Why does a child in a wagon seem to fall backward when you give the wa2ns r(oe1h;0f2ett ctgon a sharp pullto fe r2(120;nhtestc forward?

A box rests on the (frictionless) w3d,zqi .oj vc8g;ow+ bed of a truck. The truck driver 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 terms of Newton’s laws, 8;iqoz+dcjww3g.,o v as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explaisr mi.idx43sdd kkj) 74*l9jzn.

Only one force acts on an object. Can the obje0 gyfzjq8:ow (ct have zero acceleration? Can it have zero velocity: owjzq(0y8 gf? Explain.

When a golf ball is j jdxf5m:p. pj yro6(6j2 +wbydropped to the pavement, it bounces back up. (a) Is a force needj6jpojr5 xy.:dy6wbm +f( pj2ed to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the op(u7z(okv 9*h 7ty yifmposite dire*yv9 ( hofizt 7kum(y7ction?

Why might your foot hurt if you kick a heavy desku)a6 ; t*l p9*swe5p 4x6ffum8belbhc or a wall?

  When you are running and want to stop quickly, you must decelerate quickl/bfy 0,hznb53vyk4a6lrl mr 3y. (a) What i 3mrv6y,3fhbl4a/ nkr05yb z ls 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 sectio 98ve8kv:wxcxc7*59dybggh zn 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 the person gives a slow and steady pull? Explainb g 88*e:9dccywvvxhg7 x95zk your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. W, w+y).vo33plzg zkrchy then doesn’t the heavier rock fall faste,zzp3lr)c3w k. +vgoyr?

Would a spring scale carried to the Moon givej r .iv(w3jmo2 accurate results if the scale had been calibrated (a) in pounds, omv3o( j2wir j.r (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attacn415vkg pz7ahnyw- 5i hed 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, oravhk gn5 wn4i 57py-1z (c) decrease? Explain.

When an object falls freelyzc8,p i s,0gxk under the 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 and opposite force on the Earth. Why do ,sc,08zkip xgesn’t the Earth move?

Compare the effort (or forca 1m*bid,2tfra, up,ze) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to uam1,drz t*,apb2fi, throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of dzta) p/ l1r0hwar (Fig. 4–37) pulls with equal force on the other team. What, then, determines which teh01plta )rdz/ am will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descri/564o gq9dekx(*dzrutbt3z8gt( ii dbe the “reaction” forceg kdt8 t4*3t9i(b zogeruizd qdx65 /( (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on th/, yfpwl*27-:u ag chorr:t zje ground, how large a force does the ground exert on you? Why doesn’t this h:2-gur: lt pj rca ,*o/f7yzwforce make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’ss huu+xrwwu.o )96gw * car is struck viol*6) ouuwwhu.+s gwrx9ently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of b ,.-hdb6 selva flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerab,ld.h6e s -vbtes. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afteb5od6 uv.ub- (9 y cfne9uxp,tr the block reaches its highe 5bfun9tvd 9 pb(.oc-u ,xe6uyst point, it slides back down but the 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 inclined plank2 3wu;p*nfbf plxx)6ovy 6a.kfag4-e? 26 n- b.o a x*afgylu4kfpw;v36fxp)kAssume the mechanism functions properly, even at an angle.

  What force is needed to acceleratn wkq.x.dnxw-(ddr;k-5)n pld+.wvp e a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a ck/b/6bm(.;6prqoh q 8mg5dl7f3fjy fby0vdnd rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelert8pv2fix j cc4-h4. h g4hme(bate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oi p3*llqh70lfeq o ,lu. dzmisc3+d)*f 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 z3rk t,4x xbw,:tk bq9if the car is traveling at 95km/bwz3t,: ,k4b9 ktxrx qh? -  

  What average force is needed to acd+q0 qb(-kqhhdg o/4w celerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alo 0w4kdbq+d( h-h qoqg/ng the barrel of a rifle?   

