Why does a child in a wagon seem (iij r(q:v hf ,i2psdyc(9:y gto fall backward when you give the wagon a sharp pull forwar(:2h: , dr9fji((vq cyisgpyid?

A box rests on the (frictionless) bed of a truck. The truckl(zsjs6my ak/f(yf 4 +6zed 4u driver starts the truck and acceleraf46ea(ymjklz/4 uds y +6sz(ftes 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 the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no ldl o59yb ;aham:. .b slr2lw:forces acting on it? Explain.

Only one force acts on an object. Can thea8vq tn+n;nkb1 k/ uk) object have zero acceleration? Can it h;q n uba8+t)kk nkn1/vave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounavqxk-(t e-uhgp z-p;l( v q7+ces back up. (a) Is a force needed to make it bounce back up? (bkq-(avpzveu-qgp t l;x( -h7+ ) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opxd + ls.w3s ;yedah48h83 cyypposite dire.hdwyc48 +spyax;8hy dls33e ction?

Why might your foot hurt if you kick a heavy deskj,:y p1q q;9rvb iu/eepmvrg-hq:o 2 , or a wall?

  When you are running and want to stop quickly, you must decelerate quickle :t6ip/b;mj,a/ws w iy. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own expeript;sijw ami6/, b:e/wence) 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 threvq;ze7.esf ;l ad from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). sfq.vle;e7 z; 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 answers.

The force of gravity on a 2-kg roct07 .s8t dt79g3v vcmlso4hpxk is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fcp 3vgost.s7 xm08t4 dhvtl9 7all faster?

Would a spring scale carried to the Moon give accurate results if the scale had it/5*3ua)htik t0 oeebeen calibrated (a) in pounds, or (b) in kil) e *oiehut ti0tka5/3ograms?

You pull a box with a constant force across a frictionless table using anjz tzu4+jwyzb 31 ,u7r attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration jzjuyr1b4u,7 z t3z+w of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of graviil5+;nlu5c7 ynr1 v lgty there is a net force mg exertcln7ul rnyv li+1g55; ed on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) need:zxn,9 e.z lu;;tgejjml 6x;4wyh 5eded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given sx myz zuht :wl; ,e6e4dx;gjjnl;5 .9epeed on the Moon and on Earth.

According to Newton’s third law, each teamsi( sa4/bm1tp in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, dett /sms1pa4 bi(ermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. gcx8h55b wu 6uDescribe 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 what ou56chg u8bxw 5bject it is exerted.

When you stand still on la(rncin ohs36+m8 le6o5 t)k the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise u sa3c856n)lioolnte 6 m+ r(khp into the air?

Whiplash sometimes results from an automobile ahw t(fo w3 *2gewdn5h5ccident when the victim’s car is struck violently from the rear. Explain why the head of the victim s5(dgno*5wfh tw w 2h3eeems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerat n avrggf+goa4xp4x*5xzhv4b4 (g( 3 mes, the crate remains where it is on the gp (br(xao34g5 xvx*4hn4a gzg v4+mftruck, 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 nw;vxahzv8.5m ki78 sthe block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent 5 ;8.hksvnzxw 7ivm 8athan on the ascent. Why?

What would your bathroom scalev 9w4xur1+qk p read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even qx9ku r+ 4v1pwat an angle.

  What force is needed to accelerate a child on a sled at 1dqza uk x207d/5txh(shns0zy65 1x lm.25m/s$^2$?   

  A net force of 265 N accelerates a bybk vi5n.;n .aike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension musg-vc,hr nlzmi: ah*ro,(( +t mwib 8p;t a 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 a j ):g69)gc l7(y zswt:vcie pu$76-\mathrm{kg}$ 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 rebr3x ,o;yet1l o m 0o*bqu-o4tquired to stop an 1100-kg car in 8.0 s if the car is traveling at e btq oo0u;1y,xbl*4o3-rmto 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from restmld0wepl i55:/d xrhw; vkb0:hn ;zlb ;w )n8u to 125m/s over a distance of 0.800 m a5i;zbdw ;/ndkhlpw lw:8xl )v 0eh:m5r b;n0ulong the barrel of a rifle?   

