Why does a child in a wagon seem to fall backward when you give the wagofwai ie ifevc41z,2q(g u31 b+n a sharp pull 32+11giai,i e zvwcb4uf( efq forward?

A box rests on the (frictionless) bed of a truck. The trymi,sod- a7idw.u 77ftj.z7d uck driver starts the truck and accelerates forward. The box immediately starts7umdi dfs7,ja ..i-7o wzt7y d to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an objjl;.p3. .e cuoq.+kjaluu3 lgect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero atkz6q lo ga*2:rso+-x z0leg+ cceleration? Can it have zero o0o+6 2lexqgka gzlz*-t :s+rvelocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up+qx ya: (vhri6mxc43bjas +1s8 u9lfi. (a) Is a force needed to make it bomsrf1lih xja s+36qib (c+uyva 9x:48unce back up? (b) If so, what exerts the force?

If you walk along a log,b-iu bs0ch41 vw6:,srhva sr floating on a lake, why does the log move in the opposit6 rb:bvh4 h01svcwr,i,a-usse direction?

Why might your foot yms (,:pe7 k; vo7jbxd.lkd:ihurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must4 zoo0i yxi6fny;lp2qfv0 xh -w;y 0x3 decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleratpzy;2fo6xyo 0qxi;h3nf 0wv40xl i- yion 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 sectiong/c8bj ;j px1j 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 st 8;jpx g1cjjb/one 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-kb9o-/ n(3neutbh+/a joh 0rocg rock. Why thencu0/aonh/r -bt jh3e b+ono(9 doesn’t the heavier rock fall faster?

Would a spring scale carried tekjyshxwoqmk-qy93 .)*/ 2 ivg8w s6f o the Moon give accurate results if the scale had been calibra.hk- )y 2yw /f6 gje3*xos89qqmskiw vted (a) in pounds, or (b) in kilograms?

You pull a box with a constant forccmh8;jih mvxyf; kj5+xx 38p; e across a frictionless table using an attached rope held horjmvj;hi;5; m8y 3cf+khx 8p xxizontally. 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.

When an object falls freely under the influence of gravity there is a hz,n*;h xon0c,e *yq ud4,knn net force mg exert* cz,n 4;x,0ndnh,ohquye* nked on it by the Earth. Yet by Newton’s third law 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.tbljz,r *iit mi) (: k9wut6a you are on the Moon with the force tmaj:w.9i( 6lrbuzi,t*i)k tneeded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third lmo iu,wm:x* 3-f/fye3a k +xkraw, each team in a tug of war (Fig. 4–37) pulls with equx / o3y*w,emmf:ukk 3 -a+rxifal force on the other team. What, then, determines which team will win?

A person exerts an upward force oq wowmhr* r8pma/3;h: f 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third lr8rm 3wwhhm* /a q;o:paw) 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 the ground, how large a force does the ground exert on /)i(qmj( +lipg 7gprv you?i)vj7(qgp /(prigml + Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victi3o:(gim3ug5 j weoz8cqa,h4 rm’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatiogo(mh3qej,a 3g: 54 wc8iozurn. Is it really?

A heavy crate rests on the bed of a flatbed truck. When vrymw. g+)e8*mpb:x f the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acc .bpgfy +xv:mew)* 8rmelerate?

A block is given a push so that it slides u+nd*es8dwi3 o p a ramp. After the block reaches its highest point, it slides back down but the magnitude of its accedsw*n di83+eo leration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incliymb3,hknif 0 2ned plane? Assume the mechanism functions properly, even at2bhi, mk0n y3f an angle.

  What force is needed to accelerate a child om) 8oi ;1pnvbjn a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bi0j k-sli he mdq irle226pvq6k6+u;(rke 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 jfo dmu 69c:s:withstand 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 of9d7+vzllo9y4 e4,cwdvkkt *2oaw /dc lg1zx3 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 a 9:, ptk:moo*4ctdejx n 1100-kg car in 8.0 s if the car is traveling 4odkx9m p*t:j,o:ce tat 95km/h? -  

  What average force is needed to accj/hob,okvp gl m. 2h519ue02q; gvr i7hvc*hvelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alon.ju2ivo g0r2p v ;ch7ev hvh *h9mo51/kl,qgbg the barrel of a rifle?   

