Why does a child in a wagon seem to fall backward when you give the wagon6hv s-u7h htz 4md5oc8 a sharp pull ocmth648s h zh 5-duv7forward?

A box rests on the (frictionlessi1w4)v b q glolu(-,gvzq8/r,v 9ysu/f4qfcb) 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 /cv-r( ygv wsf,q1,4 8 o 4/ibqq9u ulzlvg)bfbeside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting onuyn8st ) fuv5z11 t**c ar3sep;j+pqg it? Explain.

Only one force acts on an object. Can the 4ps +7hhdj8)cdb9rj k object have zero acceleration? Can it have zero velocity? hb 9hspdj4kj7)8 cr+dExplain.

When a golf ball is dropped to the pavement, itny go6:p8,c s- otkrq- bounces back up. (a) Is a force needed t6g-y, orko8n- cpq :tso make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating o0,vx5 gbla dz:n a lake, why does the log move in the opposite direction?a xd,b50zgl v:

Why might your foot hurt if you kick alfy;.; p jab1c heavy desk or a wall?

  When you are running and want to stop q:dg j(kdb* r1 8gbq0+d xjft)fuickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using y*0+k (:g)bfx frd d81qtjdbgjour 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 fb5 2;xb2bchoxine thread from the ceiling, and a section 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,cb;b h5 ox22xb 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 g1(5i2dsmx oias great as that on a 1-kg rock. Why then doesn’t the heavier rock fasgo x1i 5(mdi2ll faster?

Would a spring scale carried to the Moon give accurate results if the scale hrbh- 69m6v dwjad been calibrated (a) in pounds, orw669 mvrbh-dj (b) in kilograms?

You pull a box with a constant forv gk pqo+wdi7c0/6g)ice 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) increase, or (c) decrease? Expq6/gw0c go)i+ivk p7 dlain.

When an object falls freely under the influence of gravity there is a net fohjx csx(f9:f* rce mg exerted on it by the Earth. Yet by Newton’s third law the ofxs:c fxh9*j(bject 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 object w q8f0i(mc0pc f 4wylivx*nq35hen you are on the Moon with the force needed to l qn 0fm83 4xlvc0ipqw5f(ci*yift 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,lp j,sc; 82bpm each team in a tug of war (Fig. 4–37) pulls with equal8,bpmjpc2;l s force on the other team. What, then, determines which team will win?

A person exerts an upward 8l z3fp x10 hav.r9g2vprzv3nf u7*rxforce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object0pfzrp ru1 xn7 xv38gf a3v .vlr*2z9h it is exerted, and (d) by what object it is exerted.

When you stand still 0y.hj eszykv 0l ;i6:mon the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into thvj m0he k0zsyi.6y l;:e air?

Whiplash sometimes results from an automobile accident when the ,y q tdmreya94sc4q4bzvk),1victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrs 4bq,1m qta,44)y e9dkcyrvz own backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the tru**.n /ciaa : kpggk(yfck accelerates, the (*: afyckg*g p/nak i.crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block t-rz+ d0ja5 frbqa (.hreaches its highest point, it slides back down but the magnituder (0 ahz+j r-5fbaqt.d of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an injo) nnn b.l:n/clined plane? Assume the mechanism funbnj/nn) on:l. ctions properly, even at an angle.

  What force is needed to accelerate a child on a sled at u4tkdd9d 1dw4 1.25m/s$^2$?   

  A net force of 265 N accelerates a bi8 shf) kyw0a90n,cqgym9 :onhke 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 used to accelerate /sk)ti3r/33umpr d1 l1 x )gqu qwy 0+kmfhmo.a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a y,dy6ts; vmw )$76-\mathrm{kg}$ 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 c.)q+t(hnx j tk66bmujar in 8.0 s if the car is traveling at 6jbhnjm tk ).(6uqt+x95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet frokt g) lp3i.xm4m rest to 125m/s over a distance of 0.800 m along t)p.mxi3tkg4l he barrel of a rifle?   

