Why does a child in a *v1rg-y mbtzrbfki:, 54h o3wwagon seem to fall backward when you give the wagon a sharp pull forward?hyo: gbb, 5tmr 3zf-k ivwr*41

A box rests on the (frictionless) bed of a cy.g:l awfum+v3jn, 6./f o watruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide towa. vu3fga6oj/ amcw :,ylfn w.+rd the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explzmk *5(ke.eun2h *rnvain.

Only one force acts on an object. Can the object have zero acceleration? Can6/zwx8 en*7 e4f jaudm it have zero veloc udee7x 6*fj/ 4mwna8zity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is anq0als(0ggvz7gdd2/y c c3y:w5gn. h force needed to make it bounce back up? (b) If so, what gg/0y0 y.gzn (dvqdc3ws5ca2hl n g7 :exerts the force?

If you walk along a log floating on a lake, why does the log move in the 08+-qn.st mijgv6wtf r8 yjb .opposite dy +ibqftg8w6v8 r jmt.sj.0-n irection?

Why might your foot hurt if you kick xrc-7;vmcv df((+b 8ekd j(h)1zya wr a heavy desk or a wall?

  When you are running and want to stop qu. t+ okgmoipzuak6 41-ickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Espmi4 okotz.6+ u1-akgtimate (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 sect9dy5 xm(k7 tonion of the 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 ndk59 m7ot yx(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 that1 us m05edu2p;osqy -l on a 1-kg rock. Why then doesn’t the heavierd 2uyqo-1;upm0 5essl rock fall faster?

Would a spring scale c scqv- ts871pvarried to the Moon give accurate results if the scale had been calibrated (a) in posvsvp8q7-c t1 unds, or (b) in kilograms?

You pull a box with a constant force acro40npfia:zv t8r ;:ft+auak m.ss a frictionless table using an attached rope held horizontally. If you now pull the rope wtv4rk tm:u8+ ;:iaaa n.0pfz fith 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 u 6f5ogpa22 vuthere is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earthuv 5aup2 62gof. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object aeq ;j54k8jn0v y f9bgwhen you are on the Moon with the force nenjv; fkby0 8g94 aeq5jeded 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.

According to Newton’s third law, eac n7y+xx1z d0d*1gigpmh team in a tug of war (Fig. 4–37) pulls with epz+1x0mx iyg g7d*d1n qual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag otx++oysye l b9d(68v2f rekh+f groceries. Describe the “rea 6lhy(bd89ekf +x+2yeort s+v ction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still otjvgj65 pcs6a(:lge.dt98 x un the ground, how large a force does the ground exert on you? Why doesn’t this forceajd u: ts96.glt65c 8vpg( xej make you rise up into the air?

Whiplash sometimes results from an atn9 8eh14 paj*u(q hhsutomobile accident when the victim’s car is struck qh1shaue 9h*8npt j4(violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed rc:m(kl)z )o1sk q*u mof a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerate s))1rlq*(m o: umkkzcs. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the n- n0wtrb n *2/awqoa1-abif (sf0a7q block reaches its highest point, it slides back down but the magnitude of its nwqf*bn0 0an/ a1(btrsw- 7oa2q-aifacceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourselfnvl5xb19ws *uz7 *gj w on an inclined plane? Assume the mechanism functions properlxv9gzwj*1l 5su*nb 7wy, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/su3(,eids8xej v3)fx ( ctwji 0kt:p +m$^2$?   

  A net force of 265 N acd: wg.d 48viuszh7y+n oz m,i0celerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstan2pgp) cri7m0 uywq p:(ift8ecc-6wx 5 k- i;bsd 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 cqmi/ +x/n/m-zj. mqkxj )1r ya $76-\mathrm{kg}$ 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-giihue jn7zrwsrl)3.;xl4vb3:6 u7e kg car in 8.0 s if the car is traveling wnue ev 3z34b) : l6.us;j i7xlgrh7riat 95km/h? -  

  What average force is needed to accelerate a lqt-jg-7i c0z+,cv xde+4xmv wqh :4d 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a riz74-v qv+leid4c 0d,xt c+:g-hxqjmw fle?   

