Why does a child in a wagon seem to fall backward when you giw .x;1b 4 ifbq)dfxdksy+(.jsve the wagon a sharp pull forwa xf+ s.jbwf4sybd1 )x(.qi;kdrd?

A box rests on the (frictionless) bed of a truck. The truck driver starts the tr yrvyiw3:m n,pv /1-rjuck and accelerates forward. The box immediately starts to slide towa3yyr /n1pm w,i-r:jvv rd 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 object is zero, are no forces acting on it? ztn: bu/6h .tjExplain.

Only one force acts on an object. Can the ; qkuc;f:mt /mic6t p.object have zero acceleration? Can it have ze kp:;ctci mmf6 ;/qtu.ro velocity? Explain.

When a golf ball is dropped to the pavemw h n5o:buw: r-owz;n-ent, it bounces back up. (a) Is a force needed to make it bouncwu no:b5-o z;wrh: n-we back up? (b) If so, what exerts the force?

If you walk along a log floating od9h nq i cx;r3mr 1eyfa;i1+squ01g m8n a lake, why does the log move in the opposite direq1;g 8 9mdrh i1qf+ye3cmari uxs;10nction?

Why might your foot hurt djfg.3j *)njz (g9+i+a ecw pkif you kick a heavy desk or a wall?

  When you are running and u)x )ax* bppyjei.0+pq* /lod want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) thuy.)x*d ip+0/qlpep*a bjo)x e maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same 1847ix gbhhuk6 q4i: sgva0qxthread 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? Explain your absh0qkiag:4 ux 74q6g8hi1vx nswers.

The force of gravity on wx zkj8,:g (qq7 4b4qr9 qkraxa 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rocxj8brrq(q4kqx74 ,a: g qk 9zwk fall faster?

Would a spring scale carrie sqmwpt .np4)(d to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogtpp ms ).n(wq4rams?

You pull a box with a constant force across a fezt-fsknz( a; iit a2a/me3+ x .3e2g:mfoza.rictionless table using an attached rope held horinaeii /kx 23m.ae+tmzea( 2sza f;-t:g.z3o f zontally. 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 infl cvo2fsx*- la)uence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton)2xvf*o -scal ’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*v/5apug*4yaz dr(y)fmv c3 s 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon a/5vdvgy*sf pz y*rum(3a )ac4nd on Earth.

According to Newton’s third law, oxms.f*vcy57kfn x0/1. nqwm each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team s0yfvmn o7q1/mk * f .5n.cwxxwill win?

A person exerts an upwa1(-wdt j2r spufa4kg1rd force of 40 N to hold a bag of groceries. Describe the “rg41 urd(fapjk2-w 1steaction” 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 the ground, how large a force does th1+p qzk vw+tn a(pov;r6lxi-2e ground exert on you? Why doesn’t this force make you rise up into r l 12qv+( k;pwazpo+nx6i vt-the air?

Whiplash sometimes results from an automobile accs;-zhq h4 d-jcident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is -;q4csj hzhd- it really?

A heavy crate rests on the belgbk-iv v vz(7p1) ms4d of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force cause4 ps zgvlk-b)v(7vi m1s the crate to accelerate?

A block is given a push so that it gg,/): fc ,5h:w :6st/znypuzwqbtii5n.n lkslides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the desce )/::6 g5nqn5tghnc,z.sy wl:z w iukb,pi ft/nt than on the ascent. Why?

What would your bathroom scale read if you weighed h -knkmigr x4 ,-,r 7ovlgk5 gaj56ev*yourself on an inclined plane? Assume the mecmk6k7 h-o e5rl v- 4,iagkx*gvg ,rnj5hanism functions properly, even at an angle.

