Why does a child in a wagon sq3dj2 v yvw4y-9po ili.q01 wveem to fall backward when you give the wagon a sharp pul1v 9l3 jw-iyvp 4voqidq w2.0yl forward?

A box rests on the (frictio. nz ;u/7-hxplfenw2 hnless) bed of a truck. The truck driver starts the true. h /h-fn7l2z;pnxuwck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an oehim *3b i2r pcdec- :6cg 1q-,(ffqjebject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero pcpx5;lk j iwn 5om 4p78g:r;facceleration? Can it hwl5r knpm 54 p;j;i:7pcxf8ogave zero velocity? Explain.

When a golf ball is droppeop 3; 1etgvz+wd to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (bt 1zwo;g ev+p3) If so, what exerts the force?

If you walk along a log floating ozhz2 d4.ifi7dt.3 futynz :p;n a lake, why does the log move in the opposite directiou; . t2zi:inyp4.ffz 7htd 3zdn?

Why might your foot hurt if you kikdi9 fr-ip,jh66wr4f. pw) byck a heavy desk or a wall?

  When you are running and want to stop krdfc,o/,1hw 8dn5ok quickly, you must 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 o/d,ok wr,c8hf odn5k1f a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, a 9- -w vh*m kg,1p2anm3dkeughnd 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 breamgedvug,wnp ahkm h129*-k3 -k: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as + 9bbawym,dr7 great as that on a 1-kg rock. Why the,9+b wb m7ayrdn doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resa odv6k j-k.vt n/ 24llpqg9k m2y2hn4ults if the scale had been calibrated (a) in pkj ak tn2492vy.2pllmgk46vh q/ -ndoounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an at/o b v5k0.yfgttached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (witb0fotv5/.yg k h the box remaining flat 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 influenc4em.25h i4m2qhjet yw e of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite f4 5 mmj ieh.het42y2qworce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when youg/ y+c+w ddryl5/e y,g are on the Moon c/re +yd5gg d/lyw, y+with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulldpl 4s1hl b5 7 0+w;nxxuox)ots with equal force on the other team. What, then, determines which team will winnlo47w)u t lx sbx5o+hp0;x1d?

A person exerts an upward force of 40 N 45bs ;er:0 ncbp6:y u gkvfo,lpg,0yuto hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by f ,o;s ug0g4kp60l cu:5rn:, ye bbpvystating (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 force do bytb7k3 +(o a9wf+ifoou12gtes the ground exert on you? Why does3wo9tbf+ 1t 7bgy+fuo (i2ko an’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vicv: a m)x:l+o+vpz yx9btim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrplz bvamx9y:++):oxv own backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the t t2 v8c arrour8i82c,fruck accelerates, the crate 8 r82ico raf,t8rc2vuremains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that ith2 i nnrt:0e e2lfgf82 slides up a ramp. After the block reaches its highest point, it slides back lrgf0hi ntee :2 f82n2down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed youij- dy4wh,m i4rself on an inclined plane? Assume the d -jihm,4yw4i mechanism functions properly, even at an angle.

  What force is needed to accelerate aw3nbv4 xqj+u* child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ri3l/(kvq0glmo /o dy (rder at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960)9 h.nvhb l0hy;*h yyr$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a +xh* ujkcptq9f-y523rh gxy ; $76-\mathrm{kg}$ 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 idz/47lctqa 2 ,rw:) lz7y mfidf the car is trave az c7qd/i42w): z,ml7tlrydfling at 95km/h? -  