A fisherman yanks a fish vertically out of the water with n0 .,nfbgwm4ywlq*( c an acceleration of 2.5(,l m*4cbnfgyq. w 0nw $\mathrm{~m} / \mathrm{s}^{2}$ 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 quar :cvfka77k6x hter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be 6;m q j,*owajsdesigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces j qj*;6ao,mw sthe 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 sca+jk)ha jk/ 9v-qwzuf 9smfd-6zj ;em)le in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weigfkhmzjm9-z 6fw9vk s; j)u) dq+a/j-eht. 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 maximum strength ofo5)ov)s -s+vv k63)hplvp c pe 21,750 N. What maximum upwv )h) s3 olv6vpp-v 5eopkc+s)ard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelagmk h baqe q9+/ ehh.dk(+c+(eration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of tm9+chkhqa+kee (a/(q b d. hg+heir weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strrlov d5+cdq 2zy83 r n dmwyj+5ei(z*9ikes the ground below, he bends his knees so that his torso decelerates overj 3+5iwv8r9nzdycl d+y q5*(rmoe2dz 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 b ip8lyo o o4,n2vp(qc-u bm0i(ox runs vertically upward over a puli m8b q0clvi2y-o ,o((u4npo pley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram fo gbw-ddh v7:mg*5ibt 6oqo:v.r a basketball 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 8 ku/fws pxv.tqub :.hx8,s)mbaseball (a) at the moment it is hit by the bat, and again (b) after it has left thpxqb.m k :fuh8x.su/ t )8,vswe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fo4dc xp 1k3jd7grce must be exerted in what direction so that the resultant of the two jdg13x4p d7ckforces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between tj1-(jogzvit*0d8l k ewo buildings 10.0 m apart. The sag in the rope when she 18l(e d ti-z*gjj0kvo 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 masslesuds2nm / kv1prqiok /uf0h /(2s 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 1s3/;ri2k6mzo,vf 5tu nokwz* 4.0$-\mathrm{kg}$ 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 hom0yf-4daeqn 7 using unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces n-q aye7f0dm4 $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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, Fig. 4-47 dhrx q+c7faff6678sxs(fb2 r . Determine the ratio of the tefqfah67 +xs8x6df7 src 2fr(bnsion 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 bucket-pulley apparatus showeu m 18rwy+uhy8i:9enn in Fig. 4-48. ( hru1uy+: mie8eywn89a) 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 bex;uz1xff ) m46kh,n.k6xau 4fo qzp 9lgan, 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 (mawbds g5k3ep h 7d;az-)ss $ 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 contnbwe ebjw8 ;e68kvb,y06a1ksact with each other, as shown in Fig. 4-51. A force ;wy k jws68,eva6bbee1 bkn 08 $\overrightarrow{\mathbf{F}}$ 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 abolhrv48; qg,9oao( h ,b 2qbeoive 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 heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the p;i,re 2 ,hq obh9v (qlgoba8o4ulley.]   

Suppose two boxes on a eor1g2f3/sosr pw 2m 9frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the accelerats 2 3oo1pmrew92s/gfr ion 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 kinetic friction be6pq f iq8q u/;m/attg8tween 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 requpnusfhi g: 8f cr2465gired 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 av- l5kx.(gy1igw,aqkb9o6m c t 0.20g. What minimum coefficient of static friction must exist between your feet and t mqla- 6ockxg(.g51 b,vi9kywhe floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffici7ve7k 1 ztnl 5gyo0kso72n*m went of static friction between the tires and m7kwnozyo*v02 517t g senk 7lthe ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street p20o9 1vp igckiavement is about 0.8. On how steep a hill (maximum anglci 1p2kv09og ie) 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 deceleratefqz. nc y1r//g+kzn04:5ap,swg 2wpexhb wj3 at -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 rou ;(i,up 2r *f:hcwij6x6pubrv gh 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 s;bb-,d*,e s7 llq qa-h rcjg2hurface have a very high coefficient of static frictiqhh;ql,a*-2rejb s g-,7bldc 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 friction fo 6jbd+vu n1ymi/ r:x 2/vtry:t ilme)6r 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 (E 7qal gg d0c6*eys.dm2xample 4-20) how large a mass would box A have to have to prevent any mota gdcy62lm0e. 7dq *gsion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wid.h-x -z2lcbgll it go, given that the coefficient of kinetic friction is 0.20 anxcb.d-g2hl z- d the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , ay1i, lf,45oo w );rfpjsbg z7are in contact and at rest on a horizontal surface (ls,o7 o5gabf);jypr f 1,w 4izFig. 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 o4t +jmqm 6ue wmi*b:+a heavy crate. The coefficient of static friction between the crate 46e qmmowmi+*btu:j+ 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 slide against the cab of the truck?   

