Why does a child in a wagon seem bsqvb6y 8; 7teto fall backward when you give the wagon a sharp pull fv 8;by6be ts7qorward?

A box rests on the (frictionless) bed of a truck. The truck drivpwa 6tszu9l6.hxe:e2 er starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in z9xeep :.6alth6su2w 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:96a;en uoim68 yf4a6es iqeu forces acting on it? Explain.

Only one force acts on an object. Ca , jh:ig8t.qian the object have zero acceleration? Can it have zgahtji:q , 8.iero velocity? Explain.

When a golf ball is dropped to the pavement, it bounceaejztxt96a(q5 .to s+ s back up. (a) Is a force needed to make it bounce back up? (b) If so, what exertsqj5tt x az6(+seoa t9. the force?

If you walk along a logi3bv)on-.* af q vy7-qjtboi 4 floating on a lake, why does the log move in the opposite direction*b oqi)o7t-3bjav-nyv i4 .fq?

Why might your foot hurt if you kick a he(sv i2o2na05am2s. 5vi f7iqzj f4qeaavy desk or a wall?

  When you are running and want to stop quicklym8e85oc.nw1 )y frdw b9 ousx:8 zm7jt, you must decelerate quickly. (a) What is the origin of the force that causes you to sy:)5oj87 wntmez w b8.ufd 1srxo8 cm9top? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine th*ay;hez:si. ,s7)zb 9,dsk4rfjlqc e read from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if dbq sy,r9s7cf;)aie h:k*j,e4zl sz. the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as g( tccl09omh8*3s j9rhcwhrt *reat as that on a 1-kg rock. Why then doesn’t the heavier 9l hoc0mttw38sch9hrj(* c r* rock fall faster?

Would a spring scale carried to the Moon give accurate results if t4w 3vp:hv33do c,ps.(etb rmohe scale had been cal (v.pt h :d3mco bwves,p3o4r3ibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant forcie,ck *krm5-* dcmm: ghlu-c)e across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration h:k- k*d5em-gclcm r m*)ui ,cof the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there i;naz 2ry s2ik2s a net force mg exerted on it by the Earth. Yet by Newton’s third law22r nk;yiz sa2 the object exerts an equal and 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 bhx p4r t: (mbkk9) fr-oax1l8the Moon with the force needed tooaxrk4 bmthb( f8 p9l :)1rkx- lift 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 law, each team in a tug 4f/zoy/u2fk dk ksz34 of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which tek4z/fsf 3kukzdy2o/ 4am will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe tf+zrn)ay2.0 uq ( pzq.nzkbm3 he “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on whatkz3b)uf 0q.+ a(2nyz. pzmnr q object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does thes 6qy3uuf,vq 9 ground exert on you? Why doesn’t this force make you rise up intoq9 vfyqs ,6uu3 the air?

Whiplash sometimes results from an gv +,p/yfmrk a)2l45t20uuk7 p lshyzz*p6xiautomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thr v2zkm 5yp/ l0 2y,x6r )itlkfa4psgz+*up7 huown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck aopi 8+69um(6qg nqqs iccelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate iu8sq n6( poqm g+iq69to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itstf 79g/:7 2vw ynlrnvkyq:b d8 highest point, it slides back down but the magnitude / b rw dy:tvkql:7nn97vgfy28of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourssu (zdhel+xk3ir t5 gyy8jd:1b - l2(pelf on an inclined plane? Assume the mechanid1 y (lu x bd2j 3g8ri5hy+:lpset-(kzsm functions properly, even at an angle.

  What force is needed to accelera8y uehj*rfoze846: 74tww p lcte a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikelailb( 4nn9oe;em 9 15 kcx;qf 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 withstansgqgmc2 -f9kg7-,6(l o cvs xpd 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 huj* wa*,wmk/a $76-\mathrm{kg}$ 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 8scoknk6.fs/4f9(ubgu gf. q*.0 s if the car is traveling at 95ko9nfuq4 sc g*.b/gukks.ff6 ( m/h? -  

  What average force is needed ,n r) ykw7++ldf1 t pw,.hdpqtto accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a wdlq),,hyfntpwt7kd 1+.+ pr rifle?   

