye7- xsbs; *aotch where the effective coefficient of fricj e-;0sol(s -bq ai*cpya 7c/xtion 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 portion of52ou3(ts g8 k.cf9o,rlo)dd+hsadkz;xc rz + 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 accelerate on a level road from r8kxftozos+c k c rs 59hr(zgd+o,32)d d.lau;est 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, dangle7 bs6i 516jj.jnxpeo ws her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Ship n .xe6716wjsjjo 5be 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 seve7 :4 ncuope3weral ramps connecting different parts of the stonw4 oeu7:cpe 3re.
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 ne+d ks muljj6:,x; dnb5eded to lift the piano (mass M ) using the pulley apparatus showluj+,mjx6bk ;:dn 5dsn 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 acceleratu:wd1*qj uwx +a li/:qing 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 engineer considtya(u +3+3zk xcn drj0ers the followingkxyu3d(ca +n 03r jt+z 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 Italiapn/ pobdc0e9gkbsa /w24 4rn )n 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 sak4a +k:gwg0s :yr5y trfety 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. 463kws0:5:tgr gayy4+ k r). (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 boae/9a8qybtef0c) d- blt 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 allu+4,qpj wf nd8owed 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 wujm2 r qs,dpb.em.3ngd2 l ,x/ho are roped together are ascending an ice field inclined at2dx.ju 2rq3.bmem d,nl p ,sg/ 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.