A fisherman yanks a fish vertically out of the watf)zwodf e7ekyg9z18h( j 6yf6er with an acceleration of 2.5 ()fozygk7h1z djf9 ye68f6we $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track o jpcx48ta4.hlk7 pc) (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 k*i uesr l+0m,.0fidkjg ) is to be designed so that the maximum acceleration ims rji0+ue ikld.,* f0s 0.0680 g . What 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 q+jil(1e+aok8x 9nu a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration o8 q+oaa uk+n1jl9ix( ef the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has d -u6ckwh( w5fxe:u/rtfb4o .a maximum strength of 21,750 N. What maximum upward accb:uk/6 w x-fwre td och5f(4.ueleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelerat9cub .taxl5s0 ion of two falling sky divers (mass 132 kg including parachute) when thbc9xs al.0t5u e 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 roofq, aa* s/j jc67xpu1gh of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso de,j1h 6*p /jxgca 7auqscelerates 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. ) ks2j z v8rto 9mcu3*xd/hs--z k9yyrA rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley398uy- r x-k cdh*yo2rvzm skj/)s z9t weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbalky8eac;zhbz 80y q 9eap1s l9)l 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 momen lggz( yb(10hut it is hit by the bat, and again (b) after it has gu z0yg((hbl1 left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A secoez+rlk p;ejo/ 7 nv--ind 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vecj/-+oe nr zp;-k7 vleitor diagram.

  Arlene is to walk across aj4pq .)l-oykc-agt8m "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mid . qtg8 )kyc--ljmpa4opoint 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 massfm+i;,n) hog bless 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 14.0(j2j;.kqbafv a h/ :aw$-\mathrm{kg}$ 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 unitz -zy8su4w5d/f 91b wdi5rt+xhtj x-u to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of -dzu4ft jhz/xui w9wbx1d-5y8ts+r5the 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,fe ep9la(wcm gc: np0a,8y)4p Fig. 4-47 . Determine the ratio of the tension in the coupling betw,0wp9a:pa nepfc4lem8 ( )cygeen the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pull1 l,ccj6 sm.20cprkf ys herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard r k,jlmsc.2pcyc01 6fmust 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 zb8*n oxuo o4w, ub*v4began, 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 (massej8hcng g+ /1l-6 mlnf $ 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 p k xz6u va/;oox-o*a2with each other, as shown in Fig. 4-51. A fpu2x 6x ;oz/ov-aak* oorce $\overrightarrow{\mathbf{F}}$ 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 eae r4l.1*u-ayc6ruuyk ch 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 heavie-.uyc1krule 6 ru *4yar one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frit6rt4. f g(nxweg :jk)ctionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fi fj6t t ge:4)kgxw(n.rg. 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 friction b,ubz( wt*yu)g5d nhi. kea n*1etween 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 requia- kh3t)1*,ou ,gq qgy mmugh0red to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20gr *x4l kgjr-.o. What minimum coefficient 4xk o r-*g.jlrof static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undev( h 2xn+g+jld7y,j murgo if the coefficient of static friction between the tires and the g,h xl+2ngd7 y+jvmj( uround is 0.80?   

