Why does a child in a wagon seem to fall backward when you give the w0iqt 7bhxzy9.3j si 3w 7may/bagon a sharp pull forwarxzm yb.hq/i7339iyjb wtsa07d?

A box rests on the (frictionless) bed of a truck. The truck driver st1mt 6kcku9 9xmarts the truck and accelerates6k99 xtm1kcum forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting+wh cx ks1(x.f:-f7uqd1jg lu on it? Explain.

Only one force acts on an object. Can the object have zero accelea 1g8 nz)ujz2aration? Can it have zero)a81g2 z azjun velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Ishl deq:a( ig.iue.rm+, p7,cv a force needed to make it bounce back up? (b) If so, w v , 7:+q(dg.ueplm ,aic.irhehat exerts the force?

If you walk along a log floating on a lake, why does the log,t3(l+xmw:nun6jn e * v hmgl4e f)yo1 move in the opposite direcmnmv4ow,e(u n):3exnl *ht 61lgjfy+tion?

Why might your foot u bv3kjx184k b, ke8cwhurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (7t(b(tz ob-gf . 7guzsa) What is the origin of the force that causes you to g. (f7tt zu 7s(zb-bogstop? (b) Estimate (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 sectwdw9 k +;/qbys)a+nq/fo:o h qion 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 the thread likely to break: below the stone or above it? What if the person gives a shboyq) w9+ of+s: na/w; dqkq/low and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is tw6np 9/l p7kqtuice as great as that on a 1-kg rock. Why then kplptnu 9/ 7q6doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moh f;89yrcig(g on give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogramsic8(9;fr g ygh?

You pull a box with a constant force across a friction bhx:utlglofv 6i2+:gv1cbaw4:f / l: less 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) defxcvwh2/l+4vig:o: bta:b ufl 1: gl 6crease? Explain.

When an object falls freely under the influence of gravity there is anny,t32 8if:oo.u k wx net force mg exerted on it by 8n koi3t,ox2:y.f nu wthe Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on the 0e2p,ii.zru1xj d6i gMoon with the force needed to lift it on Earth. Compare the forcuiz 1x0 . ,dgpi6irej2e needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law,i(t(sz fin7;lax 0* jb each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, detei(*nbt0 j;zfil x( as7rmines which team will win?

A person exerts an upward force of 40 N to hold a bag of grhnofb+*9g ,l z b6ka/koceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magni ak/ fob9zlkg,hb+*6 ntude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the grxbhw a-v,5mrb3n+ )hcound exert on you? Why doesn’t this force make you rise up into t,rhwhc m x )bbnv3a-+5he air?

Whiplash sometimes resa*hp ei/c14eo ults from an automobile accident when the victim’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 reallyep 4 heao/1ic*?

A heavy crate rests on the bed of a flatbed t/4 do 7d ye-;dbgobfwae5,k a:bbbk7,ruck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force ogabbdb5 ;:foede ,7 /wb -,kk47a dybcauses the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaeon ;u;n1k4vc*v 9vx y/a2yvjches its highest point, it slides back down but the magnitude of its acceleration is less on the desc;ony nxce1v;u42/ v 9yakvv* jent than on the ascent. Why?

What would your bathroom scale read if y*tm+vp5u gpf5g r 58maou weighed yourself on an inclined plane? Assume tt 5gp8m 5frg+a* pmvu5he mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25mxm,:q3s6e smds..qp hn47 spm/s$^2$?   

  A net force of 265 N acceleratesyn2jnx4*tfv0 kr 0 6bb 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 is used to ,3m)+ 8 uxvouuqk x +db2+cvcmaccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight om)6iqc:r ;0q/ytisu*6v x s krf a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car i5 t8qawlxo3f;; nlmz/ n 8.0 s if the car is traveling at 9/ ;nw tzf3;lqm5xo8la 5km/h? -  

