Why does a child in a g7f4, 7x luqm8 )xy3cc;bslqywagon seem to fall backward when you give the wagon a sharp pul yl3q 7u)qx8 7bgclx,4m ;ysfcl forward?

A box rests on the (frictionless) bed of a truck. The truck /dtj v7 j;12h x8ejsz9,s qvzydriver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside thevd8jq2zvhst 1j y7se; ,x jz/9 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? Expnufvv 7/vwq3 e;/r i8 n rqyez+2gz53ylain.

Only one force acts on an objsyvjy- r k6kmc:p09 7yect. Can the object have zero acceleration? Can it have zero jk-s 9y:y7pc0 yv6 rkmvelocity? Explain.

When a golf ball is dropz*(qlrwlt( s) c+ vae+ped to the pavement, it bounces back up. (a) Is a force needed to make it bounce backl)+rz*aqswle (c+( t v up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mp( wt pb9bc29tove in the opposite directib9pcp tw(b2t9on?

Why might your foot hurt if you kick a heavy de,u2thndehfz+ x0l - 1csk or a wall?

  When you are running and want to stop quickly,/ u n)v qssunonpq65(; you must decelerate quickly. (a) What is the origin of the force that causes you to stop? )u/nns ;(qq ov6 p5snu(b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of hox3c2 z+0xmothe 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 theomz 0xc2ox3 h+ 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 o :0 feujihotda;l ,h/5n a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavt,lo ef ;u:h0d 5aj/ihier rock fall faster?

Would a spring scale carried to the Moon givep scvv1xvt01 ,s .1dvs accurate results if the scale had been calibratpc1s 1,vvvdssx0v t. 1ed (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrosh0fi2tf )l tc0lzo5sb4v,y 5a s a frictionless table using an attached rope fli t oy4,sh v25actf50l )z0bheld 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 under the influence of gravity thycj9me3y ei(9s3z p*jq (bsr1ere is a net force mg exerted on it by thsby9( r 3*jcezi ypm sje(139qe 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 f 0dfe-x7m4ouobject when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.m7 def uf4x-o0

According to Newton’s third law, each team in a1 hwjx8bx2wc ep xgf;cq+kd.y3oq1 +v8rk g73 tug of war (Fig. 4–37) pulls with equal force on the other team.++ ceqxx;qd8xwypc217hkk8 ob rgg jwf3. v13 What, then, determines which team will win?

A person exerts an upward force of 40 N to hold mhwiczc8i z yf;ool1 :o4,,:9vu8vz qa bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by lwo9:ou m ,yzz,8 civfchi;1v:8ozq4what object it is exerted.

When you stand still on the ground, how large a force dofzpp*ll p0)nsh. bq9 1es the ground exert on you? Why doesn’t this force make you rise up into the f 9 p0lbsph.*pz)1qnlair?

Whiplash sometimes results from an automobile accident when the victim’s cagzqb 8k/;aje9 h80vu ir is struck violently from the rear. Explain why the head of the victim sjb q8iue9/8;0vk ghazeems to be thrown backward in this situation. Is it really?

A heavy crate rests on bp+9+aqaw9n kthe bed of a flatbed truck. When the truck accelerates, the crate remains where it i nw+9q9a+abpks on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the bloc-bwv1l*1 0qt te;d. /utyiaprq+(py jk reaches its highest point, it slides back down but the magnitude of its acceleration is less onjw1.( vq0 uyy-tli et /bptar+ d;*pq1 the descent than on the ascent. Why?

What would your bathroom scale read if you welufl1epw w n2wr0 j b(aue5py;7n7a50ighed yourself on an inclined plane? Assume the mechanism functions properly, even at an anglenww705nu2p yaeu ;l j0 lrf1e5(w7pab .

  What force is needed to accelerate a child on a sled at 1wl-p8lclk) hdf u;.kqjb2m 7..25m/s$^2$?   

