Why does a child in a wagon seem to fall backward when oc m0w,i)eb1 zyou give the wagon a sharp pull foro1,zb) w0ic emward?

A box rests on the (frictionless) bed of y qn-xh433 9 cbz8rjgyi6orl9 a truck. The truck driver starts the truck and accelerates forward. The 4- c ynr38rx9g3hjbi9yo zql 6box 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 forcesvq gji7*8b yv* acting on it? Explain.

Only one force acts on ac .-r*8 erlruan object. Can the object have zero acceleration? Can it hav.a rl urc8-e*re zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounceh-fy4+v+d9 c fkxdc3w s back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the force?v+c wx- cf+yd94f3 khd

If you walk along a log floating on a lake, why does ilip8/h. t4vc e:a/c .j0xndqthe log move in the opposite jph i 4cl cxa0eq:.t/i/.vnd8direction?

Why might your foot hurt if yi1qk1n25ab 3: phj ,ntxn n7xxou kick a heavy desk or a wall?

  When you are running and want to stop qitqeu7;h4om7 jyfs 5o(y uy,;uickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own expeiu;7t y,qusmf e yy;5(jo74h orience) 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 threadp. wui09jmoo31 /y+m km njul3 from the ceiling, and a section of the same thread dangles from the botk/ommm+ loju j9 1n.pw0yu3i3tom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as l .hfs c.d zn;+sk3n92tonp0ithat on a 1-kg rock. Why then dok39s;0p.d ht i2 z n.lnconf+sesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if t,4o1+ wasap p.peyx d8he scale had been calibrated (a) in pounds, or (b) in kilograms?+.e4 a8pd ppx,oawsy1

You pull a box with a constant force across a frictionless table usingga4;wno,3ty/gy g8e w 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 accelyo anw;38w,gt yg e/g4eration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under1:mg:dvykm4 d the influence of gravity there is a net force mg exerted on it by the Ey4 k:1vdmdm :garth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed xrvyo48vfp78 tc6kv 4 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 speed on the Moon and7opc8v8 rkfvy46t4vx on Earth.

According to Newton’s third law, each team in a tug of vj oy+ m-l)ab:n min4qq/8e1k)wtm(o war (Fig. 4–37) pulls with equal force on the other team. What, t) (+y-w jmmm/n:ia418q e)tbn okq lovhen, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries 2 8sk r4) ,zy)xhggxiczel-f7. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its directio 8kfzrzx-e2h4,iy7gc) lx)sgn, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still m. pp.k hp j+.3 2/thnt7s:zcjh)hsc xon the ground, how large a force does the ground exert on you? Why doesn’t this force make you r:. mpsj+ ./cp khzh2.tt )nxhpjhs7 c3ise up into the air?

Whiplash sometimes results from an automobile accident when the vict)ynna ep.b *)6f ,gbppim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?f pgbn)an,)p*6yb ep.

A heavy crate rests on the bed of a flatbed truck. When the truck acceleraf2y*6+mg 8 y tqd1mqhgtes, the crate remains where it is on the truck, so it, to2g*m8yd6g+ 1 hyqmqtfo, accelerates. What force causes the crate to accelerate?

A block is given a push so that82wsen d-ma1 tyq mjmd9,/6nv it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acce2 qeajms6 yw1d /v89-mnn, mtdleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if7xd faf:9kj8 t you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at7fx9da t8 fk:j an angle.

  What force is needed to accelerate a child on a sled adu h:t zo*pgi-f:w f)hb9.gmaf 5p1 +kt 1.25m/s$^2$?   

  A net force of 265 N accelerates (v23- vxskv6xiud kn*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 withstand if it is8cmc vs*c-7pi 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 cjmv3 *mmmmk rn3b45g)k9;udz cp ,;b $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg tz w0sf5 hq012:ajx ywcar in 8.0 s if the car is traveling at00hfa w52jq :xwyt1zs 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellecul s45gka*9 y,qcqm ;n z98set from rest to 125m/s over cmu4lq; z easnc y,k8g9q*59sa distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out ofh5k ,k2/ogq zn the water with an acceleration of 2.5/,2hzqk kng5o $\mathrm{~m} / \mathrm{s}^{2}$ 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 (4/x2sb.oswh(r9 d; vecz4. p wbt 5jp*l02 $\mathrm{~m}$) 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 t85ch4y hxyt a3);dtqu4w*rs yo be designed so that the maximum acceleration is 0.0680 g . What are the maximum and mina3y5qrsy*t4h4;xhy d8wcu )timum 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 the b yd1x opm /qscvd:.(4elevator begins to move, the scale briefly reads only 0.75 ofd:y (op4c/ bqxvmd .s1 the person’s regular weight. 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 maximk4)*qs ynih-2wospnn xs *9s)um strength of 21,750 N. What maximum upward acceleration can it give the elevator without breasos- *w)q9hxsp*y4sn)knn i2king?    ( two decimal places)