A fisherman yanks a fish veroaj6hq mo(e at9mr+6tj .u4* 3n( yioee: w(jctically out of the water with an acceleration of 2.5 r (wh(3oq6yoeem ac:te(4a * 9n6oj+mj .uitj $\mathrm{~m} / \mathrm{s}^{2}$ 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 k*ta+*pbguiv6(sm ey5w ir3 qqjlfeom/ --3, a 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 mi9.zgz li . r.x*(remacceleration is 0.0680 g . What . *g(. lixem zrrmiz9.are the maximum 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 the eleva,oo, b m11c*6eammeeztor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and fe,*zom6m 1mabee 1 ,ocind the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg ele 61f8oqieka i(g85va6d-f unu vator has a maximum strength of 21,750 N. What ai f6d(kvf5g6 -8nua1 qoeui8 maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of twtpc8t/x+gx7a o falling sky divers (mass 132 kg including parachute) when the upward force of gp xtc8a7 tx/+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 s7osqr 7d 7f8kguiv 7 r4f.+bv42uwexw trikes the ground below, he bends his knees so that his torso decelerates over an ap7fwfeu xog 7b2urwrd 7 qi.4k +478vsvproximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertical djc j3js6n wc/ubv53tc2vl57ly upward over a pulley and a weight is hung from the otherltc3s3vw d7cvj cj6b u255n /j 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 divo.,2z f .mbxpxa-rb,dqdr-u8 d37j dagram 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-body diaz 9 ch330u.k8)rnyewe fx :sstgram 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 towardr)z t3w0e.cs 93s:xyn hfe k8u the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fobq/m x**.l4e b tcc)rurce must be exerted in what direction so that the resultant of crbm4* b.qc )*e xtl/uthe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wi7.bcs2m6qc 4iv 9hv +ydfkhax+2 cb h7re" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mid+yckhabihxc4hfv27.6 s dvc9m7 2b+q point 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 another l5anaa4t;7j t3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.lod 2c4n 3.mpj3 cl)ak0$-\mathrm{kg}$ 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, Antarctl/xg4q ,k6vb3w.dkvg ica, as shownv3ggw.d q 46v/x, lbkk 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 sag 9smspa y c4gg+3-da.(pshlj c)t.6ome mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the lohs.oc6ptl.djs ys3amc +)g pg4 g (-9acomotive 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 i ,6a*srrm b/ybu-:duthe bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must sh/r b ,m6y daru*ius:-be 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(mpej0t 1s l dyp*s80v;6iuuazl z(7k 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 (massgaj; zt.zx3beg i097 q $ 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 9dw qeg-;svv77ib( m 9. pceghhorizontal surface are in contact with each other, as shown in Fig. 4-51. A force 9ev;iv. p-sqd gb 9c7wm geh7($\overrightarrow{\mathbf{F}}$ 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 kqsy9 5rqn097gs8lr w 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 "launch" speed lrnr 9sgskq9qw07y58 . Assume it doesn't hit the pulley.]   

Suppose two boxes on a frin 4(tbr)r q8 tij +wa(qfh,xo1ctionless table are connected by a heavy cord of mass 1.0 kg . Calculate thetof)r8hqbqwj( 1r4ni ,t+ x(a acceleration of each box 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 o :fh)ku31d2j.pvhc( drz)phm f kinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to s xb4c9pp1/ c-yg2atjrsf6 y+vtart 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 standmnmh4tj;jd 1yfek4z9wm w v/u1wd,t/k83 7mz ing on a train accelerating at 0.20g. What minimum coefficient of staem7d/ 4kz3ym wuj,hw81 j zdwfm4/tmt 1vkn9;tic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can under ib-*n1s+t1bohc wtt:no 1mf0 go if the coefficient of static friction between the tires and the ground mc +ohsn 11n1of-tbwttb*:i0is 0.80?   

  The coefficient of static friction between hard rubber and normal streetep8*0vckt y3o pavement is about 0.8. On how steep a hill (maximum v3t8pc o* ke0yangle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80ketu0c 1x 79vs $\mathrm{~m} / \mathrm{s}^{2}$ 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 ros e0cg9r yw ,)4dnj5lqugh 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 very high coefficdk-(k a y/u0ls0mg;s bm8e:tdyp lg.8ient of static frictio y8d(ds /.kmg e0 yag:mut-8;pslbkl 0n.