On an icy day, you worry about parking your car in your z;yt/ b;s9 m)jz 2foqhdriveway, which has an incline of9yqft2z sjzb;o ;m /)h 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 nz 5z q+66ckru;dnq q,a slide 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 Fi vf)y)1mpk 1 v2 i*btj6tqqywk1n kh*9g. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial-9 w 4cmpww,m7ry r(ra speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of l vo;cn.28.ie (-o.ztizbqrf 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 roy mv t0/h 5ta)7/nlepaugh wall by someone pushing on it with a force directed upw0vlt/ y h ap/5)tanem7ard at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs c/8727yn,(m/uy h ccprmctufw an become dangerous projectiles as they melt. Consider a chunk of s 7cf/ 7rhp(/ymwuu28,ncmtc ynow 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 mi/ g7c)pkm4r*7;)wph7i wfjzf8d h ffnnimum stopping distance for an automobile traveling at speed v is equal 4)*wh8p) ifk7 h 7fdczm7w;gprjnff/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 wz/lo9s ow92h m *9wjyyhen the driver decelerates9/mzhsyw * w2yo9jol9 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 g23tt ume,uqd x7eaa es-0-7z liven 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.nhw) c 9h2*wdn8n ayv)ywu0 eilled 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 hayw cnwa*n) hvy8ud0n.9 w)eh2lf 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 between p/-c a*3nb+wkvm gt3 b $m_{1}$ 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 (inckdjm6xa-my9 8pr wf9 t835 ncoluding the bicycle) 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 mammalh6tqi u y/edd:r. 7i)3 vewxp8ian heart, at each pulse approximately 20 g of blood is ac7)xp :we/q 8.udv 3yr6et diihcelerated 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 survivigzif y x 6hroitu;h+r+)/e)l+ ng an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a hg)+f++l zriyr ;/eo)6xithu70$-\mathrm{kg}$ 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 if anh: 9 + x pxc9r(f:tuvlc.a;pcs object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must lr(cc9:fp a:ts9 v.xc;p+uxh 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 scrq5jz7 u al4z ykxh*4oh 5vg)pol1q7. ene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearlo4hx4l uz ) 1.jhg5qla*z57oqpkvry7y came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that lvjc 2,9 r;rt+ v8tam:czefw9for 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) Ignore :ljw er+9a9rf,vzcv 2t8;m tcfriction.   
(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 falls grh + nh7z8kd555 m before reaching thd +rh8khgn57ze ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steadkn+dyk ; mxs/n9gxy153r3wdeu kk6 h1y speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the5wmuh1red k ygs3kx/13+ 9 6;d xkkynn muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the re0-z,9kgkprsqcf7 6v7n qv 4mhdesign 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 hk s67,vq0f 7cg-9z mqvkprn4hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch fromv6s bpu:hqm+ iz1 q2z wfohv5rt-24e7 a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-52qm5qp4u16z wht 2ve+ -rb isfhz7ov:8). 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 ra +y,bi4iuy:jt mps connecting different parts of the sto ,ji+u :it4yybre.
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 nee 0auevf9 2b2zkv29 iagded to lift the piano (mass M ) using the pulley apparatus shown0v2fua9ke9gia b 22vz 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 5jiv yv4;*usi 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 chi a-uydgn-fpqk4)0g p; ld-restraint chair, an engineer considers the following ; udf-4pg)qgnp y-ak0set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,e8 n*hcn y4y5o000 $\mathrm{~kg}$) . 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 ropes of similar0 :hfubl ;sfj. 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 constfu.;f 0lsjh:bant, 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 a1et+2zjil(fw* qq8vb " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach kw12 (qke/ .gr dlf1dna 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 are roped together are ascending an ice field q xfl +qvkb4:jxl.54 einclinq .f xj4xk vle5l:+b4qed 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.