Why does a child in a wagon seem to fall bazyjp30v- qs rm7yn30 qckward when you give the wagon a sharp pull forward?7z r0yqvpy3n0sqj - 3m

A box rests on the (frictionless) bed of a truck. The truck dn mt;0sjwghq69n5 bo;river starts the truck a;6mnh0 jbq9gt5n;o wsnd accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of z5lp2g8g i*+ye l dw1uan object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the ob-l 8z p7qlp*sry7uxmht6 k zud7zd77 ,ject have zero acceleration? Can it havsr-pzd77 u 8d*zt776u y p klhqm7zl,xe zero velocity? Explain.

When a golf ball is dropped to the pav 2qd))yhxmjcv+k:g *)(-q1i a xkij gcement, it bounces back up. (a) Is a force needed to make it bounce back xm+v2c (jyjqk1g) ic hx-q aid*):gk)up? (b) If so, what exerts the force?

If you walk along a log floating on a7,gobp5fy)v o ; l ci.+j -q;w9yeixsv lake, why does the log move in the opposite dipvbg5voiy;9,xq clij+ ; es)yo.7 fw- rection?

Why might your foot hurt if you kicg:ymw0rxq8+gp, ,8h: eshemoh 0:xpck a heavy desk or a wall?

  When you are running and ruv6x7gx+3 iemvx6b4 want to stop quickly, you must decelerate quickly. (a) xix r7gb+vm6 3ev64x uWhat is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sameb b8 l/:i;wi c9+nhekh 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 likelywb8 h c /:hlk+9e;iinb to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. 2+1tzd6ouh9 ekc am u8Why then doesn’t the heavier rock fall8eht 92k+zu6 douc1 am faster?

Would a spring scale carried to the Moon gyv.e /vt(s4xf8/tz jiive accurate results if the scale had been calibrated (a) in pounds, or (/.vit(x/ tje8vz4sy f b) in kilograms?

You pull a box with a constant force across a frictionless taqm v9.xs35+zovp 8tb able using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.8 vp9+v .ob3xm5zstqa

When an object falls freely under the influence of gravity there is a net i-ppai; 93m0 gwzf5q bforce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force ba gw3ip0- mip5;fz9qon the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift lii i*/:pa 2eva 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 o*/aiip i:2 elvn Earth.

According to Newton’s third law, each team in a tug of war (Figx/jc *ll:oew /r 78snz. 4–37) pulls with equal force on the other team. What, then, determinlnj:zw *re /l 8/x7scoes which team will win?

A person exerts an upward force of 40 N to h hg.yevsps u* st .hfe4.-ut7/old 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 exer7ps.u. e* /hy hgu evt-s4fs.tted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground el wm up/.gxt(/bm.in5 ety 94exert on you? Why doesn’t this force make you mx/94ep btie 5(y.nlutwgm/.rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’se,v7xnw ove 6* xvu;kd lo26t. car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward idko6x v6,w2;.x v on tev*l7eun this situation. Is it really?

A heavy crate rests on the bed of a flatbed trucke,wnxt 9bq v7-. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causesqb ,-tew7nx9 v the crate to accelerate?

A block is given a push so that it9x d+ bw6.bechrj6vh / slides up a ramp. After the block reaches its highest point, it slides back down but t j6+b6 /.ehbxvr wcdh9he magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclin25 :ok)(f atpmbt7k5bb1o nxued plane? Assume the mechanism fo (7p5:mkot1fanxu)bt2b k 5 bunctions properly, even at an angle.