  What force is needed to accelerate a ch4lccbt q5;(h1 .a aj.+pw 3ood1ipl bhild on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratr : ,kux9 q8wfft4 amm840fepoes a bike 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 *j71-yvf2 ylh uurjyz2rzu2 4kxsq9 *rope 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 of g *-h9fu8w jtha $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the botgy6;5*))2bkt2svp,a rx5 wdqrsw car is traveling at 5 bstp) b6;xso k2atd,r )v*gwwr52yq95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest tzg7wi.f8i o*o n/6 lmro 125m/s over a disr/z wn*f6io i.8g7moltance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acpt-4lo70-ms qc1 tdk uceleration of 2.540u1s-t ckd-tpq7 olm $\mathrm{~m} / \mathrm{s}^{2}$ 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-mhzc:hw)hr-c) ile 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 acceleration5xhxw: s 2ae9v is 0.0680 g . We 9xs:52xaw vhhat 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 motion3nx 1p7vv pxv/less 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 fip73xv/pv1nv x nd the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a max4 cg, c+qnxj:nr+5 rxkimum strength of 21,750 N. What maximum upward acceleration can x4rncr: xk,c 5qnjg++ it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg i 6axqeurbn(+4ncluding parachute) when the upward force of air resistance ix+ (6aq 4nbures 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 mpuly-:lq df f3q+) ;lj0uof 3strikes the ground below, he bends his knees uplfl3;f fq) 3u+d0jqlom:-y so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N k 4sgjy rfue4yna(;5 hsea5 g xr4g:-vb-xj;/rests on a table. A rope tied to the box runs vertically upward over a pulley and a weigh;xan4ajysv4skf :e5g rx-g-(u4 ebgjr;y5h/t 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 player h *w5 zsl86tfm
(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)b)zba2kd stut;k (-b + at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfbk2k;ba-(s z db+t tu)ield.

A 650-N force acts in a nortibkb : k 66qnyn r7bj7w-6,ljlhwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces by-6: ,b676nklq7 jl rnibwkjpoints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "higg .gurl7;x; j,rldoro2 r 70oih wire" strung horizontally between two buildings 10.0u2x go. r7; ;ogird0jlr,lor7 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless7cv 7+ps3ga lhqh4 y2q 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,axkcyj0dl *l a) (,ytuv/8mt .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 Mp;zk/2,ah fn ccMurdo Base, Antarctica, as shown in Fig. 4-46. /hnak2fzc; p,The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behin2,g 1 o-nqcegmd it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive anmn2 q,cgg o1-ed 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 pullr4h,7a dd y1scp, ;aets herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hp rd,s1;h a 7t,ycdea4erself 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 behhuqsbjg d/;8y/i3ch ,x37y p gan, 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 (e-soy0 + hkqp**w fzd+mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each o4 zsttqj)yy1l) ,e*kother, as sh ) yj*stelk1, qzo4ty)own in 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 F 7qy u27nrynv. s 7 q/9d*mgtm6zw;qqsig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine th/t7;y vn qs ryu7w9q*sq6g q.nd 7z2mme 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 table are connected by a heavy coru/7r0dci4zsp d of mass 1.0 kg . Calculate the acceleration of r/ c0iu47dspz 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 of kinetic friction w:k)v i ,iglwfrm a0j3 nx07mnm +:3se w/)fuebetween 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 req* tm-uohyja qdqfnoyk83.u95 5spu )7uired 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 fe id/t-d/rz0kd) l ;i0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to sli0;e kdi //fz d)t-lridde?   

  What is the maximum acceleration a car can undergo if the coefficiem+hg5j i6z fb230tf 7gur g yk7wttw x81c3u8bnt of static friction between the tires and theb8ym7bf8 g1ku0w3c zx j+ ug3gitf7hwrt652t ground is 0.80?   