  What average force is needed to accelerag /r:jyg y3vpherw ;n i8s-m3npj+w v;0je-5rte a 7.00-gram pellet from rest to 125m/s over a0/w ewg8piy:r+3e;mj 5v --r3j ;g ryjhnpnvs distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically o-0 v3w)uo q7qdi d62q wa1djbbut of the water with an acceleration of 2.5 qaq2d vw70bu q di)j3d-wb1 6o$\mathrm{~m} / \mathrm{s}^{2}$ 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 traci7hkekt gv.o/uqq,x3;m3p0. i7g nas k (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 ) isgv/s r .x1 0ww yrx*mzbpp.17 d+aho7f to be designed so that the maximum acceleration is 0.0680 g . What are the maximum aroafpp1y *01bsz/7 m.d+wr 7vhgxw x .nd minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevatorjmor1-7n za; i. When the elevator begins to move, the scale briefly reads only 0-izorj1 ;m a7n.75 of 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 dhf6 a)4e8m i1vqgqz0a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breakin fz1a eqhq0i4v)6 8mgdg?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 1 w0ch;u,.a/lwu pelf4 32 kg including parachute) when the upward force of air resistance w,laup0f l. wec;hu 4/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.j or)obx 2bymuk *14j) aa g:)-zm, q(7rfamfm When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his tors:(ojg 4 a*x, m-7a)j ay)bf)1kmmzqf rbmru2oo (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. aa(,th y4h vjwesu9:.A rope tied to the box runs vertically upward over a pulley and a weight is hung from the ot4h y 9h.sjv t,u(aae:wher 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 for a basketball p1qx: mtgzym ;a dn8xggok9-3) layer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-bodycv((h;vz s* cf diagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat an*(h;(cv szfcvd is flying toward the outfield.

A 650-N force acts in a northx(vc7wigc,n p*z* xu8w +y z5r35bsr owesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.xwr5rs (yv*cpxc wgn8+ 7boz3,z*iu5

  Arlene is to walk across a "high wirewu i uaa ;,1gss1at;u.cmnd*q r6:c1t" strung horizontally between two buildings 10.0 m api u q;wnc.u 6rd,t:aas1umat;c11g* sart. 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 massless cord from ap7yow1 3;xxlrl- )w xonother 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 14.6eip wa1* b ai(l1jxu+0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, az l :29(h7pcn sjq-;ga(ezgfqs shown in Fig. 4-46. The sum of t nfjqz;cgl(s (g2:hap z -q97ehe 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 pullin6cv3xy7o s4m 2quwh,sg two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive s,qu4 w 3o762xhc yvmsand 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 pullsu/h y+4 /fmpwve)vvg4 herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How ey+hf/wvm4 /pvg)u4v 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 by/ czo wv*5 5e3j*2mpj9we doregan, 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 (maa3(t-br e- wz(skxcgn;7rxe ,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 b j(3w 7zjn2gjsurface are in contact with each other, as shown in Fig. 4-53wnj( z2j7gjb 1. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abjv: s0yf 9r6 m/xq3zbwove the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximuw90b/qzs6 x:mvy3 jrf m 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord /a..l : jd+7wpu7osylz-tsci of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown iijwz.c7yul7t :/sp. sod-la+ n 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 betweenrv7h ,-te (ucr a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required w) kev)fj2pg rynv3d(h)(g*lejz ip9l x 3h)* 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 acceleratii *4vhqo uxipka9;;9z ng at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor ifq;u;ko9i 9ahzvpi 4*x you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of 93 (7xadjqw- 6 heb y x:buz:sc;jsvr7static friction between the tires and the ground is 0.8a69dxss xe jh r:c77qv3jy(:; -bw ubz0?   