A fisherman yanks a fish verticallee73p hnbe(8 jo/6lpj y out of the water with an acceleration of 2.5 hjep npj o8e(/63le7b $\mathrm{~m} / \mathrm{s}^{2}$ 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 trackyiyc)0: wljg . (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 designe*u,2d6 t *4yhj;xa,s rujxiamd so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor shouldu,ar*xsu*2m; jxja6t d,yih 4 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 b14 :y- w/ng(i vfodlkvathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular wei(ing4oy1 l f/ d:-kvvwght. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125cr( ;cc3bkn0 6b(dj at-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the t(k ;bnd c brccaj036(elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diversqj8vs*e fweh c 2 gnrhp xvx3705.,5lv (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth8g3 075rv2e5enwvs. cfp*h,j xh lqv x 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 a; g22 hxzp1mgusg;a +house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over s uzxgpggm+ 1aa2;2;han 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 box ruh-: ami5c58km,yh zbl ns 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 otherk ly,mzih 85ch- b5m:a side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for af jql sj(ym6/ hfck.2)q;:pt c 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 thqx1 prj7+ 4cwue moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfield.1j+ xrc 4upwq7

A 650-N force acts in a northwesterly direction. A second 650-N fg nvt 8v;9gum*k3e p,morce must be exerted in what direction so that the resultant of the two forces points westward? Illuvp;*,3gk9gne mmt v 8ustrate your answer with a vector diagram.

  Arlene is to walk across a "h3g jg)*lyb vj2qge1h 6igh wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoi le32g)qgb 16ghjv*jynt 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+( x .txxd7coh by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14z:i kp+ z7gg/a.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a newwhk0(rn49 (g+l4n)ju.zava9v o 2dh5bn f gub location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The h ugljuf 9adb59 n(nrag b0w4kv4. hv(+no z2)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,;t(ekj*lh h zl93ru z/ Fig. 4-47 . Determine the ratio of th h9r tj(lk;hz*zu el/3e 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 bucket-pulley apparrupe,3 78l-e)q6( j rwbj,mmcdv,o fuatus shown in Fig. 4-48. (a) How hard must she pull downward to raisj)8 e ,,,(7umvj uwd qc6bef-l3mr rpoe 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 dszct;2b mo* z 0ja6lfi .3/fjbegan, 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 (ma v ndbn(0 n)7iu;flly0ss $ 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 friction* i8q iff lms f:y,*e0 ycp-q734ciuqtless horizontal surface are in contact with each other, as shown in Fig. 4-51. A force *qi4cpfq:f7c, li mt-s3y8 *ui0fqe y $\overrightarrow{\mathbf{F}}$ 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 m9)cb u* i5wux3d1ew )(cavo xr 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 red)c)u31eox5c 9uxa (wb vwr* ileased? [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 frictionles-d8yr7hdfin23bu e5r0i j/c q s table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at/dhi r-ecb5q 2jf ui3rd8n07y 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 frictf u2p1k7f: 8+r:i2ol a cik xrvmd0+ftion 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 isg,2w0vx0f :mko pnl5t required 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 acln/ yus8p/b i*fm 0g *5kl)f7wee8eek celerating at 0.20g. What minimum coefficient of static frimfye 08 7geil 8nbku/we5)p*lfks/*ection must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car cah3l+vn ypiv4nc9vu19n undergo if the coefficient of static friction between the4c vuvy vnp9hnli19+3 tires and the ground is 0.80?   

  The coefficient of static friction betweenn6v 6l .zvt(cn hard rubber and normal street pavement 6nvcnv(z6.t l is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate atrr-:3a1 2kd;13peki*prp il ka joev , -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 3lk,p0sl65fat w2: ayubt:sl a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphaltym1 l,g/; uav31vv7grp7p fyx surface have a very high coefficient of 1 /avp mvfgyy 3x7 ;l1vrp7u,gstatic friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction for a po/m(ht r4kk)$ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would bo 3r6ss9bh xrh0x A have to ha s30hhrxs6rb9ve to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across tx7 -fu3j) p p 0jvbhc7c/t2yiak0 ,pwyhe floor. How far will it go, given that the coefficient of kinetic frwtpcjp a3yjyk07b7-2)fuh/p0 c,ivx iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 11g. wpd*hsvvv,l1h9n 5 0 kg , are in contact and at rest on a horizontal surface (vglh5wvh *. p1n svd,9Fig. 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 he x 3mq+mit;1 avs6zybe8ci1k8avy 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 cbmv y ei t8; c6m3zsqx11+k8airate slide against the cab of the truck?   