  What average force is need51.np uw ib:yyed to accelerate a 7.00-gram pellet from rest to 125m/s over y: b.1py 5iunwa distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out ofrsu( gsa 5*.y)i*oojw the water with an acceleration of 2.5i gwy.so)** u(5ojsar $\mathrm{~m} / \mathrm{s}^{2}$ 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 tq im ml- qi3s7)ws55afrack (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 the maximum p d6bwr2 g e0a3d-1g3vjq,mtt acceleration is 0.0680 g . What are ther33beqtgv6t0w-ja 1m2 pg ,dd 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 elevator. When the elevato-ua whp hn0g5*r begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elp0awuhghn- *5 evator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a+rkszd1 a)6 pvo v)hgzew7 x5/ maximum strength of 21,750 N. What maz6xd a+ shr1ep 5z)vwovkg)7/ ximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky div3 r1xvxrgf 12kw5mjd -ers (mass 132 kg including parachute) when the upward force of air resistance 1m312g rx j5-kfwrv dxis 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 hou,mmkijv7tk2.18qsb r se 3.9-m high. 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 torso (excluding legs) b2krvjq ms.m1 kit8,7 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 vertically u:8 ,o7jlrdzkzcur) env4 7 dh1pward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on n4, z:je )rr87z1l dov7dhcu kthe 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 baskf -iyz;6)vd/ t6 d+educ pzz6retball 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 ba3q ++jpvo*z*skw atl(oe:24 yomh3uj seball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying uo (: 2oyajjqwo+lez*+33spm vkt* h4toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be eg /p +3hyy gs)xag 1r9,vokdg1/dhtw.xerted in what direction so that the resultant of the two forces points wesgah9 yy)ktx1p3g dhg /r wvd/g.+1 s,otward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" nlxma m7x . g*mi6hb546mrp d8c f;lj(strung horizontally between two buildings 10.0 7hnx r;8 llgd*6jam5fmpb(i6c 4xm m.m apart. 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 another t - w(.ikasl2t 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.q 6qwl(vgp+h 9em+4;/yi bnk,mao. ny0$-\mathrm{kg}$ 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:9frjw 1cbki, df* fkt7w7r 7q at McMurdo Base, Antarctica, as shown in Fig. 4-ib ,djr97w k1 f*qw :7rftk7fc46. 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 iudc l)jxz;0.6 wvk+qtwo cars of the same mass behind it, Fig. 4-47 . x c.w+ ;)quj6dk0l vizDetermine the ratio of the 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 heg5fhmbl6 w9m +rself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mu5fw mh+9lgmb 6st 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 racila(1fx,p uefv0 ;pc 5e began, 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 bloct.mf6 n7x *+eehyon5n 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 contact wiv4*h;)va iof* hbq7cr4tkg 6ith each other, as shown in Fig. 4- ktvgv hb6r iif*4;7qc4)o*h a51. 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. gm8 )4ecl-*ozeoqlj1 4-52 are each initially 1.80 m above the ground, and the massless frictionles *e1 q8lj eg-czm4lo)os pulley is 4.8 m above the ground. What maximum 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 of mass e f kr* 6xq7rpv wkup1b7p67a(1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagra*v7apxkf p 6euw7br 7kpr1 6(qms 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 between uo hz v9p5guw5e1lq -7a 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 require*/ p.ude)z kaid to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. Whpmir g)5y p85d ikj6;xat minimum coefficient of static friction must exist between your feet and the floojm5k ;yxp5i6rp g)i8dr if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffic6ojbbpk5km7y323 e q wient of static y5bo37 m k63eq jw2pkbfriction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pave(javh: s2;0ms *9omx yho*yqz ment is about 0.8. On how steep a hill (maximum angle) can you leave x*hhsy:90a ;2 msyzjv*mqo( o 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 -495xutos6p ;y. 6 cmxcm.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 onpmjzm zo xe 8a8kp-k1k,1/e p/ a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface hcu ) ql2u1r9kqave a very high coefficient of s2curqq1 luk)9tatic 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 frictionsxk 7n35ww xf6 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 maxy8aq- 0vcc jnv97d.kom) f.y ss would box A have to have to prevent any motion from occurring? Ass-.j7c .yv nqva0docfym ) 9x8kume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fl6w nl0 ;d8g h.m8(uo dbqiyra:oor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiabuy0ndwoq8 i ; ar8mgh(.:6l dl speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact anw5)g sue+9 w 1rosdai*m:wdz3d at rest on a horizontal surface (Fig. 4-54). A 6 d5wmwi*w9) z1gad s:r3so+u e20$-\mathrm{N}$ 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 staticxo b.qfm8en 3gw/0nt 7 friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the c 3q/xnbo 8.efg0wm 7tnab of the truck?   