  A net force of 265 N accelerates a bike:h0kly,egn8 ) z sn-pfo q0fno7js3k+ 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 withstand if it is u rw8mf .ko,oj *itr-i+ws-b3 msed 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 a w e .n+7eiqxuz982acq $76-\mathrm{kg}$ 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 if3j8uji/ x a*vf the car is traveling a*jx/ i3ajuvf8t 95km/h? -  

  What average force is needed to accelerate a 7.kb3rq8+lfhy7 05 tvc m lvm+c*00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle? bkcm0 tmcl37lf5 y+ vhr*v8+q  

A fisherman yanks a fish vertically out of the wq3,j+ (ijvpcvw )ufg* ater with an acceleration of 2.5 g*u,j vjq+cw(3 f i)vp$\mathrm{~m} / \mathrm{s}^{2}$ 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-milgn p2- 9keaq7je 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 der7aiu7 f bdcr -2q*-kg ) is to be designed so that the maximum acceleration ir*b dc7 -fdur2-eqai7s 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 bathroom scal 5dy6gs)mtx buiat1 1/e 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 accelerat5ugs ay1b)6i/tdx1m tion of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum str9 3 rdvuqhipt9o ;-mhzajx7,, ength of 21,750 N. What maximum upward acceleration can it give the elevatoq u t,a d ivzp,9xom-;h3jhr97r without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divertny b2w))5 slbs (mass 132 kg including parachute) when the upward force of air resistance is equal to onys b25t)nb)lwe-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 cq1jw ca(rnu*ne +.31ehzht9 3.9-m high. When he strikes the ground below, he bends his knees so that his torso deceler *n(cnj.r9 te1ch+qa1zwe3huates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the boxm3j,8 3lqrz yfls-q: g runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table 8 ,3lqyrlf-mj3 :gsz qexerts 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 baskv 90lig d4..:- ed(wh w6sptgou9cjl/fo-k n metball 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 moment it is hit by l-jgn1f 2 nhl.the bat, and again (b) after it has left the bat and is fly. l -ljhnfgn12ing toward the outfield.

A 650-N force acts in a northwesterly direction. A secondj di 8+.ghaba7 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector ij+7haga8.b ddiagram.

  Arlene is to walk across a "high wire" strung horizontally betwh9ji nse- 6, (ahj-wknpf5hlt42gw.;1bu p uh een two buildings 10.0 m apart. The sag in the rope when she is at the mi s1hp uehnbwfwah-t k5j9,;4(.62 l pu i-njhgdpoint 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 bucketm5y7 ybdw f )ri 6pdni99.,n: ggktq.b is hanging by a massless 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 14.0n;u j07 umtln6$-\mathrm{kg}$ 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 housinglsfb 8wi(7 u+a.y j-uv unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcesbafs w8jul-(y .7v+iu $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 iwdbg4kz 5dp9bp/ d:a3) pt2xy ,l-xqit, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fiyxq2dat:4-dwb p3,)p pkdb9z g xil5/ rst car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using t0q dixyiv1qhy (fi 8./he bucket-pulley apparatus shown in Fig.(i0 8 xq/1.qvfd hiyyi 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, ags6+lg3 q6x tnrrj*,b 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 (,9dss j:*y vycmass $ 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 con7kjfc(l xq4/ e;6b2, kp rauhjtact with each other, as shown in Fig./ j,qp f7j2xk lbkc;4hra6(eu 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m av 2xrgt9 3mpd-bove 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 hept-d93xm 2 rvgavier 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 cordwteg msd 5xc*91i -c8j of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, usin 9cx8*5w1sed i-mcg jtg 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 kinetfp2nf /viw:nf0; n owi -ms(a7ic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is requir4sf/ bv.m3vaev 845cg mng)hgk8 f nb0ed 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 0.2dp sn7*n2fc+ n0g. What minimum coefficient of static friction must exist between your feet and the floor if you are not p 2dn7sf+*ncnto slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta10sdeuuyes*w /d:1u etic friction between the tireeds/e 1usd1 0ewy:*uus and the ground is 0.80?   

  The coefficient of static frictiodx34x (zn fbzuur bap2 l7w)54n between hard rubber and normal street pavement is)2b xfdwpuzb (a7xru4zn3l45 about 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 -4.8xja 9h 72bi*szen b +wv(ej5(v0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 9k m:prrmoe-:w lx/e5 nn92k hon 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 a very high co+(hn)4hiie bw efficient of static friction. +n he4(iihb)w