  (a) What is the acceleration of two falling4d 4v1pdfggy9 sky divers (mass 132 kg including parachute) when the upward force of air resista4 yvdf91pg4 gdnce 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. When he e; 9u .m2t*vytoseq8 k3*lxrostrikes the ground below, he bends his knmy*le* t.uk;q 283reo9vtxos ees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests tul3mm3:k iy :gryscl)h83 1ion a table. A rope tied to 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 the weight hanging on the other side of the pulley :hscy3mt ykil g3 8m:r)3l1uiweighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dikc*ww+f 98j4-7jzglyqp aox *agram for 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 baseball (a) at the moment it is hit by the xwn w7 ugn((g*bat, ((* ux7ngnwwg and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northww5n ypebuj*28esterly direction. A second 650-N force must be exerted in what direction so that the resultant of the tw82ew *uynb5jp o forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" stwai 0x xkmr0)3rung horizontally between two buildings 10.0 m apart.x00) 3aikx mrw The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a masslesyptwimw08- )fs cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.r 8:wqepljfw:f/ 5d0s0$-\mathrm{kg}$ 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-8ykn4juok8- s-*dndg2v qhb9 biui. to a new location at McMurdo Base, Antarctica, as s usbd*k yq8b ndjv9un8-h2i-ok4gi .-hown in Fig. 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 o d+ nus j5 yjl4uc-uvn2l:5t5the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplinul5 ytvlo5d- c+4n5j u u:2sjng 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 s cu zmdps1+(5shown in Fig. 4-48. (a) msc5d u1s pz+(How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began,adn(tq kf56 :3mm*cj c 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 bloc4 rdxjt v.ap*2tr wxca*m*v: :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 horizont i7ebrh*h;lg.al surface are in contact with each other, as shown in Fig. 4-51. A eg.l7br h h*;iforce $\overrightarrow{\mathbf{F}}$ 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. 9ujl(nywhyq n2hx1v.v; + mwpta/p+44-52 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 systewu wvn+4(9mvn;1ya+hq x. ph 2tl/jpym 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord 83bhzfx,xa ed3z3 6 ox,hsyfn67kcm(of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagramsen f(hz63zy xfx7,mbka3d3,6xoh8c s 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 betweenrb* vsdr0z7ji43tz,ge1k3rr 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 redy+ j qbp;7si 3sen()s(6zzsx quired 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 jc3(sjgv* 6k6 xf*uc np0/ddz0.20g. What minimum coefficient of static friction must exist between your feet and txn6v*udsdjf /0c 3 gc kj*p6(zhe floor if you are not to slide?   

  What is the maximum accelerati6 ktfgpidor.ys3*li h: )ju82on a car can undergo if the coefficient of static frictiony2 fhkru6d p :o3j*is.8ligt) between the tires and the ground is 0.80?   