On an icy day, you worry about parking your car id:cwxnm5 9n3d n your driveway, which has an inm59d c3xd: wnncline 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 wiomh+2l*, : oqrj*xzn9c)zy gmth 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. 4-55 lies on a plane tilted at an anglyew+nw *+sl a)e $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 ;op jc/n eaj8.$\mathrm{~m} / \mathrm{s}$ 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 wk;8 vf y atqz,ua,s45utt:l1 qdau-n-ith 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 againxru fu6gfv0z* - d6ywc:).cc*aaqmx;m15sl vst a rough wall by someone pushing on it with a force directed upward at 56: uyumq fxafs*-.dcz ;xc )a1mlv *wg r60vc 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 dangerou p dd4kl2n qh *owgop4e5o985vs projectiles as they melt. Consider a chunk of snow at the ridge oql5dp5h*ew vo no8k 2dpg 449of 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 distance for an autom5a*t2j264j ge zqojfgr9.-a opjn b -robile traveling at speed v is equal .j-poqe 5roaj9fgt4z2 -6*gba jrjn2 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 dash wh 0h/g* vw73y,b avzgwien the driver decelerates from 40g, wazh*/bviy7w3vg 5 $\mathrm{~km} / \mathrm{h}$ 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 gbn-l6 uubne:9v+ehnrjlis /,j :.kr 7iven an 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 fill6;onk2/ppvs60mzoo, 9k e vmn ed to the packing station 11.0 m away. The belt is initially stationary and must finishkzk26/0smv o6pnm; on,9v pe o 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 betweenl zf,3a mr6s )v6 mbmcd+n8n4u $m_{1}$ 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 6ex) )onpgeb4 d.7qiw. 5 kg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammaiw6zm4vg7: r4avm9/pi kw-zalian heart, at each pulse approximately 20 g ofg4wa wirm4/zz:vkm vipa 67 -9 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 ch 1y v+gk9:u 7yye+d9a,:o ed)afdvunlance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculde++vkun 1 a9dfeydulg:: y7ao9v) ,yate 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 producamdq s:l+e./p d;2e yaed by an earthquake is a , and if an object is goipl.qaeae:sd / ;2mdy+ng to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident ) yd seqrub);3x*a6poinvolving two cars, measure 72-m-long skid marks of one of the cosrpx6)u*) ba3e dq;y ars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hilw6f7t)wu*sg3pk umg 6 l (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fas* pf6w gs3uu) 7ktwmg6t is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tkpewugps +,ep: 7)xc -g-j6giower of Pisa and falls 55 m before reachin :+,sgkjw)6egcupgp e --p7x ig the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steadeevv zv4p z 13o5vs1c4y speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the3evz44s5ev 1pcz vov1 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 working on the redesign of a hilly pom e+sonr9:d /jrtion of a city. An important consideration is how steep the /od9+njrs e:mroads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch f 6/d8vtoqqabr 8t9o 8. y.jtylrom a thin piece of string while the jetliner she is in takes off from JFK Airport (Figoq y8.dbvoj.6taryt/98 tlq 8 . 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 bz7zzkmbx-jw; z j./0 le several ramps connecting different parts of the stor/wxkblz-z m . ;0z7jzje.
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 is4te ehz)sfc-9928l d z/ejrj e needed to lift the piano (mass M ) using the pullel2-esdejcjr e 949z8 /zte)hfy 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 accel*lr30zgc*0em5/nte d(u fgzzerating 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 chair, an engineer considers the foldvb f4;qw*+:.io o58cgybsqikvn5 2 ylowing set o +28qi;:ovb*f.5yq wivgon5 4k dyb csf 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)o;cxm.-4kpc ou 5 hor 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 andcd2z o56 w1;-zwix tdc 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 rw wdzdtci1 x-c6;52oz ope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using y wpe;qolrzv)v/ .q:b9bj9k) t)vex i.au *y5a " 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 alh1lqpubsty3w-*sk9;d 1/j:l q4ucnq 5 siu 3plowed 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 8;pgbge2-bvfy mc5pt: j9cg , roped together are ascending an ice field inclined at 21g tcvj ,2bg- 98f:pgc;bmpy5e.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.