Why does a child in a wagon seem to fall backward when y2rlrfmh6o8 y ue5jy /,ou give the wagon a sharp pull forwarl6o hm u5f /2ry8ejry,d?

A box rests on the (frictionless) bed of a truck. The truck driver starts t8fqy fnf0lsja*x(;6the 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 t8 fasf( 6jlxfy nq;*0of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Exp0w)xdcp 8jo80o fn*yix yp(k:lain.

Only one force acts on an object. Can the objec6i)u0 nfv+empd9f(i dt have zero acceleration? Can it have zero velv9)+peidu0i dfn6f ( mocity? Explain.

When a golf ball is dropped to the pavemeui 83nv rp8vq()j hj:qnt, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts th3r j q:v)(u8njq 8viphe force?

If you walk along a log floating on a lak 0cklv5dx/co)vg * (xae, why does the log move in the opposite a c*vokxcg0dv/) (5lx direction?

Why might your foot hurt if you kick a heavy desk or a wall6y, kbx xzob)5 + tuc4spx 7yw5kdk:e4?

  When you are running and want to stop quickly, you must decelerate0 l tud,;;gjl9d 04bzn +rmobz quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the n0 +z;d4l0z ,d9gmb;jb trol umaximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threahffm tp)b9 -y3lyc18zd 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, where is the thread likely to brea39lfz8cmhy1f p-t)byk: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity onx :.jl8vnvu7y.e 6s pp a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock falxslej.uvn7:6 p8.pyvl faster?

Would a spring scale carried to the *+:q c 8apnubg5 m kvum59nwhz3rk3+oMoon give accurate results if the scale had km3nhpnv urbg o5kcaw5+38*9uzq:+ mbeen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a con1f 4am2i3p (w8ncwuzt:opu 5wtl/ (txstant force 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 t5: (ui wlp31 ncopt/a (mwut8zf4xw 2flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net forc x:fouqlj,x) 6e mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force f:xulx) q6jo,on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are oz.7ka8+ *pgk zn+y vrcn the Moon with the c+8kykzpg*a.7rvzn+ 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 and on Earth.

According to Newton’s third law, each team in a tug of war (jl0y5*xf 8 digf0x, zvFig. 4–37) pulls with equal for jx5l,*0d8yzigxv0 ff ce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe the la,lykxk1e.gz(e6n7 n 96 wmj “re7jw 96m1ez axne ,k6(yll.ngkaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the gx.xz8vlmiv 9uplq1;; round, how large a force does the ground exert on you? Why doesn’t this force make you rise 8.vp9;quvlxx l;m zi1up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car i 9 ucq6xtx1orv99ws w85dn bv2s struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. wr2d195w6 tb oxuv9qv9n sc8 xIs it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerad ke5/h19k1, ebcuw cates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate 9ce/5a1bwek k1c,uh d to accelerate?

A block is given a push so that it slides up a ramp. After the block v14ee+v+d6+ oapnag g6unkv,reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent,6 ++v pn+u14vegek ago dv6na than on the ascent. Why?

What would your bathroom scale read if you w50u-a xf2 kyywk hoi84eighed yourself on an inclined plane? Assume the mechanism functions properly, even at 8f -y iyok 42xak05wuhan angle.

