Why does a child in a wagon seem to fallfykx18q3ok-wlz 4k9 q backward when you give the wagon a sharp pull fork9z1x q y8lqfwk3k o4-ward?

A box rests on the (frictionless) bed of a truck. The truck driver star5, v cmwh0lkt/ts 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 omvl,0hw5 /ktc n 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 acting9dumo2 ,)t - qveea5uj on it? Explain.

Only one force acts on an object. Can the o0)lc5ya 6yixm1;sx8if ofknf 5 4d *fobject have zero acceleration? Can it have i;fyo lo)1xk ff 46cxa805fy*sn 5mdizero velocity? Explain.

When a golf ball is dropped to 38 kfvw4i4o,o +ijdjea+v z b1the pavement, it bounces back up. (a) Is a force needed to make it bounce+3e+f4o, d48oav1 biwvk jzij back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposi+k;lkf :eq r-dfkq-:ste direct--:f lfqeqrsk+k k:d ;ion?

Why might your foot -zp3yw:)em7l9j h:hpc ) jvyzhurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you mus5o)dsok rz2kov;0pmz97 z*pgt decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person runnin)0 zz97dm;p5 vp z*oso2ogkrkg at top speed to come to rest.    m/s$^2$

A stone hangs by a finemp)d j:b-cu8y 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, where is the thread liku): ydbpcj -8mely 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 rockb-teuc2xq9u/za;tvg 648 f ir is twice as great as that on a 1-kg rock. Why theai ve;zu 62r-t9x u4b8c /qfgtn doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon9lcnv)r q(;txx 7o+fn give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogcl7 x9 n qt;+fvroxn)(rams?

You pull a box with a cons zfw3+jtd(a; a1s;mbutant 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 flat on the table), do (ujmsa b1t;a;zd 3fw+es 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 forx7k :h4+ bufrtce mg exerted on it by the Earth. Yet by Newton’s third law the objecrxbh k4t+f:u 7t 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 who l/u h395vqh -dp*ojeen you are on the Moon with the force needed to lift it on Earth. Compare the force nee h 5ue-oovp/3 qh9*jldded 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 (Fig. 4–3mj +cg2ybay3l77 yk, r7) pulls with equal force on the other team. What, then, determines which team willb r2 ,l+ygky73cm7 jya win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe tbw.4qi6 0pqs7 w0 p(*rsqv uhq.vh;xfhe “reaction” force (Newtqssupwh00vqvwb 7.i q rhpf.*qx6 4;( on’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 ground, how large a foao8;0fs f2g rhrce does the ground exert on you? Why doesn’t tg ro0fs 28f;ahhis force make you rise up into the air?

Whiplash sometimes results from an automobile accident b3jo 1;ob+vk5q1eni1uomhk(3 )p rdhwhen 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 really?k (o1bkiooq u5h3 vpbe1 mnh)d+3r1 ;j

A heavy crate rests on the bed of a flatblq3 p+lwfrk x,o7(9 pbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. Whatlb xr(9+7 foqppw,lk3 force causes the crate to accelerate?

A block is given a push so that it slides * ofze 1h.mdu 1.0y8kdrt93pz)ljuhpup a ramp. After the block reaches its ht u1dp).*dzl1rfmzk0o ju y3eh. 8p h9ighest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale readliyhxs171el bqn6odp64ar : 0 if you weighed yourself on an inclined plane? Assbo1pxd4srn0 7: y6 6aqil1ehl ume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25jm--ow+w/j / lo spzx1m/s$^2$?   

  A net force of 265 N accelerates v3x6l:vj,- ,a 8 7dljflamxoua 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 withiqu tc uiahc8be2 -e22(,ogw7stand 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 a gi6i4;b0kbznc1 q8fo9mo-bgsvzv4 v (8,nhm $76-\mathrm{kg}$ 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 in 8.0 s if the car i ;ygw,gs,aq) gy:frmp*- .ahrs traveling at 95km/h? -mfwhsrrya)y- g p,g,*g:.a; q  

  What average force is needed tanj 1be(i8 w8fo accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the ba8i j1a (newfb8rrel of a rifle?   