  What force is needed to accelerate a cop)6uguqcanve ;1svk37 6o q1hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at oghfr..xgdio071 l/iz0h g(k 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to aca . ra8mb3nr6d(m7rixcelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o.5wz crvs e5 ;)(vnydxf 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 8.0 s if th3( yhn x8x5ps4ny8x6 kkjbgp)e car is traveliyxp(s8)pgxn 68 khjb nx5y 3k4ng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gramb ni h 2hiok(;bwvq.)u;d4:lr pellet from rest to 125m/s over a distance of 0.800 m an ld(w;2h 4 ubqr h);o.:ikibvlong the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelev ow3oud1c0zr* p :q:vration of 2.5 3p* qcv0uw zd:1or:ov$\mathrm{~m} / \mathrm{s}^{2}$ 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-millf9(oebaa;h mh1 h a:)e 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 add8oi9x 8 kp /kh v2x.:ihmrh3cceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cm8xo2rkd8p:x 3v d9hh.i/hk iable? 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. hpz 86mmws29 bWhen the elevator sm2p 6wh89mbzbegins to move, the 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 maximum strength o5,eufd ih( 1b)1qhmxqtak*rb (im3s4 f 21,750 N. What maximum uptm qi1*is x3mdr,kb1hbqhf(e)5( u4award acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dibx x39rcy .q5p85qxdy wun m50vers (mass 132 kg including parachutxu.9 xqx 5cr 5p yb0mnw3dy58qe) 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 h2t; r c:pneyqetx .t;kk1r 81we strikes the ground below, he bends his kn ;kt1 nrq.r;yxtcw8:pete2 k 1ees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope 58)nuar +v/4n rytptftied to the box runs vertically upward over a pulley and a weight is hung fr8 rr)4pnv5f/ tuy a+tnom 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 a basketball plhtw xgia7/ cnsd1/5h(ayer
(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 basebuu 7+;e zz;dxtall (a) at the moment it is hit by the bat, and again (b) after it has l+udex;zut;z7 eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directt he2gly3g7 w:ion. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a 27g :twle3ygh vector diagram.

  Arlene is to walk across a "high wire" strung horizodf ;lt bl,g,d75q0zdjntally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint dg flbdtz5d j 7l,q,;0is 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 mzj lndv 07c3u-assless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1ec5r1zv. wyo9 4.0$-\mathrm{kg}$ 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 McMu-vfb2c5 ns5 onr*bt(crdo Base, Antarctica, as shownn(2 5rb*5c- snobfc vt in 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, zte65ny yor8wrkz3zo n/f2w6 wt 5:8m Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotzmt3z 8rnn26wt5y8 o6:5 kyw/rw fzeoive 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 4 pnt7oa fym7)using the bucket-pulley apparatus shown in Fig. 4-48. (a) 4yt7fn m7po)aHow 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 we 99ot,z8r.moazf q8 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 (mass+ 2:g-opy-* hjbaelmt c 6x)hc $ 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 witzh: r0y3xou) lh each other, as shown ry)olh: z ux03in 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 initially 1.80 m above , *ynmc38re a(ui7q :7qbwwqnthe 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 euan 3qwqb,*7n7(c8m :ryqiwits "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table ar+vyp71x;5nihv;3 v ld5keejk e connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the +k;5i y vnxhkjv3de;5v1elp7tension 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 frqz /6els03tx;vn0e ibiction 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 p)aw)*7,0 v nhvlm tt1,tbf. ikjh.yjto 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. Wha l/ 1 m5dhf 6enz:bjqxpid0f 7jhg+0;+knw 6zat minimum coefficient of static friction must exist be/i dwmx+p:051 j0n66lhknzha qd fz7f;bjeg+ tween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stat w:nai;s-9yy pic fn-ipysy9w a: ;riction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pa c6cnykx9 z9z2k i64jjvement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? jxz 9y962cni6cj 4zkk  $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.8+t t3tu pt(bb+s9i vm00 $\mathrm{~m} / \mathrm{s}^{2}$ 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 2 8iz)q df*nwkavro0)rough 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 witlyjopm (y6cmt/t2 k0;i ww0g);h/ mf yh an asphalt surface have a very high coefficient of statifl/ ywwjm tp0 6(y)0ctyo;;/ khmg2m ic 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 kinetic friction fork;ys 1) jiyp ,n*rsf.r 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 bkz8-pe .1ocslarge a mass would box A have to have to prevent any motion from occurring? As-. 1ocsekpb8z sume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Howub1y3ifl f5ia(dj cks j*5v89 far will it go, given that the coefficient of kinetic frictiofk8avju1ld(s 53i 9ybf*j 5 cin is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in .iv wktv(m g)vf)w)y95 v 8ohlcontact and at rest on a horizontal surface (Fig. 4-54). A 62.ohyivv )k ww)8 9lvft)(mgv50$-\mathrm{N}$ 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 c9 b*e23t )g+cdpowfp;.e lbfprate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the drivere g; .p)bdowe3f+p9cpl* f t2b can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking y /bzf r2zk,2gkour car in your driveway, which has an ingr zk22 kzbf/,cline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide c1h xqbz:we:xf6 ugzcs6 s051with 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 liesl,ba)1 a+nacyg1 73ygzi-a lq on a 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 spe,d nnaqrfx.u5r:4vx fu86m- bed 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 1scb 5 +qxd)xnthe 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 pushing on it gpi i5bc5ot496nurhxre2u dm+ s0lo v h+219dwith a force directed upwa6 c+hle ni5b2 +id2p gtru45dso 1 x9umvrh0o9rd 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 dang6jab,qm b/ghq (8goc,csor:cj - -2 frerous projectiles as they melt. Cf8cc,aqj- /sj rbr2b cm :-,hq(6 ggooonsider 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 stopping distance for an automobil re0zpe w/x)nm; -vjr1 7qpe)de traveling at speed v is equal d0e e ) j;rz7n)qpv1-ermxw/p 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 the8, xqth ijc60q dash when the driver deceleratesicqj,hqt x08 6 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 igt7v 71 zy-uc m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor mw tr a,/*,yjjbelt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most ra,tj*,jw/ rymapid 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 o oj9xp17du7o k. jl1cff kinetic friction 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 (includingos47 dtgtm ,nhu44xx9eshi)a) x0/ef 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 simplified modeli 5* f .imk7k73alyvyw of a mammalian heart, at each pulse approximately 20 g of blood is acceyw.iav7ly7*m3ikf 5 k lerated 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 e9833( x /wppt +lkci3ib eshhchance of surviving an automobile crash if the deceleration is no more than 30 " g xphp silwh3b+(8cte9e ik33 / '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 , andcdl-wdrw0l 8+ if an objecw cd8+w0drll- t is going 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 accql ; xb)8z,k.dth f6wgident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficientwl)gtdqxhf.b 6z,k ; 8 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-eftiq2be4+w- vd1et. ky/ r:-*c d wzkin-4 means 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 traveling 55 m? (a) Ignore friction. t:q41eckf+ ret2 dwk /deyw-vi-.*bz   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped fro-)4w txc gxsm j28pye.m the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance? x .xs4wc tpm )28yeg-j  