  What force is needed to accelerate a child ffj :nxdm2b57on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates gyxser: m:jr6w77d t,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 withstandsx uj47xftx8 vb5l.0l if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of ag:p(9muyjc048r eugvf fg, /i $76-\mathrm{kg}$ 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-kh*l 9rpgv35e7 kwpn/d .3ac0h9wrv gog car in 8.0 s if the car is traargp.o39v *dvnk/rl 79 5whp3 e g0chwveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelleth-.etc ihx40ioj d 7e5 from rest to 125m/s 54ioh.e7d0ehixt- cj over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically jx pa i*.zq88tmxu:+g out of the water with an acceleration of 2.5 . iz8 atx8g*: pmxqu+j$\mathrm{~m} / \mathrm{s}^{2}$ 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 tra jkb:mlb8d/6 wck (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so tumwq9k bf* 45mhat the maximum acceleration is 0.04 k9wb *uq5fmm680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless ele,g:ivk* j2hje6fd e2 evator. When the elevator begins to move, the scalvfk 2e,jde e gji*6:2he briefly reads only 0.75 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 elevay-+ e rumlrrc68i7n7 ck2ipw*tor has a maximum strength of 21,750 N. What maximum upward acceleration can it give thep* 2lry8rwi7ec uc+m6 n7ir-k elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallik hr pg(i+v vcoj;*2s2ng sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-four roic(pv2kh +2*svj;gth 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 strikes the groumxd 3m,0rmucq(ay h(,eu7n3 vnd below, he bends his knees so thaurnmedmvcu,( ,33xq y0h(m7at 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 on a table h48q8effbpg5 u fx6/ hn91rtd. 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 force96pr fu8 1hx5 e tbff4ng8d/qh 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 basketbf0cm il qz.n8pq3jsmnjp 2212 all 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 (.22m b d+;u rua/ i)y rnvorm;7bqe-eea) at the moment it is hit by the bat, and again (b) after it has left the bat and is flyingbu2; reebo -rr7me;+aivydnm/ q).u 2 toward the outfield.

A 650-N force acts in a northwesterly direc.ldce idy80deft)1s+tion. A second 650-N force must be exerted in what direction so0ie.lc+ ydtsde f81d) that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horicv e3 ,4vdbyv :/a7wogzontally between two buildings 10.0 m apart. The sac d w,vvb 3a74yov/e:gg 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 han1 g2j kmchst).ging 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 14.a fd+1 iq ll;(xj)b.k4qf; xee0$-\mathrm{kg}$ 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 hokywov c: )e0a2q0 5bnausing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcn 0a:vwykq )e 0bo52caes $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 behq v7nnxd/ v+*l(d ky9n2 +rmecind it, Fig. 4-47 . Determine the ratio of t7mr2v( qkdd+c*+9xn ylven n/he 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 co(y fx az-)c0herself upward using the bucket-pulley apparatus shown in Fig. 4-48. fo xc0(-)cazy (a) 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 beq-9:s yy6 zqdq5r8h5e d se;hugan, 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 bloca8 dg1 7xgn-+hmm m bepq32kvq*.m gg+k (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in 7kczv.zc0w. gcontact with each other, as shown in Fig. 4-51. A fzvc.7 0g z.ckworce $\overrightarrow{\mathbf{F}}$ 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 above the ground, xj0kjev* x0y0oq0 ue3and the massless frictionless pulley is 4.8 m above the ground. What maximum height does o3ev00q0yekx jjx0 u*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 frictionlex,a0u u,;az o(zmm +p(/euvsass table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, uvsuoa; uezmax ,,/ap m(z(+ 0using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction bl xyf /f709ed( nqu0)dfek +kpetween 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 to startbl)4g13w idf r 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 os hf.0q2 zbs6n62ryf9 y9yoq in a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you hiyozq6 byy r92s0ffns .29q6are not to slide?   

  What is the maximum acceleratio;d2:ng y.mr xivqqa4a(ba- r+n a car can undergo if the coefficient of static friction between the tires and the ground isq2-a gmva4(ar+r .xb:n;qy id 0.80?   

  The coefficient of static friction bet54f9oldf/ lw 3 oq/uwz,co;xb-8 epya ween hard rubber and normal street pavement is about 0.8.aow-co34/fz;9dyb58que/ lo pw, fxl 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 at -4bq k(z a 6tom a9(jvlv1h)8 d1ybo5sl7.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ksgotwp,g3f qj5 );8ja 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 asphalt surface have a very high coeff5;r)kv:(4( gkil mjeio1hjp iicient of static fk;el 1 )(oivp :ki(4m5rhgjjiriction.