  The coefficient of static friction between hard rubber and normall,ule0 xbukr5.aoj * zf3rw+* street pavement is about 0.8. On how steep a hill (maximua.,bf zu5ew*ro +u*xklr0j3 l m 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 -2 imvyk d5nx gu:r9u/5:mbqqej l7* 2j4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a (njc i5catjzc4x , sww*d-4 :yrough 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 surre.j 8uwp y+p-7 p8z 4eytq f2,m9qpntface have a very high coefficient of static frictio4epqzp pt,y.8 jrwfe t+m-pyq8 n927un.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction 0sw5j nuu.ry(qdfczt4v.5 1 b 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 smec8s/i+(y q mass would box A have to have to prevent any motion from oce(cm8q/+si sy curring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrosfv6far(w h6)*murh *zi1in.c s the floor. How far will it go, given that the coefficient of )zhmu vc.ai*(f f*rh6riw61n kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , nlmtrrzj+7e a *dz,bx2( t3g. are in contact and at rest on a horizontal surface (Fig. . nlb(jr d,7t+3*eaz2tzxrmg4-54). 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 statisww;9vq3eal u*wp+ r 8m/xm6l c friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can dlx*9l p m +/ea ;uwwvrmq8w63secelerate 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 driveway, which hape(;osd.8ttt ;r3ouhs an inclihotu ot(8.t;;rs 3 epdne 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 witha 4)k5gu.k(ml dd1hte 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 Figrzk;pmc8q7 b.. mwz7 r. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an ini2b2 *tx rqnb0x ni dy05f4hy7vtial 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 steepest hill wit9a; n1sfcm9bd d ap9pep7z+b 0h 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-; nmq ee d3bw8+xe2dq by someone pushing on it with a e qx8e2+dmwqbnd-e;3force 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 f 3l d-tdib,xqb ;.ja7become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a q-j;b7itdlax., 3f b dpitch 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 anlh6e(d4aied d+n6gwr12 ))vkctmi 2j automobile traveling at speed v is equaltd6)+) vme1( ka6i4rige2 dlj2dnwhc 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 da)x65( ,bokpygw szm6 r1cqq3zshboard of a car slides forward on the dash when the driver decelerates from 5 sw, 6o byzp3g6zc)m1x(rqkq45 $\mathrm{~km} / \mathrm{h}$ 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 1x1ndao 1x vbv hoa0(0 m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they ar;p:,4e meopio5qsm 8ye 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 o4op;:se8qm,my 5iepfor 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 frictioa x , 0i2i 6ii0zd1pb8mcozmq4n 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 8 gp.u75js-t fig mmak6,i0hxdown 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 hlord1 .v9: kbpulse approximately . 9hdb :v1rkol20 g of blood 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 automobile crash if the i au1l0g ,,t *+:6kegqu gmtgedeceleration is no more than 30 " g 's." Calculate the force ou1ueggqg: +lae*,,0m tg k t6in 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 producedde stsrf t9 k7ujzyjtg.l2+lv u.5/6 - by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at leastz7yd2 -svl ejj+6 tku lt.gfr.9u5 t/s $\mu_{\mathrm{s}}=a / g$ . (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 involving two cars,o ihcyrvq*zp/kr8; 17 measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction b8y ;*ihvp/k7qrz oc1 retween 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 hilaozc cwwp15e/nj(76 n l (1-in-4 means that for each 4 m traveled along the road, the elevation 5wn/c 6(zja1ocn7 pwe change is 1 m). How fast is it going when it reaches the bottom 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 Leanczub9h:0pq,x00: s2 umikw u eing Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air,0wxu2zh qumsk p:ue9:cb 00i resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wyoz,v:+/j a v6zjcq.bherez:jj o6c.qav/y +v,bz the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly pou* i-5xev x q pk*(3t9rq:jzysrtion of a city. An important consideration is how steep the roads can be sok ez3u r*pt5i*vxyqj: -s(qx9 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 from a thin di((k0er.m -qwn/ jb:y4-cc xhst*ev piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that them hies(n-dc ctx:be -/w(0ry*qk4v.j 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 uks..zy6ig 7 aqb3uq:several ramps connecting different parts of k6 qugu.zai:qyb3 s7.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 + 2- a5kfer;dg)a ireepiano (mass M ) using the pulley apparatad-re2i;) r5f gekea+us shown in

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

  A jet aircraft is accelerating at 37b+nv* ,(+xg2hjwc lgldaf u1.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 considers the fzf*.jb6m b ) mp28jcyrzd+n6qollowing set of conditfm.n c6z+p d68 bmzbjjq 2ry)*ions:
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 Itali;gyk0ey hj0.i:4nvf+pc q mp (an 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, usep-sd civ 2s 07egti*:hzlm-*i 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 e*: -tvzci*h si07-2mspgli dpro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10xn fk:,cqk4h *9sy+: 3fpbjxy -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 speedclp; 9c7uf fd*7 p k4frb2fqy 3tjv/y7 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 togethemngof+. nf ;h(z(r; tzr are ascending an ice field inclino;;z(f n(mr h.fnt+ gzed at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.