Why does a child in a wagon seem t2h,ij rpmd) wkq1q0,b7czhl /o fall backward when you give the wagon a shar)c2q rdi 1,pw,70hlhqmzbjk / p pull forward?

A box rests on the (frictidl 6 *l djj50tfm3x5;,m ew8(inhjgjbf: ,nw tonless) 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. Discuj5 h:m di;wf* ed,3(8jtbltnl, n0j6mj 5xgw fss 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 objeeb*z29 pvhbb* ct is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object haw f g3 c:8,;dex7taq3hc :mmms0hxgh.ve zero acceleration? Can it havecegf;a3m:q h :g07smwc ,.d xm8t3hx h zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forc2fkmu :u 5zk00dhrxh -e n5xh z0u0fdmk h2k:u-r eeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why doe wzftsh7f ;jf6u6l /, bn:d0ozs the log move in the opposite dirtof 6jfnd; wb s06,h/z f7u:zlection?

Why might your foot hurt if you kick a heavy 8 8g6j8itlw7 ttyi8ibdesk or a wall?

  When you are running and want to stop quickly, you qqwh- rtsy w k06ao8 :kmior.063*kwxmust decelerate quickly. (a) What is the origin of the force 8 q 66kho3a:q wkro wt0kwys0*i .-rxmthat 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 wq5no4z zj:,ard9f0 s-0o kde the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the d:w0a zsj4qn ,eoo 09fkddr-z5angling thread, where is the thread likely 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. Wwze7eswm4a g*,;pm ttrv r3( *hy ts* m w4t ,;agr*tem vezwr3(p7hen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale haditzg+em4 iee-n 20p -h,n5pots2 nqi+ been calibrated (a) in pounds, oi24ieh+2+5-ne o gn0qp-ipt, ztnes mr (b) in kilograms?

You pull a box with a constant forc3 d8vb.:(uwdv dgvr5be across a frictionless table using an attached rovb8d.gd3bu(dvw r: 5v pe 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.

When an object falls freely undb ogv-4 1/rzhzer the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Ne zbg-v14zho r/wton’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 oi9.qd-.5y podq,b w evbject when you are on the Moon with the force needed eoqwq d.,y5 vidb9- .pto lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37)n; f6xti)l5fd pulls with equal force on the other team. What, then, det )nx;it l5ffd6ermines which team will win?

A person exerts an upbq6 6kf2wvt) oward force of 40 N to hold a bag of groceries. Describe the bfw2qt6)v6 k o“reaction” force (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 thkjn(tv(4em u ;4 3v ljin dy79jwxeu1+vq5lq)e ground, how large a force does the ground exert on you? Why doesn’t this force make you rise lm4v)i7lw4jujq3 e nqk jte1v ;udn9+vx5( y(up into the air?

Whiplash sometimes results froo:n zpxqc+l0bvt. x* ;m an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to :o.qx;n vz +0x*pbltcbe thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flail*j ru)r5vc1 b9axi1 tbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force caui9xvc1i 5a *rb1jru) lses the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachex so sq/b)m(j 10m orwz+1ux5gs its hi rmbsojx5wu/ om(q zs1g+0 1)xghest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathr5o *nh.y2h e1rvamz cu3z3m-aoom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at anr3hm mho3a z nuz521.e*a vcy- angle.

  What force is needed to accelerate a child on a sled atx9wgx tc25u:)b;z8qqhx - tq c 1hfa*f 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridece5k 2jk* ulg/:mi clm7te 1bn:sh2n1r 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 t. d 9e obezb2,y4,ccpfo accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of(omt 2 :1 :djepzacwh. 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 requir12l1klt yvjk7 ed to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h?l 72ykt jlvk11 -  