A fisherman yanks a fish vertically out of the water ws3xb7 nee bgeb.jz*y 5:q28wy ith an acceleration of 2.5gbqezb8: y njsy3w 57 2.eb*ex $\mathrm{~m} / \mathrm{s}^{2}$ 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-mi/ 2zpm0wy078pe0*xl kyus:v vgl wz6d7b 4yydle track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the5f0, :mew5 jt jq7eppg maximum acceleration is 0.0680 g . What are the maximum and minim 5w 7mpejg ,5t:0qjpfeum 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 s46f b0*xio, xqafup+;lx o0 cbcale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the+f* xb0ob;ailupxfq 406ocx, acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg ein-wpn3 jk.m0- s4f)pyza ed0levator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator w- ksez04-0 p p).nmiyfdnja3without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including p**4ji okklk jla ;asc22- h f+.5pjlmqarachute) when the upward force of air resistance is equal to one-fourth of5kjlmq4j+*-.kfph o;s cjak l2 li*2a 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 t2 tc1oy:fz nzl7cz-:7+ *ug;k oi jbxshe ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torsgt*o7f s i7l 2:zkcny uz;+: zoxjb-c1o (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 runs verticallf/x * w/tny9l7 1brfr4rd/szuy 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 r*74fbw/s/9dzy/x rr1 tulfn 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 p5dfbq jo y;-x9m;22s.rkny czlayer
(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 (aas8u6 wp /2jsb) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward tas6u8w s/ jpb2he outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be e xy5a0srcci;7 /qhan ;r (rd4xxerted in what direction so that the resultant of the two forirdxyq5ch ra7s/ 0nca;;4x( rces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acroszqsib1g bies ih9;ajn,+ j-;, s a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at thenjsqib -as ;zig+,e9i,hbj; 1 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 hjp( yz2m7yw od1)a gf(gea -h:anging 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 1e vir j;(u5/cz4.0$-\mathrm{kg}$ 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 tqo 7pip3r6*xd e15 yedo a new location at McMurdo Base, Antarctica, as s5 e pi*qox61d3edr py7hown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behindbi*/wb w ju7ct :y4s.d it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first carswd7/bj iyu. c b:*4wt $\left(F_{\mathrm{T} 1}\right)$ , 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 us4hdz hk 3: dp/j5lreq/ing the bucket-pulley apparatus shown in Fig. 4-48. (a) q le3jp4zr:h5hk/d /dHow hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, qquv ; 4z.9wpu/pehiv jk3 ;)va 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 block2jb 1 l,h ge:9;ymoijf sqhq:5 (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 contact with each. oye+hrn l77b, pu*ic k6s:uv other, as shown ivb *lh+uie67u k :nr 7spocy,.n Fig. 4-51. 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 above the ground, z tmn2 k -h :xgu1zye4y12w6l1fgbp e*and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the *umw4zk2-: 1 h6gnl xgz 12beeyytf1plighter 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 conns bit0.ay :l3oected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each o: atbl0.y3 isbox and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of klbb 9p6a m2p,tinetic friction 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 is required to se-3fujksrsn yz2v 7*ox-(e6ltart a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. Wgj:/ 4gzmp3go hat minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? z: jg3og g4pm/  

  What is the maximum acceleration a car cana hha )cw0p md47aap-4 undergo if the coefficient of static friction betwep0hah)w4a mc4pad -7 aen the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubby7 fxisn 9e- a(to r(::i 4fw9xfxk,zfer and normal street pavement is about 0.8. On how steep a hill (maximyrix9 k7-4f (nox: :x9fsw(if,fz taeum 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 brs3*qn+67 a x+ofwl-mq*ceo n8v e z8at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a c6pv. :h;c *1askrgcj 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 s1s.ypw ,a.*th, fm phwith an asphalt surface have a very high coefficient of static fric p ymshp1ta, .s*f,.hwtion.