  The coefficient of static friction between hax 1ytz-k 7e7scrd rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leazt7 y7esck-1 xve a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80 lg 6kud cn1r4)ah)vk4$\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough nhc5*iw)h ay5 1)b acc30$^{\circ}$ 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, o6lxmq(,mj0:b fze o surface have a very high coefficient 0lzf, o( oj6mmqx,:ebof static 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 drik w*: r96tv8zskw6 for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 5ayg.xcjz ,jxc6t 3+whv d h.f2u1j6 l4-20) how large a mass would box A have to have to p1vcxxcztwj j..a26 ,l6gj3huf5y +d hrevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How ck5hxmk 8 peq- i-pcyq 7m.p90far will it go, given that the coefficient of kinetce-9mq8xmp5 0cpqiky- p h7k. ic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at res.s khq(bkyby6gx,h9 o y9e,j+t on a horizontal surface (Fig. 4-54). A x.eo 6y9yb(9qygb, +kjhs kh, 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of sta79n m elfy-:1e*o 6 phmcwuei2tic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can d ci l*hn:71y p9e6euf2-m ewomecelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking y9ar1zw gx/uua9bs, *pv 3)hhqour car in your driveway, which has an inclinegxpqbz1 v ua3/h,9a*r9)hs uw of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a sli8mf 5xf*3d59avbcr (jx*y pz rde with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. n2mysb3v,l/yzovw9n2 8j n,j4-55 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 ip9z22 kw8xynznitial 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 wd5+k r r cov6p9odsla6i i,k*1ith 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 by0,- afgu edb+r someone pushing on it with a force directed upward a,agf +-r0bed ut 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 rob okz,d74m4qv ofs can become dangerous projectiles as they melt. Consio,bm4 4dk7vz qder a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distan,xz jx4k) +( decq4ryice for an automobile traveling at speed v is equaxkdj+)z ry4ic, xq4e(l 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 slid8m;n9oju +q*o: sonn7bnnnb ,es forward on the dash when the driver decen,nnnoo*+mbu :7 qnn8b; jo s9lerates 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 anuu p3: 5vr:ifp 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 filled iwi.; +3ycke0mf p3jvkt0o5e;: srrd to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of stakpk.fi0e sj; 5 rr;0o vmi3w+ e:3dtcytic 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 kiqrakv+*63ces7jx ex y u0q3b.netic 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 a 6.(w jvg: zmb:+hrve4w p3q x+:v0$^{\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 mammal,rmtvi xs 9:z w+x5)nlian heart, at each pulse approximately 20 g of blood inwz:x+sxil 9, r5mvt )s accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash ifzfds 33 o,.f-e;mhaumwm(e - i the deceleration is no more than 30 " g 's." Calculate the force ,- a 3ifus;(ome e h3md.-mzwfon a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an objec ( g xthl/ls0m.:j+txqp xi1biaa;,k-t is going to "hold its place" on the ground, show that theii:ltg, xk;1qha(/xalb p 0+.jstm x- 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 involvinfs8pkoj zmmv,e:e4 4,szb50 mg 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 omsf pmz: ,8se 4ek04vb ,m5zjthat car assuming a level road.   

  A car starts rolling down a 1-bt,j9478md uo1 dpyndin-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (t8bmd noj947 dup,y d1a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and f+huz7;wo:- . guyar vij) rxc(alls 55 m before reaching the ground with a speed of What was the aaj:cri;wx 7 hguu+yv r.z)o(-verage force of air resistance?   

  A cyclist is coasting a3fbs gird1t 1gd j*nf /v,sc.,t a steady speed of 12m/s but enters a muddy stretch where the e j ftgrb n*s1, v/13fcd.isd,gffective 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 upon emerging?   

  A city planner is wor7 fmhz26 ki1czking on the redesign 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 hills without slowing down. A particular small car, with a ma7kfzch 2 i1mz6ss 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, d7 wsuvz2 2yj.gy, ubr8angles her watch from a thin piece of string while the jetliner sybgujw r,s y87uz2v.2he is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to bu*5qw jwtj; ;yt8 ny3ce several ramps connecting different parts of the store.;*wjyt58tnj w;cu 3 qy
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 n o5,;vxcc d5rru/a r)oeeded to lift the piano (mass M ) using the pulley )ar u5ox;r r/ o5dccv,apparatus 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 acce3pi1/ksxp , ej mjc).dlerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chi y;5yioup ,q;cyz/a:air, an engineer considers the following iy;qiy;:y up 5ao,c/zset 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 tonsbk7xqq( /q ihgk+e4g . (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 r,n frw c5f+nt)opes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance )c,t r+nfnw 5fof 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " wtt.yyfp yb6 t0/4fl3 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 6d dno ;g2i,b 87ctcwbto reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped : nx2u4yf6nt jtogether are ascending an ice field inclined atfy2t:u x4j n6n 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.