Why does a child in a wag x1jqcy8 u0fm/on seem to fall backward when you give the wagon a sharp pull forwac / yx0j81qufmrd?

A box rests on the (fricti vggy cvt*p8/;onless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. 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 pyg vt8c*;gv/ who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? vhsu hn*ssh(2 aqw97, Explain.

Only one force acts on an objuoslr5 hx vw 1z.61/vject. Can the object have zero acceleration? Can it have zero velocity? Explr/lz 1v.sw5jv6xoh u1ain.

When a golf ball is dropped to the pavement, it bounces nne(9mpko9/r2l-fk s o:b x9yback up. (a) Is a force needed to make it boup 99xnno:rls e /k k9-fo2(mbynce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mov; 98fo8 hipubylx(:j ne in the opposite direcnf98op8h uyx:;bj( il tion?

Why might your foot hurt if you kick a heavy dedqrsfx1:5 6,j oiix(lsk or a wall?

  When you are running and want to stop quickly, you must(863r(l*sjs7o sxzpnin/lwn decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speil s(3wz6*nn pnxr/sol(j 8s7 ed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the q*r m49s5gqoivha/ d*ifx z48 ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a personvo5rm/ 8gd9 q*zhif4i a4*xqs 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 rock is twice as great as tha f6xj rq0:js-jt on a 1-kg rock. Why then doesn’t the heaviex: js0jrjfq-6 r rock fall faster?

Would a spring scale carried to the Moon+1/waz*v ab x rln/i/x give accurate results if the scale had been calibrated (a+avw1zn/r i/*x/ab lx ) in pounds, or (b) in kilograms?

You pull a box with a constant f(k vp(.tug i0vorce across a frictionless table using an 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 of the box (a) remain the same, (b) increas.i v(k gu(0vtpe, or (c) decrease? Explain.

When an object falls freely under t,9 9ukgehr7vjda9 7 hbhe influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s thik9vd e9hr g7,9b7uha jrd 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 ob0yu .zzg4 s.tmw 0bnrj7- 3mc+ia8xqaject 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 andxsjri8zgm 7z - y+atban04mcu0..3 wq on Earth.

According to Newton’s third law, each tyl2z/ lk (.) frtjanu*pu-/xmeam in a tug of war (Fig. 4–37) pulls with equal forcm (l2frk/xnta j.-*ply )zuu/ e on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N t s4 zzu.tk)ug0o hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its dgkuzt0u)4 zs.irection, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how*k (rj/4y)t4j; kqwfe 9wmgd c large a force does the ground exert on you? Why doesng9w4;qkcjmdftj/e*wkr ()y4’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident whenxk ,beo. 3byw1a4 g;ab the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown bgake,bw ao4.;yx1 b3backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed t 2j:.dqv lgy wwe87r8 ftv-h(hruck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelee:wh.y2wv -h v g8(8f7ltj qrdrate?

A block is given a push so that it*a7:j.;cc rnmm 9 zc:ey bj+qs slides up a ramp. After the block reaches its highest point9ca r:: jqzm7csmbc .y*;j ne+, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read1vg2q qohyuo6ldx f gx7 ,9)r; if you weighed yourself on an inclined plane? Assume the mechanism functions properly, evq9)yv ;hg6 x,g lo2xo1qdu rf7en at an angle.

  What force is needed to accelerate a child on a sled at 8h8cq8 tb co0c4g(9 bz uvzid,1.25m/s$^2$?   