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 kinejir2uyt 77.*;v g+ywyj22d hgo .uo jwtic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would9i9 lsl3iu*k w box A have to have to prevent any motion from ow* kiul9 i9ls3ccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fix,9qgp 20+zes u,esrrmr 7 g8a8eo a3c*ph8kloor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed o 8pai8*pq m rhees zr97ex8a,cs,k+ro3g0 2 ugf 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg ag4 p/hn*0b:ccsn:rg gbk// wxnd 110 kg , are in contact and at rest on a horizontal surface ( xns*bc/kgrnh bgg/0 :pw/4 :cFig. 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 coefficiengp e:ih+a07+ *lifj -tbij1d mt of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avo + 0+j-dgfhij: *ime tlpa17biid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your capn8wqiji8/-t 7 asm8cm+m;n j0hm2obr in your driveway, which has an inclibsm/q +tman nc87im p o288jh0jmiw; -ne 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 slidei2.a d 3 9eqhov;k8hnn bsbei,c43; ox with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an vyprj wbny+15wo/ gtm1 58az(r c6 s3gangle $\theta=22.0^{\circ}$ 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 sp5:w cy;u+tzbs eed 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 steabe1l ,al8v8j epest 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 withpb sl8*h;ygdd/jzis spek+ i- l:t 38* a force directed upward at 28 z*d:ysh;- p8+d/llpt ik*i3bje s8sg $^{\circ}$ 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 mqq2ngbj -6/dmd u6rm+ic n-rkyro ,3 +elt. Consider a chunk of snow at the ridge of a roof with a pitc++qdb6 ykm r-uig nc n,r-r26o 3j/mdqh 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 automobile traveling at speeg)4gg-, (+yuku blyxj d v is equal tol b4- (+kgyjuxg)yg, u $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 t.y luel*1kihd u9)gc 6he driver dece 9.iy1udlc* )lgk6 huelerates 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( b262pa0y z f7z4piidm stq+s 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 are filled to the packingqd1bs 6o*i39m hwmz*m 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 distai9o 13qhmzw mbm*s*6dnce, 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 frictio31n uue;c)m gbb-dwa 7n 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,l.-z:s0j.i ep.9s g s+na w9 ejzamrs coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart,t6mcfy j/4t+ddlw bp8y3c7n 1 at each pulse approximately 20 g of blood i3+c wdm4blnc 1/jtd67 fy8tpys 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 tn tygn.jh e:4):yz8xif the deceleration is no more than j eg .x:yz)4 nnt:yh8t30 " 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 ear+r j6fh: ,uha jp/zm)pthquake is a , and if an object is going to "hold its place" on the ground, )zhja6pr:fhp u+mj, /show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accid32dbb6tvdn:p)wo f j+ ent involving two cars, measure 72-m-long skid marks of one of the cars jt2bbfp)w36ovn:+dd, 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 th n tspn .q7x9j /8mus+6szkqk4at for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches4s6jn7+q /sqzk.tnm9uk xp8s 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 y:s )uq( sx*ul6lm; y+k pq8phthe top of the Leaning Tower of Pisa and falls 55 m beforeuyx(lq*;sk6pq yp+)sh :8mu l reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at em44p2 -q qr 8ano8ddta steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretcqddaqn24om8pe4-r t 8h 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 redespn o0a:u9w s*jign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small p:osu 9*na0wjcar, 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 thr + ;iq8l dz8vubs7,experiments, dangles her watch from a thin piece of string wh88;+ dqbr i,sl7zht vuile 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 supermarket, there are to be several ramps conn4 xgs9r htt)18wd3v gcecting differen sdtc418hgt w3xg9rv)t 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 qfgzpvx- /eg x;.e0g+v5d w; h M ) using the pulley apparatus .xg gx/5z+gh ; vefpqe ;0w-dvshown 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 3.5 z+xk 6rh8hzvs,z x:y jv.fe)g e/l*h0$\mathrm{~m} / \mathrm{s}^{2}$ 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 forwt65 n7 xz4v1kx,uzru a child-restraint chair, an engineer considers the following set of ,xznt zk rx617u wv4u5conditions:
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 Ise9g( ul u3+qev fha.4talian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropeskekh20 *m ve/ckki3/*g crw6n 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 n3ir0 ckekc h*//ewv* k 2kmg6multiples 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 " 10-1 tttwi)v r/ .p8gh,aq 6$\mathrm{~b}$ 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 sv95s qtwz6co8 8zn wtcj2h 40opeed 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 togeth c x*dpw 2 v10x0+pesz5nyhy2der are ascending an ice field inclined at 21.0 ypw0ehc yn0xddv +5spx*21z2$^{\circ}$ 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.