A fisherman yanks a fish vertically cyq-5igij8 c d,fqqgy3 ;.ak9out of the water with an acceleration of 2.5 a i8c j-3q,gqyk9gc i f.5ydq;$\mathrm{~m} / \mathrm{s}^{2}$ 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-milemgzs+* 5 n6rcz 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 tha2; qr2wdd e,jyt the maximum acceleration is 0.0680 g . What are the maximum ,2dew;2jdy qr and minimum forces the motor should exert 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 bathroom scale in a motionless elevator. When thfqha7: how7p0dp 17ezm7li l. e elevator begins to move, the scale briefly reads only 0.75 of the persphzl1aed7: lf70q oiwmhp 7. 7on’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 maximum strength reumn5+ id7m+,iqzo4 of 21,750 N. What maximum upward do+muez,mi n45qr7 i+ acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includi9d fpqcq)k -1ing parachute) when the upward force of air resistance is equal to one-fourth of theq)f -k91pcqidir 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 groun k)7t-d l;:taqsg*ghwd below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 7tkta:-g;h gs qdlw *)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 5up7gsx 4/lija table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determ7uis4gx/ 5pjl ine 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 f800tvz:8rr xr hdc tb,or 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-body diagram of a baseball (a) at the moment it is hit777wyimh f3qv by the bat, and againyfhimv7qw773 (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fo hg + /zd2k-nql6ifh:nc9xb; pa67elcrce must be exerted in what direction so that the resultant of the two forc izec+axnl:f dl kn /qh6bhp769g2;c-es points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buishgvi s7)/ mof zc 9l atpzs:s422z/miu*8ia;ldings 10.0 m apart. The sag in the rope when /zs22ao4)zp g 78t ih/;:aicv flssimzsu m*9she 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 iks6prv- u)(gcord 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 1i(by1w w,o ry vef-n794.0$-\mathrm{kg}$ 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 r d.u, k) zm2g +pgo7opuqi++oat McMurdo Base, Antarctica, as shown inu ).+odgg,7iu+r z+kqopmp 2 o 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, Ff-idhkp 0;rdlyxcnw,cq6b5 k4ye9pv. v9,m. ig. 4-47 . Determine the ratio of the tension in the coupling between the lov.r9n b5 0,hk4m fdlppw;x ei y,cy-.q9dcv6kcomotive 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 herjyyh*e7/ -ajag 6y eta3rgd/ 1self upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mustta7j-a 1hy ey6g rdy3 a/j*/ge 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 racp c liy5-h ceqyq/9g42e began, 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 block (mvq, ,vjm36,kbae r2r d8d/bc4tbras7 ass $ 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 each5fjs 2u;;rht;c0 n cwg other, as shown in Fig. 4-51. A force0w r;2c;h5;n stg fjuc $\overrightarrow{\mathbf{F}}$ 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. 6 w vnpxupk plo.12n6zko2mmcz 98k+84-52 are each initially 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 moment the heavier one hits the ground. This is its "lauz nw2oclmkpm8 6o. 2pnkpv+ 8z691kxunch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlv+*hu- 9s v*f(ga oe7j0jxt:euzmms8ess 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 cordsfez j *m-o7g( vm :seat 98*hj+u0vux, 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 frictio9rv *.runh:pon 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 requiz*x8ck(b- h fvred 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 -,)bd bpw2enzstanding on a train accelerating at 0.20g. What minimum coe,) b2zpw dneb-fficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car 0wyt-kc bg(g.ya-v o/ can undergo if the coefficient of static friction between the tires and the groundbcgvw k--t gy0.ya(/o is 0.80?   

  The coefficient of static friction between hard rubber andsad zx /fompl)0 fwr:l k:z1)fn,l9-o normal street pavement is about 0.8. On how steep a hill (maximum angle) can you lm0 1 floof )-zwadlln/):fxkp9 zsr, :eave 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 j ybxx fq660hr lb5-m,-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 mpt-hl1. 8is318- g ay mrannb 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a ve9xtq -qeka /qekqed-x *o6 ,l:ry high coefficient of staticqq,: 6ke xo*qq9/ax tke -d-le friction.