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 ki-9 twb8j/n ,grxp : ye0xatba+netic 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 4-20) how large a mass y (ih-6eatd(iwould box A have to have to prevent any motioe -i(yit6a d(hn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acros mtp ++:,iaykhs the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed tky ip+hma,:+of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg 28gxlt4w1mwj2b9 l nb7e gnx9 and 110 kg , are in contact and at rest on a horizontal e l128m7w29njxltg gb9xwn b 4surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefu,g-:xrb j69v gjchs)w h;k f0ficient 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 hurk0h6x9s , hwj:vgbj ;cf-g)aving the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yo)utp50fkuv38rgt t5ty i)t)6yy/ yazur driveway, which has an incline ofyf8ky) tttpu)tz viy)03tgy5u 5ra /6 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 -.4octjs k5ep) x9ce6cyhpc/ 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. 4-55azy 0w:p9tq *9vp5 5xj7sdhv x 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 -*z ir02s (lw:5 yc fmj a+txkzpw4:xrof 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 0+ 5uw vg1krtf5r sh0n7bf*uztop of the 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 pushing on dn55s(l0vqos it with a f5osdl ns0(q 5vorce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as tq xxa2;bd:w e1hey melt. C: x12bw;qd xeaonsider 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 rn i+xp5t;kba;w2sd5 an,v;gdistance for an automobile traveling at speed v is equakw a;its;n+;5 g,ar ndb v5px2l to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the da-(kc 6pkood/+6jyk hsae+dh )sh when the driver deceleratph( jd/+6kek-hs d6k +o)coyaes 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 in 61-wrgc+bn dfitial 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 convttkvm7c* b1jj rd. 8j4eyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish 4 1j.t *r8vkjjmd b7tcwith 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 /d* bf qnd0lij035sm/e dq7n c2s ib9bfriction 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 68w5,o/ +a1lmw(zkl8m ia ui*es,ijr s.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 oiyh 8v+4k.zex0ah aw (f a mammalian heart, at each pulse approximately 20 g oviewaxkhz.ah4 ( 8 y0+f blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if;u h94 ,zqk)gf keuuz) the deceleration is no more than 30 " g uq9; )zgu4f)khkzu,e '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 an earthqua 7iy1r dv/tk 7cw.mnstun 11r-ke is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least 1ws-c11/n dm.ktvr7 7yirut n$\mu_{\mathrm{s}}=a / g$ . (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 involv/mju3dt d+6qp nl.;xs(. zn eping two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coeffi e;p6 xn +.udp(3j zt/qdl.smncient 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 travae3 xpdu +q qgd, e416:5g,fvn4czq fheled along the road, the elevation change is 1 m). How fast is it going w1x,h5 fd gd+6e acqvue4 4gqqz3n,f:phen 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 the Lean +2 8avpe;l*dn(kepgzing Tower of Pisa and falls 55 m before reaching the ground zve2aknp8eg;+(l*p d with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed () l x ) )w1dpztg7n;q)jxigb*wtl)ys 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 w(d )ip7t) )ybwxl );g l1t*gzjq n)xswithout having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign )cd e2b mc7m/i hv.l5sof 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 mi) d.2 7bsl/emhc5cv 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 physics experiments, dangles hea dg: ;sm,2(.r(rtxggxgz 4mtr watch from a thin piece of string while the jetliner she .t,gz(:gmgst dar 2 r(4;mgxxis 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 f.yictj 6+ g78of53p lgp9rjvbe several ramps connecting different parts of the store. gt683975cjpr.vfyg fji +pl o
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to ijrr35i g1,qo1-rzk mlift the piano (mass M ) using the pulley apparatus shoo3i-j,r g q1zmk r5i1rwn 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 accelera4hb l2jpsvqw9 t*1bg:ting 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-res :mq-/(w9 rx58md 0aspiuri aaa+xt5htraint chair, an engineer considers the following 5d -9a0:x/iam5 h+rpr8 axa qts u(miwset 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-carwxrz 7z,e+*um ig-xz. Italian train 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, Billgh( l:buagb1, and Karen, use safety 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. 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?, gu:b1 l(habg

A fisherman in a boat is using a " 1nw5 v.15 puuhn: kt) mpya/bw+0-1 $\mathrm{~b}$ 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 tallo; r byn4w;(jp8nnv3g building is allowed 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 ascending an ice field inclin7xhr(f ) lb:phed p fh x(:rbl7)hat 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.