Why does a child in a wago( (c;brzvet bavd(,uk z1( 8xdn seem to fall backward when you give the wagon a shar(1( z,zdd(vbb(ear8xv ;tcukp pull forward?

A box rests on the (frictionless) bed of a truck. The t54v9f(,/ucie ykoi xdruck driver starts the truck and accelerates forward. The box immediately starts t/u oiviyf4d (,c5xk e9o 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 fhmwv 2*c:wt+t c2 ruw 1a-mjz1orces acting on it? Explain.

Only one force acts on an object. Can the oum67c- dxemk,xh g4. hx3ueymn*l 6;ibject have zero acceleration? Can it havee3m ymxm6*cld h 46niu,x;7 xh .ge-ku zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forfwjp *7 s*xze7ce needed to make it bounce back u *zswjpx* 7f7ep? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the l9:o t aem l9utzo5y0k.og move in the opposite direc :0zk.yo9mu9 tloe5tation?

Why might your foot hurt if you kick a heahb;vp6h/ fm: yoga*x7vy desk or a wall?

  When you are running and want rvh +w0s*no+x,g x 6ojto stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate o xo+r,gswn0ohx *+6jv f 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 secti/ qqmzzejlx)aot ()39 on of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to qq zx3jemz )t)9a/ (lobreak: 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 great as that on a imqczmo l/t6z7a /e-* 1-kg rock. Why then doesn’t the heavier rock fall fa-6*/zoezm/ miat7lqc ster?

Would a spring scale carried to the Moon give accurate results if the scale had + tuio5 bl*muvp 59q pu))(pd/mt qgf.been calibr*)omvu /9bg.ql()qpt mp up tif +5ud5ated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a fric-;vx m rz;(/qligjf1v tionless 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;;/qvm1 gl zj(v -irxf) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under on5 g3i2fj0wre qsq51the 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 a 21n55gfjes3 o0iqrwq nd opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on thenuizeyh 9ndbgc3ju.5s*k ( y7df -o)3 Moon with the force needed to lift k5f ozc3yi9*-jhs7dbe)y nnguu3. d(it on Earth. 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 lawk hy:g24syb; :o6:*lt:s,hjzge m deg, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. Whag:y:o ts4k*2; 6ls:mj :ey zgebhhd ,gt, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bs h;x2ixm/g 8aag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnit/xhi 82xg ma;sude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the grou8ifd/ 38. g .elnvobertha74cnd, how large a force does the ground exert on you? Why doesn’t this force make you rise up into thene848o .lf/ev h.gt3radc b7i air?

Whiplash sometimes results from an autom7 4;tw/p6e 1lvp 6rej4.pla,khflxr p obile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be h pj;p6 w ex,lvlrt7464/lp1fka.e rp thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed trucd 0z6fpgd jye+08z(tu k. When the truck accelerates, the crate remains where it is on the truck, so it, too, acceleratt80g+ye z zdupf60jd (es. What force causes the crate to accelerate?

A block is given a push so that it slid)6p6uy-dh qmo es up a ramp. After the block reaches its highest point, it sliq h)du p6-oym6des back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read ifs3t4 :hzwjdh* you weighed yourself on an inclined plane? Assume the mechanism functions pr dstzhh j3w4*:operly, even at an angle.

  What force is needed to accelerate a childm:csg l65w(b y on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rimb):qd8zp 25qa v j5s 8vi)jgxder at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsta cvc5ic7r5ys9nd 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 a9tu*:fbfh0 lx oj/*wp- ,s x8yaethp* $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 lo+ ,yezc z3rxs9l m1/k99yqgs if the car is traveling at 95/qzso+gmr lc 9l9ke9zyy,x13 km/h? -  