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 kiop3 /hd4 rqb8 *onh.kynetic 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 mass would box A have tou 6-*hcb2sz ll have to prevent any motion from occurring?-lbu2lzs*6c h Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrosgu1pd jvfd,*)+f vz9aj89 nvhfx + 7vvs the floor. How far will it go, given that the coefficient of k*8)vjufvfgz 7nx+9v+ 9vjfa1dp ,dvh inetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg ailvj5ex5,o teo5 2kca/gu0c(nd 110 kg , are in contact and at rest on a horizontalave (u5ioj 5o2t ,/ckegx0 5cl surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of s qmv k(/w,bbym6 w.5aitatic friction between the crate and the bed of the truck is 0.7bwvb6.mmk(5/ iw ya, q5. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your caru c/l wvxn0qlv0w n 7*bx/mu/1 in your driveway, which has an incline *wqn l/b v0x 7/lu1nxmwc0v/uof 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 0vvf3ou r:t/ na slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plan.7seenlue- -. qh:vh qe 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 speed of 3.04k qbncqq7exctv; d +e m;2,t) $\mathrm{~m} / \mathrm{s}$ 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 hilla0ssjk izkng6 s6 t-)m/34ctj 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 pusjy: 9ohk9si p ( ,fim:ge)+qx2 kbfxa4hing on it with a force directed upwa92+ 4fsj)xkq i:(:9hi om,gaefpkxbyrd 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 roof -ppf4px*hj rfu4 u5+xs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pr4*-f p+xjhux54u fp 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 minimu2c7y1 3tzowwh cqj x9cfwh;. 7m stopping distance for an automobile traveling at speed v13j hhc wocwtwqx97 y7fzc; .2 is equal 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 the dash when the drivj2o 1skc;-rbier deceleratejc o1;i-rb2sks 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 initial sped tn58x3xtej 4ed $ 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 conve)t m*nm1+edfryor belt 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 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 andnmm+) ed ft*1r 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 kinet u:i5y8rwyx -sw *7f2hpk ewtx2) z6zvic 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 (including the bicycle) cant3nxt 4b*(ucko jfef pb56h0h:0 9 jvz 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 model of a mammalian heart, at eac* k( exn+xn*ktn0 cf6kh pulse approximately 20 g of blood is accelerated*enx(* ktk6fcn0 k xn+ 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 a4/ gns+r c*dqs(be2kautomobile crash if the deceleration is no more than 30 " g 's." Cn a(ds*4+es2qgc/b k ralculate 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 yc2m g,33 stdm, and if an object is going to "hold its mt gsc,y33dm2 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 s.-e/vyuki,r1 ib)ww 2a 2yh fmcene of an accident involving two cars, meaewi2 ym1).r-f,i 2bkh auw/yvsure 72-m-long 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 1-in-4 hill (1-in-4 means that fp/9tf f1;4t cn9vxh ymor each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after h/m4fvyp99 n;xtcf 1t 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 they2 wcp)gk8 hgp7m2kme b26)j q top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a spc7k2 m)26k)ygm8jp g2wpqhebeed of What was the average force of air resistance?   

  A cyclist is coasting +dpk gb; gynwt/ ge/)xe)x5f( at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without havi5tedg)wpb yge(;kf x+ )/ nx/gng to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesignp8 ja rrms *cbec.;k42n9r-in of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up therki*2.4scn- 89c panbrmje r; 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,tfxkr/m7p(xibzf4u/a.+ sx 3 dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notirx4xz b./7s+t3f/amup i(fxk ces 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 sej) 7iz bwbl05uveral ramps connecting different pabbliw7z ) j5u0rts of 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 n ta0b 0v:fg2vl s.fs1lift the piano (mass M ) using the pulley apparatus shown s0n1ag:tbvl.2f fsv0 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 dlb-x8iw z kdq*inbe.v * mpit+jl0 /bd)o3; 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 cki f7k-;-dozkhair, an engineer considers the follo 7--kkiofzdk;wing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian trai5c) j k;)/ptv qum7 a.mye;rnjn 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 iwhez2cjkr99 stxj4 1n)tg, 9safety 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 )c 9t gjkth99iwx42n 1rej,zs 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 boat is using a " 1.cajza+5-5d c:c nysz 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 buv.yd 2b4fg-myfnr9l oox6t0 ; ilding 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 ascendi x) qc4s8h2:;ocqu5vygceuae1p ;)bkk9 v (emng an ice field inclined at gu sc1ck)ve p;xhkc5 9y 2bqe( 48q)ovm a;:eu21.0$^{\circ}$ 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.