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 kineticsjzlbou.lxhp uj:at 4a8t/)/ g/ph :gh *c15s friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a masfwp8q1 hd9w3rk6kg5is would box A have to have to prevent any motion from occur6 r5q3phd9f gwi1wkk8ring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floo-oyh1mgz m3z pd n) cp25;7jicr. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imp)o-5;p2zcn pi mzgdy1j m3h7carts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in cony; vsvhe:3yy2(i )u nqtact and at rest on a horizontal surh3yqn)ysi:;eu2 ( v yvface (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 h(*t;jrhhg,-b x 3ibwstatic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at whichgb3bjr xh-i* ,wh th;( 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 y9wzqwj /iz (4c.ld6 etkvi i:-our car in your driveway, which has an incline of 1jw/v -4 iwiizq6(dlk 9z.:tc e2$^{\circ}$ . 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 slide6 kps 65xh:awz idd c1g(aqd9. 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 tilted at an aruudj r088s 2ogd (mf 2-qvxk7ngle $\theta=22.0^{\circ}$ 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 osdn91rmm 4; 8l:t lcrdf 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 thex9-o l wgl;9g2 f0og02vphwwk steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pusf *,r(wc 4aqsr)vx6(eee 0afdhing on it with a force direcxefsvd6 a)ea4qr,w ( *e0crf(ted 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 projecl8n sw1 2h)1r b1ekkbrtiles as they melt. Conr18b 2r sel1n)bwk1k hsider a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum+f;srp.adefg.tq 3adi;j v5 . stopping distance for an automobile traveling at speed v is equal pt .e sff;a.j.a;3i5rdgdv +q 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 dau7dw -*k-y gpapi:( wmshboard of a car slides forward on the dash when the driver deceleratespg*ydu:p-7-mi (awwk 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 mp0qxyr zi3y91 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 convevmyfz +8m.l;eyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zeromfv;.zl8 em+y 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 frictiok.t5dqb*rftv 14*ta tn 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 dow xza9;mduuu/ 9n a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse app7jd3 s*s7: ipwmvrv5 zroximately 20 g of blood is accelerated from 0r5mvsi773 zsvw p: jd*.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 dr+yz r d8 ),)4vqvzrjpm u*-qlwr7b6p eceleration is no more than 30 " vpbwu zvqzlrpd 4r 6y),rj8-m)+rq* 7 g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquakmf vfeu4 /24uado+j7j e is a , and if an object is g juo4 2m+7vdjf u/efa4oing to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accid)y)di( .k .ofi o1l3j oobgk2oent 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 oj.)fo1g iok.3yod)o(kl2ib 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 m0 opo:ct5 hp:lx:p k8beans that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after 8p ot0oc:bx::p5hkpl 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 txxt)7 et umrhs(2;yt -op of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speedx xt 2h7-e(s;r)yt mtu of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of k(;ycb0l2/ hc,cvg ih12m/s but enters a 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 so, what will be the speed upon e g/;, 0bkc2chcyvi h(lmerging?   

  A city planner is working on the redesw rtzk87*k2o j6f, cx(tfd np0ign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered car ft,nktjd7wcpz*f( o8 062 kxrs can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her c-vp z 18icwfr:djqz z55r-f-watch from a thin piece of string while the jetliner she is in takes off from-qrzc d 1if5v-f:85jzz c w-pr JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be sev1x34 xs z:qwcieral ramps connecting different parts of the c :qw3iz14xsx 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 t: beup:y z)90s- smh6svghz0rhe pulley app0h u:gy)eps shzr0- z6bs9v :maratus shown in

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

  A jet aircraft is accelerating at 3.*hmad4b r/y 5dz3 n(aj5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 considers the fol7x0gmgu0j j(f 8.9;n cfvj6 pmt.teaflowing set of conditions:7. evt9 8 a;fjmnx.ucgf(mjgj0ftp0 6
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-caar:/kgyuym0pu: a.2 h 6u3 ybjr Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen*w3s5 tfmg k9fqf1yy 3x6u/h y's rope is more elastic, called a dynamic rope by climbers. uyxw yf15y 3fgt mq3/* fsh69kBill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boaai w:*qw aqpez-gn -(:t 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 bisbatz4 m8jn +gty/ zucke(cr7;e5 / :uilding is 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 together are ascending rfhg z5:- xel st6k*.ban ice field inclinedz- 5.hx k*s fg6rt:ble 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.