  What average force is needed to accelerate a 7.00-gram pellet h/.mu7xu 5n yy6 0tmwefrom rest to 125m/s ovmhx0u nmy6e.7/t5uwy er a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration o4szo4p8x y cj8f 2.5y4x s 4jpzc88o $\mathrm{~m} / \mathrm{s}^{2}$ 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 c w)22f;o+ea9 u8m(,*gbr fqkgvbmp ghover 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 ),ckswe0pj2dg5g 9 ltso that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should el9j)cp0g sgk,twed52 xert 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 motionlessz45x u j6)wg nb7vlroxvx* u4+ elevator. When the elevator begins 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 accelerationx4* o7wu)uvl5xv4 n6r+zbjxg.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maxip96vouu9-xot * ji-wcluh/ fc7;9ap m mum strength of 21,750 N. What maximum upward acceleration can it gpo6 puc 9iw -7jt x-9;vmhl*aco9 /uufive the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky he zlp,w/o km++9fxp4vbg/w+ divers (mass 132 kg including parachute) when the upward forceve4bzfw /p9g+p+m/lxw +,koh 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 h60x+ ;sl)x+eop xpzfre strikes the ground below, he bends his knees so that his torso decelerates ove e)x;06+fzoxr ps+x lpr 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. +vc 8btxueko 8xh/ ,h4A rope tied to the box runs vertically upward over a pulley and a +c4v,h tohe/8x bu8x kweight 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 pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pla*z)ad/w* prjkwfa e+exu 00*1g j+qux yer
(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 .bwo j 4sh25qkthe moment it is hit by the bat, and 2j hob wq45k.sagain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction.2tp 9g1+ lpipva 2w:wz-g;(5vjfc vvh A second 650-N force must be exerted in w vjv+ p;ghf2v9v:ap z p w2w5cg-1(itlhat direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two b7 e*dl/8dc0ecuea 7 aeuildings 10.0 m apart. The sag in the rope when she is at the midpoint i lcea8*7 /ce70eda euds 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 an+twpie: j/jl0fh)+ qem,5y 7qpnn3r hother 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,/g,q1x kp*y qmqmk2 g.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 Mcbt/s1zkk2mz +dh:u p/Murdo Base, Antarctica, as shown in F/s1+2tmub/ d z:kzkp hig. 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 pg/v xf)tqr i 1uwhv sr,(d3bi7:48ewxulling two cars of the same mass behind it, Fig. 4-47 . Determine the vgh qb8iwfed w 14v7/ s,rxur:3(ix)t ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls hershw u+3kr,7gp )6m veijelf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at const+,wk3mp7 ju rhg) v6eiant 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 bega ws )th;nz,.fr, i+ddjn, 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 0zg- ipun5:h12ygbfs $ 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 fri;jia.r:q oia * *kmu+zctionless horizontal surface are in contact with each other, as shown iaarik q **+oim:; z.ujn 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 aredj3r 67xcus,zqt f10l ;c oht7 each initially 1.80 m above the ground, and the massless frictionless pulcxh71c, rls j 0tu6fo7q3tdz;ley 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tc-f5f) bos m:t6svp9 mable are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each b5m f fpbo-s:)c9tm6 svox and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction bet1 11fz;gpq9kwbta;osween 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 requireds67hrk.)w20 o nsbeu7(e8sr mw ioxj: 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 rfdg1qb /q2 gr.k23 dmtrain accelerating at 0.20g. What minimum coefficient of static friction must exist between your 2dmdqr3gf/gk.qrb21 feet and the floor if you are not to slide?   

  What is the maximum acceleration a caa07rxqgx .-c( kazv ra h(58hwr can undergo if the coefficient of static friction between the tires and the ground is 0kg vhx -c7(z08q5axra r(hw.a .80?   