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 kinetinc3j-0x z.m6ayz 1vb7zstp1k c friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-2xe8ku-m:52c bsrd+r u 0) how large a mass would box A have to have to prevent any motion from o5e r2xu srum8-d: ck+bccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Howvtw:,o5h lq y:h5,ym)bsa7k0byg et2re5d2 m far will it go, given that the coefficient of kinetic friction is 0.20 and the push iyly)aoev r wdy g50::ebtt2bh55s,m7mkq ,2 hmparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , ariqp +op f5qje2gk1kjhzu zmn-3) 6,7le in contact and at rest on a horizontal surface (Fig. 4-54).oj5 +f,6 jlkzz3)7kp21-muehqig qp n 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 carryinx, bzaut*p4,ng a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which th*unbxa t ,z,p4e driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway,(z f uh6 1gz;hvvmx8t1 which has an incgv mz1h8thx1 fu6(vz; line of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a / jujog48.t nn28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tx7pdh 2f,15k3f rf(ue0 aqhrmilted 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 3pw 4f21 8a5mx8 hqv(aggahvginitial 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 thet/xfp v;8 egp1 steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone 9dnjl .f1q0z,m-d xio pushing on it with a force directed upfjm q1nz.0d-idlo x ,9ward 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 projectiles2c2 nnz2xcg j0 as they melt. Consider a chun202xzj2 cgncn k 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 storfgnp i85 (m6vpping distance for an automobile traveling at speed v is equagfv6 nr(i8 5mpl 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;pwes jf2tj m3dhz7/) car slides forward on the dash when the driver decelerjt/d3 fwjz7 p)2h ;esmates 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 speed *9fh2c* 9edfbs j m2js$ 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 are58 dac(xbx1 nrf5k8h5n l n(ib filled to the packing statix 8d8n (fi1r5xh5nl5 ka( bcnbon 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betwelo7-j1uf 5*ftw g2f v-sh,k *6hgggbden $m_{1}$ 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(auwvhr).)d s d9ip 8f 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 pulse apprb.td +g a os8tj3 ce:kp6k( mqt1x)+ocoximately 20 g of blood is accelerated from 0.2c1jq8:+ec a+md tos.6xbtgk(3 )o tkp5 $\mathrm{~m} / \mathrm{s}$ 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 ijkv/xrot x v54a)fx)+ f the deceleration is no more than 30axkfj rv/)5t+)vx ox 4 " 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 acceleration produced by anbdpl9.ffu/ a 4j,h hick9w92n earthquake is a , and if an object is going to "hold its place" on the ground, show th9 jwa/bu9cl.fi9 h24kd nf,hpat 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 invol 1tamhn5:xfctbd/ .p:ving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. b n1tfm:a/x:c p5dth. 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-idwpf9 o3 (v*pbn-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? (a) Ign dbp( vop93fw*ore 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 or,vjg x9y.f:tfetk) cvqp ,9*f Pisa and falls 55 m before reaching the gr :kg.v,9jc*e,yqpff 9tvrtx )ound with a speed of What was the average force of air resistance?   

  A cyclist is coastin; b bbhens k-v) 32*4wp;o.fiyxb9joz5may t4g at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerb.-*yx;4zk; ohe5t2jywnis9pv4mb ab o3)fb ging?   

  A city planner is working on the redesign of a hilly 2z/wfc) dp7)cf-m+oo to/a nuvb.qt2portion 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 fc ob27o))2qdp n v f.tot/-z+c wmu/aparticular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch /rbd;2 h2mto0k1 0z+x qk xknaxpu )3efrom a thin piece of str xk/mz1qkbe0x rxu 2)0n had2;3tpok+ing while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps conneigmtwyt1se700l5n0 ( t-zaq rcting different parts of the st0a-qrt wtgtie nl5zmy0s0 17(ore.
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 neevgnm/e/fg,i yxzcf 4 ;2e u4*uded to lift the piano (mass M ) using the pulley apee4n*z 2yvm g c/fg/ ux;u,4ifparatus 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 at 3.7.of3rkxk9z8 bbvi-0 ,oiz jl5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the +rz6fc 0oc2j 8 uuvhf:following setrh82czcuu:0 +fof6jv 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 l6;f ,qfk:3iwe b .0u jl i/k*9pib t)dsrgsm3train has a mass 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 safety ropes of similar length. Karennr,t1nv8efxme )2 6i q(dyq, k's rope is more elastic, called a dynamic rope by climbers. Bill has a statirvkqqt) 28n (d,ynei 1,6em xfc 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 rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is usu7wwpj1t2 t7 ding 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 allo8b r kh(z1;egvwed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascenazi /-ilq 6w8oding an ice field inclinew/ -qizia8l 6od 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.