A fisherman yanks a fish vertically outp 1 -( girv tc ;lqyqxdoxzp5un5/79c0 of the water with an acceleration of 2.5 p0ocqyn 97-d5i/; 5 uvrtzxq(lg c 1xp$\mathrm{~m} / \mathrm{s}^{2}$ 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 f vz/hc7gmg2 vdg2i7r ,,5sqcquarter-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; rlymuyft+(vi3 a7x* ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable73if yvm;ry *lta u+(x? 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 bhq, :- 02bx; uwyphrhmathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weighrhw:-m hqb 2 ;pxu,0yht. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a r+ qm,jgfy p72maximum strength of 21,750 N. What maximum upward acceleration can it give the elefq+7 myjrg2p ,vator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling pj:lm1 uz3)xq sky divers (mass 132 kg including parachute) when the upward force ofqu)l1m: p3xjz 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. k :ur;gcmvd dk000-vk When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the macgv kr00;k0vdkd:-m u ss 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 yntt;q 80x yd+zqt:+xto the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if dt:xq;8 +ttz0yn q+xythe 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 ban(lt nic 7x+0rb(76gay/zbb,u stgz:sketball 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 baseballx0vk8 gb3yn z c.ng j9jd/jxtip.d5hz -8 +e:u (a) at the moment it is hit by the bat, and agaig3jpx8 j9 -..c5b8 d+0u gx ez:nv/ tnkdjhzyin (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force 27 6zw28ihecc4yo*ew fuwp4i must be exerted in what direction so that the re z28f ww u* w2chc4o7pi6e4eyisultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw1nu3nvvzd28 ,*qrhve een two buildings 10.0 m apart. The sag in the rope when she z*vu,d e2v38r1vhnn q 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 massless cord from anothycr yy re(lho99iomd, -3m ;*ver 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.tjg6j ex3h94c7)czbf 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 McMurdo Baws(y2woxij y81ekgg 4 d (4z: 0 .uhbyrtt35mgse, Antarctica, as shown in Fig. 4-46. The sum of the forcky(s tr 1mug:g0 hz844t(y bgoywxd3w5.i2e j es $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 beh* bqx 93ayfzq0ind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firstb0 3f*azq 9qxy 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 the bucket-pulley apparatus shown xw,,d)be i45jkbcl d.in Fig. 4-48. (a) How hard must she pull downward to raise herself5i.c, wel)4 djbd,bx k 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 be ) o.v9a)qpss6hcfrrvg0rp44gan, 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 3acppal) iu5 ;$ 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 fridg /mf311zmuo ctionless horizontal surface are in contact with each other, as show m om/df1ug31zn 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 0wcfhafw:lj /5,5i 4zgkt3f d in Fig. 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 the acceleration of the lighter mass and f5/f4jaw cki5lh0,twzgdf3: 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 heatua5 15a +mfjfvy cord of mass 1.0 kg . Calculate the accelemf5 uaj1+taf5 ration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinebwphx2q+ 6 6uoli*0g:5myn w( miku)xtic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required 3pc n4y-n . n/eomi ky1rtk9s8trg/2f 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 a8/1m 5b3bg fcwfpfb, 8rr7muj ccelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?8 f rrb78/ u,1jfcwbbpfgmm35   

  What is the maximum m,inw/-gz vncr1)y:dacceleration a car can undergo if the coefficient of static friction between the tires and the ground is 0-)yz/ vdn,:ng iwm1c r.80?   