  The coefficient of static friction between hard rubber and normal street vj.79ymj e x0mpavement is about 0.8. On how steep a hill (maximum ange y jv0x.mmj97le) 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.,i fhkc ,m* mp;j/t mxw72ez*j80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 res v(da-.r:ub:a3zvnt* cov:n ut 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 m(1 gvefv;4 kbsurface have a very high coefficient ovv1 bm(e ;f4kgf static 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 frictio f1q0wha , :b)fkuxzb+n 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(6 htjiz68 lwkjo+ju-j7sb w* have to have to prevent any motiolzjk6w 7wju-shb o+ jjit8*(6n from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wilzgny /80r1lnj+d x/x bl it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an in8ygxx1+dn n/zrl 0b /jitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110wqg+w)8ri 5, wxq, iujkpvs;r 6++kuv kg , are in contact and at rest on a horizontal surface (Fig. 4qq,kxjv pi uw+v8;rwgr5+w ,6 u+s)ik-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 s4ad9t * z +*a,7xcxc/ahps:joci+ io ftatic friction between the crate andc/x4a xc* oa*o+ zs:ahci j,pfti d79+ 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 drz:.)5c(.b 4ybssfl 4msrhvdjb*u)m3oqff7 y iveway, which has an inclb3jmyh4( vu * q:zmfb)fd cs5s..yflor s)4b7ine 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 syv +fznxw6 0f7 a.p9gwith 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 plw0c-k( sxc7z kane 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 in9(o u-6jwoq,a1x pj +sxg-tdb itial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steep9.*n+0 va7 y cghzuj;sfpdmn6 est 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 w1.xp u( bvsxh-ivrs (;ith a .hu (psvxirb1 v-x;s(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 dangerous projectiles as they melat al bnv w0qtd+5 fg;*;l+eqn.b03qut. Consider a chunk of snow at the ridge of a roof with a pidabv0 0nwul5 bqqa nef+tq ;.;*3lgt+tch 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 automobi(3 .vcd ws6uq;f+rb6yahfy9 cle traveling at speed v is e6hu6bws 3 dca r.qvc y(f9+fy;qual 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 drivq.t77pt;.z4 fas a;mmlpzkf 9 eza t4m qp97.;ffz.7 amtplks;r decelerates 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 i. foe3x e7(2psw8)xe lsdf,iy)vni2 fnitial 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 (s4oiiwf3owg mbm)59e:v tg+ they are filled to the packing station 11.0 m away. The beggmoi 34f:owim(t)s59 ebv +wlt 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 and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic fric.4 ;zleh09p1z g8 n*ckpuculotion between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast dog q.axnmb.d;ug 3k/bd yq0ub(6mb2 z,wn a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulg* z.;rcl 0yj97bnhonse approximately 20 g of blood is accelerated from * ; hrz09ybnnlj g7.co 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 reasoh-vg*m) hyg g us1fj8f)* f2ulnable chance of surviving an automobile crash if the deceleration is hgjf fu1f)yu 2hg)vmg-*8*ls no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an vbo; tr )nnj(;earthquake is a , and if an object is going to "hold its place" on the ground, soj t;v(rb;n)n how 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 accidl.sfvkqx 3,z/ent involving two cars, measure 72fk,.vs3xl z/ q-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 for eacafy:htcv.;.g h v5ca,h 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bo5 :hv;acft, . hgyvac.ttom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Towe3nnxx z xx:f,t8 )j2ocr of Pisa and falls 55 m before reaching the ground with a speed of What was thznxj 8:3nfxx2),o tc xe average force of air resistance?   

  A cyclist is coasting at a soityrv:+p5tq-;r .* g1yd ijwteady speed of 12m/s but enters a muddy stretch where the e.tj; vq*iot:r+d-yg5 i1yrp w ffective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redec .;dmlg*( eipsign of a hilly portion of a city. An important consideration is how steep the roads cadl(e*cgimp; . n 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 experiments, dangles her watch from5ka z;ir: +bq2jtcg1yb(n;d khu (qr 6 a thin piece of string while the jetliner she is in takes q (b;;uhynq rktr2a+ki(6c 5 :gzd b1joff 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 severawn1 29h8luztt)aut o0l ramps connecting different par9ot)t208tl hnu a w1zuts 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 ) uskwe3u ) 9xayuop(j od*x/0idh1/ 3 ylming the pulley appara h3 o)pdikwju*a03/xe u91 (ly dm/xyotus 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 aci(r5gnr d2ih:wm) n w/celerating 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 engineer considrqvemsj (wrh ,8) 4qgb19j md:rr+yi: ers the follo, rqhd+4yrj ivm emr)g:(qs8 brw:91j 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 j)v.-zb5 nrdytrain 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 sakt9jqv0b mm05bh.2tt fety 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 multi0t 25tjb9qmhk0v mt .bples 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 : +,qxkyip;jw7mi vqm h7zw.4fa6f n- 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 reachyys:tq / z g579:/u)au shwck(qk,yhi 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 arlr3qxum c8k*mj r r mdi+-f7h, ,e*v0ze roped together are ascending an ice field inclined a8urm,0mrl+*zm 3,ki ec -*7h d jqvfxrt 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.