  A cyclist is coasting at a steady speed of 12m/sg fvp;cdm ljgd tm(6-6v +/yf8 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 spe6gf8- ft/jmlv6vdm( ypg + ;dced upon emerging?   

  A city planner is working on the redesign of wnj rvm,15w 3r6u8wwza hilly portion of a city. An important consideration is how steep the roads can be so thzmwv ,w u631wr8w5nj rat 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 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 1e0;2z2 pko r-rbcxrgt efu/6watch from a thin piece of string while the jetli u pk60zf2oxrb 12et -;rrceg/ner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps cq3c(vepaha/r k)*d* yy ru*fx b((uk7onnecting different parts of the stbr(3ue vuhkxafy7a*c/* y(qd() pk* rore.
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 l ee8+fek.uo. *wxi. pbift the piano (mass M ) using the pulley apparatuk.ub8f poe +*xe.ie. ws 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 axh8ea7(v2 kg mem:pr8++asof t 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 consigt-k.l4ynjs94 z7v)o5 swag nders the following set of conditionsgkj-5 s.4snlvt)4oyn a7z9w g :
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 Iy z uk t3vve7ts5,a y/gyh733d 22gqmmtalian 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:rs8up yc0* k .zmcrv7 of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm:up zcysrc87 k vm.0r* 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 s2dz7h .hyvm 3h :jpuo1+hu1 bfvvo*;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 allowed to reac+:8 t bll5s+dqlufx; 8-fdymqh 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 asu:mu: :;y zvk03ta ixkcending an ice field inclined at muuktz0k;a:3 vx :iy: 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.