On an icy day, you w* 4wein6+xmm9 0bn wjaorry about parking your car in your driveway, which has an incline ofjbax60emwi+*w 4mn n9 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 s zr7ximdyy78 wta)08 tlide 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 Fig3r o,jm oeu-kleu*8(f . 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 speed of kd:7 7 8d8un1nobhi-h eb sqr* 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 ste.a hn3oo0 -k26b m-eba2p kyo8vglg5cepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someo +aj: p.xy 1sm(fqst+dne pushing on it with a force directed upward y++(a:tms1s. p qdjxf 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 can become dangerous projectiles as they melt. C jxk; e,:eju*ronsider a chunk of snow at the ridge of a roof with a pitch oeekujx*:j;r , f $ 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 minimuml de,9):e eytkv,(mmw stopping distance for an automobile traveling at speed v ievlmw y(k,e)t,d 9e:ms 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 dashbo +fbl81flawqt)md i8; zy+kr/ard of a car slides forward on the dash when the driver y+)t dqbaz+w/8l f8r1;il kmf decelerates 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 initial h:rqb3r8x4moxx* q sh6)2me aspeed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the paqb kgv78-ut h0cking station 11.0 m away. The tq-vku87hbg0 belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient mskpw 0wmw-1kmd8i k86vsb/6 j 5nw.sof 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 down r9,)hmc rczg;1jp g-q:t20yx9n zmmu a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each puljpg h0(z in.3ose approximately 20 g of blood is accelerated nh g. o0zi(j3pfrom 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 ch usuk39l-nzn 3ance of surviving an automobile crash if the deceleration is no more than 30 "3-9unlnu3z k s 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 accelerat5pvs d6cpy.w1uj +* flion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the c sywvu*.651f+jldp c poefficient 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 schb5zu.lwh )d/ ene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before uh/ b d5.zlw)hcolliding. 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 for each 4 m tunlm* 05b bi-jraveled along the road, the elevation change is 1 m). How fast is it going bmb n iuj-l*05when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of k5-yf*la 562dc/xrqo ; um zfythe Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of o a6/5uck x2lfdf*mqyz5r -;yair resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters cm05ff3gfj .2 r-fpu xa 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 be the speed upop.m gf-f ff0cr5u 32jxn emerging?   

  A city planner is working on the redesign of a hilly pqaw+m )kxzzp-qcdy d xkmy5h1l1 wr,8 . )f3o4ortion of a city. An important consideration is how steep the rokz, )m z+coh43pr -1dd1)fq8.a5y xwmyq xkw lads 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 uc2ij/eq )yevps.- v*syf, l:physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fisylspiju) v/2q .-efye:v ,c*g. 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 severanov4+(i ftfz:wylit4cqt l)er.zq75r4:q*zl ramps connecting different parts of tz5+wr *4 4:q:ltnrqzz) .t v7floitf yc(i4eq he store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is need:ctj oh(qh4/ged to lift the piano (mass M ) using the pulley apparatuschht g4: jo/(q shown 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 alt hlh4e0f0ez 2.x(j.zfk1xv t 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 cghc8eqrg89w .hild-restraint chair, an engineer considers the followinq 8g.eh9wgc8rg 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 m6sk 199 rhawxoass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safeifvab,;+tl-- g cwf 5zty ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karewc,fvt+zal ;g- bf 5-in 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 uemu.tb.c tgc3-tsr8lsdd/s+-t c2)gsing a " 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 reakjc(e0(r uaa 7ch 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 are roped togethercpj(+ zsz0 ,hsq /s .ewejgl2+ are ascending an ice field inclinghp,0jcl +qe.ssz 2j/wez (s+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.