  A net force of 265 N accelerates a lhg lxz nph1 6 47+y0w:kw;ghag kj6/wbike 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 u6s sc, 5wnz+jk0lddw1sed 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 l6b8kcw t n4xs,p0tu,a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stopeknm+) s - uno zp7cvo3dxup:6 *rrdxsx0/3f3 an 1100-kg car in 8.0 s if the car is traveling at dcu6or7s: xkse p/v)r- 0 zxumpx f3 +3*3ndno 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fre.ao r8 k jc9o7oacw 8d-twt :wgc/4c8om rest to 125m/s over a distance o d ewccr8o.-wc74 t aca8og/8wo9:kj tf 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertica/w a9+vnnd 7kaix2ks mbh -;j9lly out of the water with an acceleration of 2.5v/n is k+-ka;mbhx2n99a 7j wd $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (gf,r;f+n:.i4i t/ quy,itdd q 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 th f, s dks10sk.yug 2ee*vtkt1+e maximum acceleration is 0.0680d20s+ktk.sgetfks 1* y 1 uv,e 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 scale in a motionless elevator. When th+8gx)i4l - ffa14dg*f tbsrwy e elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Cafxd4ffa1r4gw* -t lyis+ g) b8lculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengt-azf4v5 8 au- mxnz85m1d n3erkevku jt, f0(gh of 21,750 N. What maximum upward acceleration ca ufxvmue5nt1 akng8m,z04df-8kvr- 3a ej5z (n it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includingi wgq0z zf70h 5dyox jfv4v9t 1t9f,6i parachute) when the upward force of air resistance is equal to one-fourth ofjfd 6wigo t 9fx vzy0 t,vh4i7f05z19q 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 roo .x vz9zfm4gnhu -k)t1f of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m.m9fv -1nhz)zukx4tg. 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 thed--jnml (gne - box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the forcg- m nljd-e(n-e 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 basketbkl; d.pmk1 : ncoueqoi. r/0v0 u41rptall 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 mom on:sm-*t:d)4xvn vnzent it is hit by the bat, and again (b) after it has left nxvm:nv 4z-*n: )sdtothe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be6:cw0y0w vw8tv)w l lf exerted in what direction so that the resultant of the two forces points westward? Illustt80lf6:v0wy w vlwcw)rate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hohtu.a6ra e4p1 ig ls)7z(n z2erizontally between two buildings 10.0 m apart. The sag i r2p e(.)gu4 lzz ne7a16sitahn 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 massless cord frol:el13rmlmc(52be/n+ 5hdxi.d5b ) q zufjfym 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.y*mvo pn*; tqtfy 3 y,jle(86m0$-\mathrm{kg}$ 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 Base, Acgp 0 51q+6,cyq0cplt qdphk/u b;*gvntarctica, as shown in Fig10g,l+*p/ hp5c6kdtv q q;c0cpuy qbg. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it)f/ zcxw c.3n7epro d2, Fig. 4-47 . Determine th7 2wnf3x o cr)ezd.pc/e ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the buckeobxf8uoa( */ bt-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowo(fx8 bb o*a/uly 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, a wpy1l0m muth z0)rp6c)jw2 6bpfvq;5 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 blockhq3di .r lj6+k (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 un37mpu* f2rp in contact with each other, as shown in Figpfnpm 27r* u3u. 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 ew: faj *gdou1:5jiw2c ach 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:o fjwug wcjd:25i1a * released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cod 8lvmj0qfs50+l/,c: q zc abzrd of mass 1.0 kg . Calculate the acceleration of ezlv 0: qf/zc8m 0ac5jq+s,db lach 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 fruang1 bdaypzi jd;m2/f 6++ q(iction 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 requiremn4c alhlui5 5a2(ww-7t8y ejd 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 fhdy.: /4y9 - at kpnx4;ngpvl0.20g. What minimum coefficient of static friction must exist between your x; 4n/ptlg4kdy9- f y.hvapn :feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of staalsm/ajrg1xkb2)2f. l+de w3tic friction between the tires and the groundsaear23jb wd1xm.kg)/+2fl l is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemej,awmvuz 4p . ky;rof rq6y-+)nt is about 0.8. On how steep a hill (maximum anf,) .aqkjw-zurpv46 rm+yy o ;gle) 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 -4.80c;,p .blkt- cx $\mathrm{~m} / \mathrm{s}^{2}$ 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 30 m b878rzcrxhq42-oz0 .o p,omigb7fm$^{\circ}$ 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 y9*xhj5oh3 c1nqcx l6 have a very high coefficient of static fricti6c9q5j*cx xh1 h3noly on.

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 k9)bb hcf0w:dqf78s k 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 4g(1c )0ztdvj v-20) how large a mass would box A have to have to prevent any motion frot1v g)zcdj0(v m occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. g 7eegk, b 7vxs:svj9ow i,:0pHow far will it go, given that the coee w,:egs:gb k07ps7v ,xj9viofficient of 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 , are in+zhq 0bs6/ xqfwtj;o3 contact and at rest on a horizontal surface (Fig.o3fxwjtsq bhz0;6/ + q 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(vy 5sib,p kz6*)g :hp hmdj.o heavy crate. The coefficient 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 crjsvoh :yk,pp(5bhi. ) m6z*dgate slide against the cab of the truck?   