  What average force is neededfgq z oueud1* dd3;7)h to accelerate a 7.00-gram pellet from rest to 125m/s over a distance*d fe1hq zo3dgdu;) u7 of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration i7 oxjg4 1ml o4dsx/y*5/e qedof 2.d7 yx /mx54ls4go*q/i oje1ed5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 a7s) imrtr9jafq;/9bm quarter-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 ) is to be designed so that the maximum acrt8:qzc7vmb k 8n ui*+celeration is 0.0680 g . What are the maximum and minimum forces the motor should cntr uzvb:7q8*ki +m 8exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a baty+m 9 p2 ooso8k3jd*gshroom scale in a motionless elevator. When the elevator begins to move, the scale brie2 9*p8odomskj3ogy s +fly 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 21250/ab5c 6jgdc.nu - zddx .3dkl-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleratiobx0.uzcd . -gj dl6/ddk53nacn can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg incni mj2ro9xa*zi7w 78h1mhmz-r3 pt7kluding parachute) when the upwa9m hjrxz7w38kh mizmor 771a -i*tnp2rd 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 gryfe t72k1gkz,q 0*nxi ound below, he bends his knees so that his torso decelerates over an approximate distance of 0.70k *z2x g7,et1kifn 0yq 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.uow*c+z9(ha- a:.npn i x q/lf A rope tied to the box runs 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 weighta:i-xn/ hpuf9n.wla( q co+*z 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 dibecsk8)kie/*ggzoyxx2 8 -awhq9gvv-dr (.1 agram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body5 u;z4il oxes2gd:c2c diagram 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 i ;ecux sc2g 5oz4:l2dtoward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forx). 26liekn q;z fcv1 wo)uod+gi(n) qce must be exerted in what direction so that the resu(z qq 6d f)oi).ck12)evw ign xnuo;+lltant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizon 7fk0 qfat;5cctally between two buildings 10.0 m apart. The q0fact ;5cf7k 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 anoth k/:bbw:h5fidgoy rhat867::eui ; wper 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 14u+im0 etm*8 twtnb76i.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 Base, Antar-ohl1j,f 5veuqy6: c ucpzjm;cl/70.n a oia -ctica, as shown in Fig. 4-46. Tha;6, 1floovq- m0cyiuhu.-en7la z: p jc/5cje 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 twu+ 6,w rha4 v5drqvh3hat2g0 wo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tenrhhv6r3gqd aw520h,+v twu4asion in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatuso:n2 uitqu86 t shown in Fig. 4-48q 6nt8: utuio2. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race begao+nkhye; s mfs 7l3;7o/ecw n+n, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a blo.hbr8v1 o)(7mdfy)snx+snh ock (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 za4ds i:cor42ebvidz; 7s3(89 yew*p o*pv mz other, as shown 48z ;woi (*sv4mdai:zsd79p *e 2r vzoy3epbcin 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 in:jthd)v7 a5/wmpu t-oitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the momentumhp/-w:t oj75)vt ad the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless f upbxz p22v2b):nk0gtable are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each bop2 g2:2bxbzp) nf v0ukx 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 frict :db 8ia4in.zjion 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 requc0l ld d lr1)*iey3dy:ired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. Wh4 7yk:wvve6 sz)av+ue at minimum coefficient of static friction must exist between yourve6uk)vw +e7 zv4as y: feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if 4 8- kw:v*kqndckrxn m+*9j8per rry5 the coefficient of static rp4knrq 8r-* cw k9ny x+v*drm: 5ekj8friction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street/n odz2i()ndm pavement is about 0.8. On how steep a hd 2dno/mi(zn )ill (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 / jgn:v0 u pp+c+jd.gwvyg6c 3-4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30:/y+ g9ww4vfylc.2hzftyq/n0 n be7d$^{\circ}$ 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 asphalt5gb/es8q9hve surface have a very high coefficient of static fricti e/hgq5e8 svb9on.