  The coefficient of static friction between hard rubber and normal street padm qp50fv8p2jw+l8-vrin 4mvvement is i8w+4mdvj lpf 2m5-q 8rnvvp0about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -. mbw/je ;q9 hsdv2jje:cv07v 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 re 9q4fthyfc 5bx)otp76st on a 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 with an asphalt surface have j(u3o-xorg-ajc 2n3ra very high coefficient of sta3gr2 ( ur3-no-cjoajxtic 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 fric7qvh5z3 dz/f/;gs gvi tion 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 boj9m er 9g. nr/ 4q,j;q)n f5pj46focf drjm2sex A have to have to pre9m; j, 2on4 f9.cre r jm6)f/epn5q4gjjdrsqfvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across/+rfiyizns/yv(q /4lo- s hc6 the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spee /oyy+z filn 6/ 4sh-vic(srq/d of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horsv fp *u)q;/rfizontals/ pq;vrf*fu) 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 coeffi(yzm) f6dt jr;4gcm b6cient of static friction between the crate atm)ycb(r jgd6 f;m6z4nd the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your dr ch276j bfh6w4xdpm5le 1:cuniveway, which has an incline of26 cc7nmwbf5lj6h d:41 uhxep 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 slidex(jqm 8ox n-i* 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 onbrc-8-2m omsx 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 s pv1kz4dbz l5+/ qpuwl62g1arpeed 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 u76a8z( fjeaj2v(z ps5nybm3(hf/n wof the 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 wabbwkrbn +cu(faid6 pd 48v083 ll by someone pushing on it with a04fdbdc83p wba+ik8 rn u b(6v force directed 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 dangerous3a 2 jr) wumfm9xqj;)i projectiles as they melt. Consider a chunk of snow at the ridgejiaw 3 ujx ;f)mqr9)2m 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 fgpfpr33j cs z8ao37q 3or an automobile traveling at speed v is e3 j3aps33c8fzopqr g7qual 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 d 7 ja/ ro7qnup7(g9a1limkv t6ash when the driver decelerates frol7qavpkg1nu77r6m /9i tja(om 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 ; sno3ut,t(ars2d4 usis 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 belt from where thedydjkznelpn3x69 r ;j7 q,u4 0y are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speedy,dj x en9zl4prjq6k0du7; n3. 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 kinel.( *v87p eh80vwpy(klnircltic 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 (includidszkj 0ph-j0 8ng 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 simplifiedwjs6:/ v8wh 0ht(l+y etnx/n8oyn4d/9td h wq model of a mammalian heart, at each pulse approximately 20 g of bed0hw y wt8/qwyn8votn//+s9tl: h 6n4 (hdjxlood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an as, on,i5+1lawl nqm;j8t:joautomobile crash if the deceleration is no more than 30 " g 's." Calculate the forc 8l w:,anjno5 ;1msolt+iq, jae 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 in8.osnx te xi:z yai y3+(v38a , and if an object is going to "hold its place" on the ground, show that theo8y +vz ne3(ani i:yx8it3s .x 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 accident involv6 tnf)bb4l* dzing two cars, measure 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 zl) tnf6* bdb4road.   

  A car starts rolling t.tn/ -rqubi5 down a 1-in-4 hill (1-in-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 trbi/tu-q 5rn .taveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and fallsutnh 3 -*e: tuq4km p/yzs(s2j 55 m before reaching the groundmey*-hs:(32z utskqn up4/j t with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s bfu zvad3kzxc)u7 106p ut enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cycldx7 kaz3z0 u)uc1vpf6 ist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An imxkt(u ao2:)im8 1f57issxq6yvgr x p6portant consideration is how steepam62k giix xs rop56u8tqvs7xf )(y :1 the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from 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 2yfv ggm2 /jg::a8i n* k2nxnj kp.+baexperiments, dangles her watch from a thin piece of kk gynfgj 8jnv2aa ng+2 m2 :i:p/x*.bstring while the jetliner 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 s3iyh+0ao 2 snmh g/ b*av+rs3rupermarket, there are to be several ramps connecting differeo+b i2m*hgs n0r yvh/3sra+a3 nt parts 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 lift the piano (mass M ) p)t f t/ef u-pa5bn60wusing the pulley appwuf6b)p5t/ef tn-0aparatus 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 accu8iuk-fzpq;. tb m8-s k3db rvng9)p) elerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an k0jaam1xna: q ;n/w:91ka wmoengineer considers the follow/a 9ammkkjx1w;:nnw1aa q o:0ing 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 Italiaj88j i6qjl 4wtn 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, usy j -4 idgvjat4l+9ew7e safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her 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 huriv gy-t4jwjdl74a9 + et?

A fisherman in a boat i r 629vos(hqb6wrb84nb ;sg eps 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 reach a maximum s,*p9w00 dr ribvq v,iopeed 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 w7zi3y,n mfk3m-g azm. ho are roped together are ascending an ice field inclined at 2y- i33fngmzm7 ,ak.mz1.0$^{\circ}$ 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.