On an icy day, you worry about parkipble+-pd9fsb fh(s- *ng your car in your driveway, which has an inclineb-( fepls9f+sbhd* p- 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 p lj0h vf1.y/:wj;boksg/ : gewith 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 aot.v s y+rikhf dod5 8p79we ba/f,,2wngle $\theta=22.0^{\circ}$ 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 iniin bv;;kf,l:k,n-o.4b ojycjtial 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 )o 1t7 lt1b ih3qqo)eoduyy5-top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place ag sqeo9y2c4, t3 bo:gjiainst a rough wall by someone pushing on it with a force directed upward at tc 4 ,3ojy:qgb2o sie928$^{\circ}$ 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 dangerouspmps )n6dr/d ) projectiles as they melt. Consider a chunk)mp/ 6dpn)rds of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automoyy ) wrjg2z-k)pbglj/ n(nncp0dd: ,).v udd9 bile traveling at speed v is equal t.b:dyp),)n0 jgrgj kpdz9-l nnc/ )ud vdy2(wo $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 slideu j, k4srn33l opyra7py5c;- bs forward on the dash when the driver decelerates from7o3rul5-; 3 4byjpc nsyk,ra p 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 gifbw 2orlvsp/) (:x26o a3ip zqven 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 f(y+-d9 oahlii:a2 vfxilled 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 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 ivdy-ih( a+o :2lfa9xminimum 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.ckt8yazu mix;u4s -,( n z/gx of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast dowadht0e 6o0ml;mt ;r+e /kwshcg g1.z 5n 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 he p0/ +iuwwj.toart, at each pulse approximately 20 g of o ti/+jw.wup0 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 autorj rz 9yzhi1z)bm7-s,dy* 0ttmobile crash if the deceleration is no more than 30 " y9),tzs dz* rb1rmt7z0jiy-h 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 accelebo) 48ho(r bulration produced 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 least u b48rlbho)o( $\mu_{\mathrm{s}}=a / g$ . (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 sce,l d 6u-nxfsi8c* td wdl51nl4ne of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kil idf-wtu,*5 8n d64nxlsdl1cnetic 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 meax ;:hz 2s,fmgksi(iy5qz0rhe +.) ejb ns that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) s, s.0e hji5k(zmh r+fxqi;z2beg)y: 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 Lea9r0 avbczq-q41 sz2qdning Tower of Pisa and falls 55 m before redzq2qsz0 1v9b-c4arqaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12( 7jyb d un5j0krtzs-7m/s but enters a muddy stretch where 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 7j r5ks 0zuy btn7d-(jbe the speed upon emerging?   

  A city planner is working on the redesign of 1a:3u+fbp myc /ceyl0a 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 car, with a mass of 1100 kg , can accelerate on a level road from p+ cyef :10m/ylacub3rest 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 experisqj19c( vd6 vac8x u.aments, dangles her watch from a thin piece of string while the jetliner shevj c8(v69c au dq1.xas 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 sevep7l9s m(mcr988 l ejn7xwp+ c3lvx0 ibral ramps connecting different parts o9rc8jp0e7mi xmw8v97 (+bc3nllsl pxf 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 :9ve+p0n mwziis needed to lift the piano (mass M ) using the pulley apparatus shown in 0zm ev:9wi np+

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 accelerasi;* rtk: fj3*bs)i yfting at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an en0gt6bg rkt6x/ud;0 .fsn o*f igineer considers the following set of condi0f*t;ofdu./0 is gtnk x6gbr6 tions:
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 (660,0ik(gh:yp u -v n5-0ejz4tp)jy00 $\mathrm{~kg}$) . 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 and6tbp w,c nd/ o kniu-ne/;hh- -;uel1e Karen, use 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 purpose e-up/ok/w n,thn;e-1c6h lu -;bdines in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a "n4+7 hqg+,ls2by (jy fmx+ks u 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building iy rf4bly.yl a.27y0zqs allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who arw sxfgk3joj66i ;yp )o,- f*moe roped together are ascending an ice field inclined atj )6-g6 fipsywoo;mfjk 3o, x* 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.