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 frict1,mf bhhbs bir9 f4;)vion 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 waonie4b- d3/b ould box A have to have to prevent any moti be4oa 3d/ibn-on from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it goc jzkv wrvfn+d,:0b 67na6*em, given that the coeffijzk 7c df+rnemvw66v b,n*a0:cient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 755,g c t0j4ik eh4tms-h kg and 110 kg , are in contact and at rest on a horizontal surface ( hjs4 etcm05kitg -h4,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 static fr ra/b;ot k4ivvf.4; lciction between the crate and the bed of the truck / kar 4t;lf.i4b;vovcis 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 ppetv4 qqv+n2w1 ;vxcplcy4 .0 arking your car in your driveway, which has an incline of vt 14pv.n;cyp x2 qw0cl+evq412$^{\circ}$ . 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 slr.j 8yodar4)s ide 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 ae/ul93 b- nym+nrdwus6*xq+m plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spo .;8 jqm jlo9ob;iwl7eed 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 yzkyky 7 (z/.n0up9nwwith 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 someone pushin*9uk(5x gqeon uc03o ig on it with a force doqk (0ug* ocx inue593irected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they mrc(ly pp of8;* mqf8 jx7;;mdvelt. Consider a chunk yxocdmf lp7pq8(j;8 v; f; m*rof snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an auxnme as* *74/ tjj.pmytomobile traveling at speed v is equx4s ajtj p*.emy*n7/ mal 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 forward on j7lxq2npar.v,vr +d6s14 aof the dash when the driver deov.jdrf+,n q1 lsa 764arv x2pcelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initi. njxf-d2 3zi1z,p-hw 7d pzeeal 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 packindykfe* k c9 g6,a)mxm6g station 11.0 m away. The belt is initial*kg)x y6cam9 e,6kdmf ly 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 c-wb)gi,mw9dv i 5j6m 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 bicycle) can coast down a 6.0ee,1gzibgm., :n4 gsy $^{\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 heartiz u/x3o51gylv; yt m0vo/y2t, at each pulse approximately 20 g of blood y;/tyzi /o0 l2g1vx53mv uyto 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 c yqo3z(gwo8 5w0d.s st kx.kga3 ;;flif the deceleration is no more than 30 " gs z lsfqtg58d.03ac;k(ow y x3gw.;ko 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an juri.( q0wi6sobject is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least w.sr0ui j6(iq $\mu_{\mathrm{s}}=a / g$ . (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 carbz z,+mi- 1dqls, measure 72-m-long dq+-b 1zim,zl skid marks of one 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 1blo; rss.:/qkn( u5ol -in-4 hill (1-in-4 means that for each 4 m traveled alo;q olusn5kl:(osr .b/ ng the road, the elevation 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 thbl l6)- ahwhu+e ly.n8e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What wal y a).8h+wuh-ll6 enbs the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters aig2 *xwb r-. lrab01qc muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If sclg r0 *.1-w2rxbqabi o, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion oq,io. xg/k o5.x(eqduf 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 part/xdoe 5qkgu,o.i x.q( icular 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 exper w5-. (eqwdbtiiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices thate-b wi wt.(qd5 the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connectin,g;z4+znj jx6czr7f og different parts ofrzofx;j zg,6+7 4j ncz the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the pula. ml:h8q3g2cm e gl*g 2zaex1ley apparatus shown ie3c2h:* 2gzl a 1qgm gmx8.ealn

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 mps:w9ljrh - 7 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 cli76w7dlhkf2p+8q )pt+uwps. mp m 02bgdup *onsiders the following set oflpp8kp2*d wp6b+f77ml qusm02h) u g +pdw.ti 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 metric tons (6n.saq iv 6/561f smrdy60,000 $\mathrm{~kg}$) . 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 Karedx j s-g5cwm*hc u4m*ksjt4;fxm 66e1n, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. 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 weic4*c m1jwj6 mxe h*t6mf5u;sgd-s xk4 ght.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1i(l 1.y,6 6cve8mpgkx1b ikfi 0-1 $\mathrm{~b}$ 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 alloweofiudl819f6gd 7.cvhkv9g /qd to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fielz d ,g,+b;zz sb*wnd.3i8pph yd inclined at 21.0 ;zh ,8,p*yi.gddbs z+3 zpnwb$^{\circ}$ 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.