  The coefficient of sta fm)n.lu*aiwv0ks(8nj ()jentic friction between hard rubber and normal street pavement is about 0.8. On howu kvil wjf8n*n0m.en)) ja(s( steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -6t yfrl5q n8h34.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rouo 23 -jgts,qubgh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeff52z uzr9fe: ypicient of static pfrzz5y2 e9 u: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 kineticfoc.lg -fi2 *l 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. 4-5qyo6m il-v9lillkir 4 tu mve/9 t9:g0b u71v32 (Example 4-20) how large a mass would box A have to have to preve l4o-: ilvukr1y7umtt5 99g6ievv/l l9i m0qbnt any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slid/h)yv fx.)as qes across the floor. How far will it go, given that the coefficient of kinx)qa) sf v/.yhetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 krc r9d 450 naxfzcg:(og and 110 kg , are in contact and at rest on a horizontal surface df 0:co5z4ar9gn(rxc (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy s d .uv(-k0qivcrate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maxi .qv0uvd ks(-imum 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 parkin 0;0dcrp y5t-sm 2il: uy5bu+f rt2pmug your car in your driveway, which has an incline ofm st+2cl5 d;tr2u:ufb0 pyr0-yp5u im 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 with a5oi n -r,gxnf8 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 rnl+-h: m0)z j.kwk cpFig. 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 anz(/ b yu4ngz )gm*q*rr initial 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 n4 ddtp..o0k 5jqdp+k a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rout-guaak8. osqof v ;,q/ke(b9gh wall by someone pushing on it with a for(q9 gb.-ts;q8a/fovk a k,eo uce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery gt6jlq gj)b tufu c:;cz12n /hq-y;w4 roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with f/j4y-1)l6t;q nzhqu;jw guc g t2:cb 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 stop)z c5mjnoqvf1 guu06s t*6va8sd0su pgk2k+2 ping distance for an automobile traveling at speed v 0s82supvjfvz5kstg g am6u+ d2kn6qu*co)10 is 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 dash buyb8h1h fqx kb3g(k f7p*;-tz0wf5nboard of a car slides forward on the dash when the driver decele7 5fbk-0 bqzw(8u3p n*ytk fbhg1;xfhrates 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 initijd*d96khs ,s pc 9.m xhlnjy-7al 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 t9en0luth8hxt +hu u..hey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half teh09x un.t8uh .lh+tu he 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 coefficien+dz+u2:eamimo8c v *it 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) canp x7y sp2vr(y: 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 m+hq;r:jpvqt. 9e x-md ammalian heart, at each pulse approximately 20 g of b.qqr-p m;+ejx :9hvd tlood 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 a0g s+lm/dnt7b a.y pgoe 2lmkn; -7lz3n automobile crash if the deceleration is no more th mt7 a2dnos-nly.lgbkzl7g3p e /m 0;+an 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 acooyl3l,nw(dob m94b: celeration produced by an earthquake is a , and if an object is going to "hold its place"d nmo(4 blb3y:9ow,lo on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident in f8zgnvj*4mk2o 4hu/avolving two cars, measure 72-m-long skid marks of 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 roavan/ghz 2j4f* 4 8omukd.   

  A car starts rolling down a 1-in-4 hi. s4xv dgmks((ll (1-in-4 means that for each 4 m traveled along the road, thev.dxg((mss4 k elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top ofy6/u fzbhy *4q lbi7(p the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of6*l q /uziy4(h7yb bpf What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mu7guo4+zc)t( gl4 d8 lxk *bckzddy 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, whlo b4 c gkdc+l7(u *4g)z8xkztat will be the speed upon emerging?   

  A city planner is working on the redesign of sju1pl+( .lb8 f; y9r a)pbfiua hilly portion of a city. An important consid(bpf9bs1j+y8 i r upf)u l.al;eration 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 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 physicsp/sb a8a/b9m q experiments, dangles her watch from a thin piece of string while the jetliner she is 8m9bpaqs//ab 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 s ,h 0cvnt1d9) ip.svchf6tc vis+5yy2upermarket, there are to be several ramps connecting different parts of the store,t69v cfthhny5p vs0i12 ydivscc.)+.
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 h pa,za0 jd6oc ig8b-9) using the pulley apparatus sj bipdg90a8 -oahzc,6hown 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 atls+ 6eiuqc5(ttf9qsz(b gp57 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 ch6 0nvstdjstp ,dk y2,+ild-restraint chair, an engineer considers the following 06pjydn 2tsskt d+v, ,set 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 vaq*xxoc- . +t660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of simi-t haf s,w.fh4n62fp flar 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 ah-6fpf nf2sw. ,fht4rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a h/j09ewojch 7" 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 a maximum speed of 3.5 3iq s0 :irj)2u:6iz xmrv)jn4vjq1 l h$\mathrm{~m} / \mathrm{s}$ 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 climber. r s(bda,lg- q19iy,t7cmbzmh9k -tss who are roped together are ascending an ice field inclints1rl(-z, hs,tbm -amg.ykdiq7 9b9c ed 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.