  The coefficient of static friction between hard rubber and normal street pavemzq8v-(zwt ,+ncarx* c8qvk / gent is about 0.8. On how steep a hill (maximum angle) can you leave aac8gv qx/8 *k-+zrz v (,twqnc 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 )z04vob (ozhq-4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30f x2j8yli /7h5 lfrx6l$^{\circ}$ 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 cont- mad6hx. lm;yact with an asphalt surface have a very high coefficient of static mxh6ydl- .a;m 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 fd:4kzlmu9 dp 2riction 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 havef5::2(y zce 9;giwxbhzoyf7 n to have to prevent any motion from occurring?nf y 925byh7(ig; e:fzcx zow: Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fardf,5aq3 ay c/rh 3yf2o will it go, given that the coeff3, d f3fa5y yoqa/c2rhicient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7zb(x0+d)pfu /z9 2 rev2yjt2lw2zvv s5 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-j9z l e2rv +x20 vs2pd)uy2 tw(vf/zzb54). 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 coeffici prx46lnnyyk -f +1sk,dc3 v(uent 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 avoid having the crate-rcvlfkuyn6 k(s p1 4nyx+, 3d slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whc vb7.*t,ykbs2ji w.lich has an incli *wvi.l sj 2b,y.kcbt7ne 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 sg-v 9bcr7/2hzvf (kuxlide 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 twqp3ra/::eh 0hm m0lailted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 a2lw+0za07 v 5haqztli)k;qn $\mathrm{~m} / \mathrm{s}$ 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 with a speed sug; 7 *lbvqgum(59j hbg/+scof 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 rl8o9/ u0m-atnm (spjjough wall by someone pushing on it with a force directed upward at jos pl9-mt0an u j(m8/ 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 dangerous9)1c zx4f6yd6jn9otg 9nfdq7n njy;fso6.e l projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pi4n6cn 9 7gz. j6dyx 1fyds9eftqf)n ojn;9l6otch 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 fst9s3 qnh9a l5syml+dk 3n) z,or an automobile traveling at speed v is5nmtlq9 a+zs ys9sdl3,nk)3h equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when ysqjhq/ab8l d1b- -,ethe driver decele-b yqj,-eahsb lq8d/1rates 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 inie;d/ ibf,uap(tial 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 conveyzgi1/ 2x 1lv(a/h2 d lu x8.o*uft xzetf4z/kjor belt from where they are filled to the packing station 11.0 m a /1ul*lu /tvj(o xh2 x2e x/zfg8kd ifz4tz1.away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box 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 friction betweenkbrf3g9phy) i +jj(drp6+8v w4 sh,fp $m_{1}$ 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 b+)4a syw5;e)errpgf/ks .aekicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulsezfn+ p:5vxrgmv p1 3gq7 6q(uw approximately 20 g of blood is accelerated from 0q1p + rq gfu5vvwz3px:ng m(67.25 $\mathrm{~m} / \mathrm{s}$ 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 .5dr7u rublc.the deceleration is no 5brcurdl.7 u. 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 earthquake is a , and ;/se7mkthc. : (n*( s0 hqyvs3ytlqsgif an object is going to "hold its place" on the ground, k :gcqm/sqy;.nyls ess(*7hvt0 h t3(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 wyay 2m*hj ; kfn8mq0+gxg t.6of an accident involving two cars, measure 72-m-long skid marks o* g tm0xqhayg2kyj;w+8 mfn.6f 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 1bbe4* 6tfl 6ktir;7y e-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it goin4k tlt;e r7y6*e6bfbi g 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 Leaning Tower of Pisa and ms8udcbd3b a;qr 8:g ,u,c 3xdfalls 55 m befa,:bgb xm ;u qd3ddc3s,8c r8uore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stret/ b4nig: eg+1hae9 zeah7 -uivch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having t7gb vg h1a:- ani+/4eh zue9eio 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 portpj0)osh x zuq/hp4x l1fox.4,ion 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 slow)qs pj10uxo ,4 4zo.xhf xph/ling 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,o t;v)0qznjk a3g7*m s dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25szvgn3j70 ) t*qak;o m$^{\circ}$ 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 connecting differ:pn:m5aw( gdmc leo8k5m0s+x ent parts of (0wde o: 5+5nmkm :cmxsgap l8the 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 ) using;a9na+pv;io7w9k 3k k o+yrp h the pulley apparatus shown+9rk aw7+ho; ;opvni 93 ypkka 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 accelern*:q,z)*aebg-y5wl k y l(ygkp(6tr jd q(h,a ating 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 fbp6qpf (j:qc, or a child-restraint chair, an engineer considers the following set of conditions:(p fc,jpqb6q :
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 train has a mass of 660 metric tons (6*x,/1bsq mw7p*e jct l60,000 $\mathrm{~kg}$) . 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 a+g yv;;jt*( jm-onnnsafety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Whica;noyg*vt n ;m+- njj(h climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1hu.y .gb, fcdmb 26m*d $\mathrm{~b}$ 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 sp f *6o mu9jfm.x0yh-4hpav1vkeed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice field inclmdj e u gfyvir- hd00)5cm ,r-rg.)7qmined jiu)dmv0egy 0-g dm5mf ,rhq-crr)7.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.