Why does a child in a wagon seem to oplhz3 1qe(iq6sbusl9+ pc k.,17eju fall backward when you give the wagon a sharp pl b7.pu(, ecqhzuq i319k+ elpo6ssj1ull forward?

A box rests on the (frictionless) bey 4ec2h cbr63p20rqoj d of a truck. The truck driver starts the truck and accelerates forward. The box immediately st06h 2oryp3jq r2b4cce arts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no force,9nzs-b /hf) knxxa0z.+5o iv joyh: xs acting on it? Explain.

Only one force acts on an object. Can the object have zero a ro+ 3qkfa uha:,bp1/xcceleration? Can it have zero velocity? b:px3ofr1qauh k+,/ a Explain.

When a golf ball is dropped to the pavemh zm2no71qzhhpsl1c(t 1r 6:b ent, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exertsm n 71hht1hs2 p :clrz1(zoqb6 the force?

If you walk along a l azojt 9 n+vf)4:egqf)og floating on a lake, why does the log move in the opposite direa) 9f:z 4e no+tvgf)jqction?

Why might your foot hurt if rc w.s8d +o9bf-wauj6h *cg*dyou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly.p*bv/kn2z l v6 .:icjdiy .fk, (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum i:/if *,ykb. l nv.zckdpv j62rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, vo) yobj5 p7ij7*ru,tand a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on th pyb7,*ou toij) rv7j5e dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a z s8emyr.1q9r 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier e.yszrm981 q rrock fall faster?

Would a spring scale carried to the Moon give accurate ;bghg*o k; gi *9z/ubpresults if the scale had bgighb ;ku9z*b p g*;o/een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a f:a vt cdv:5e,hrictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) incrdvavt:, c:5h eease, or (c) decrease? Explain.

When an object falls freely under the influencectl nt;4 3zxj:;h p9fu of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law tp:z9fj ;43c; tun hxlthe object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed t:m4m4nj ckr3x o lift a 10-kg object when you are on the Moon with the force needed to lift it on Ekm4xnmj:r 4 c3arth. 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 tx) tw0d9s-l(txuw 8g weam in a tug of war (Fig. 4–37) pulls with equal force on thd s- )wxtxw(9tg0lw 8ue other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold +rzf.xx.ddmp7l zb . +a bag of groceries. Describe the “reaction” 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 ix.dm.pdz 7+x +. zfbrls exerted.

When you stand still on the ground, how large a force doex5k v )4albb.ys the ground exert on you? Why doesn’t this force make you rise up into the air?va)lb yk45x .b

Whiplash sometimes results from an automobile accident .f6ocqhm :d*nua +rm: when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is ia rhdf oq:+ mn.6um:c*t really?

A heavy crate rests on the bed of a flatbed trup)2 ga510tfpd yqq+ke ck. When the truck accelerates, the crate remains where it is on ea q5d2pfk) 1p 0t+yqgthe truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After*(d *8tdw ssoz the block reaches its highestssw *zodt(*d8 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 read idq)pxh p 6-e0kg)kar6: ; vlqef you weighed yourself on an inclined plane?:)ppk a66eqhre l -vxg0); kqd Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child whr:jx 1 c4(k qvms+gy9;( ejf-aep-don a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratkkf- 0zu1 aku(k.zf3a es 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/m+t ) ok-tb *cmcm,mw a rope withstand 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 u*7/k tj;h64xv0rk0jgzvu ix $76-\mathrm{kg}$ 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 thu;r 7(o+2t qcdnia ei:e car is traveling ate +:i;dua7o(crqt i2n 95km/h? -  

  What average force is:xw-eui 2*l g8mx(yad needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a 2ag*d( 8u iy-xe:mxlwrifle?   

A fisherman yanks a fish vertically out of the watwbmrf* -*x cs9er with an acceleration of 2.5-r wxm 9*fb*cs $\mathrm{~m} / \mathrm{s}^{2}$ 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 8fio-9 g* si /8-n mndzgy-/cy0od ee(e0zrunquarter-mile 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 the maximum accele j qq2q ibdelm,;ex) -5pfi(qe4-q 1jnration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable dm (-nq2qbq;)pq5jelx 1jefe qi-4,i? 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. Wheo l6c6s3/sdwyn the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of tlo6dw 6s3ycs/ he elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg e l+ozkg2 7e8e(f wc2iw6mcmq( levator has a maximum strength of 21,750 N. What maximum upward i foe l2cm6k( 7e cmgzqw2w+8(acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 1q k-+ucj pz ;g30,)z npyy)cch32 kg including parachute) when the upward force of air resistance is 3+yuzk jqz;pch) gccp,0 )n-yequal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he st9h a m/mjcd;t.rikes 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)d;c.ta/h9 m mj 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 tableq*tl d)x0(m bn fk9o;h. A rope tied to the box runs vertically upward over a pulley and9 txqo nfd(m)b0*lk h; a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the 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 ba/ ,n d9oihzw zhy ,f;yhl7/d y2hji(0vsketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a)v4/cpn8p l05 ozbjp1q at the moment it is hit by the bat, and again (b) after it has 1ql4b8pz5 0oc njpvp/left the bat and is flying toward the outfield.

A 650-N force acts in a 0v(v4ycup(o/peg id,northwesterly direction. A second 650-N force must be exerted in what direction so that the resuleg v vdy(, 4oi0p(/upctant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire k7zjr +*4aujr" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at theza4k7rj ru +*j 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 cy5fei2na8 ;lcdc nxilh7y:; 0ord 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 14.01o9o zm ;x)apm$-\mathrm{kg}$ 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 loc4(g;n3f:/ ahlboruc 0etuw*o ation at McMurdo Base, Antarctica, as shown in Fig. 4-46. Theceht :ooa f*r/;(03wbnuug4l 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 pullin/r9 4 v,lqevcig two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension94,e rivc l/qv 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 heo6v+q6a ol8u xrself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mustox6lo +6va q8u 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 bega(5zsn3sir 6c7sr svn /n, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass4ma/lm uzm7u: $ 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 sutuu+ zmb3hzv6)r-( kly6ui v4rface are in contact with each other, as shown h)tv4ub l vuzk+yuzrm6i6 (3- in 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 initial0zy7 d dx y4(vd5 52psktlzk-lly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: Fir4dyk(t xy5z p0vs2dlz d 5l-k7st 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 :wqcjc49b+qr connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of eachrqjcb :wc9q4+ box 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 kinetic friction betw;je/-0s 5c-wztmbmsc 802w cb fmqai: een 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 requiredi:i+k5ykx q fjc(a0mg8 x8+fk 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. What minimumz 0++/6c,rrnshh dc am7xd tk9 coefficient of static friction must erdntc,zrh9as+d7c /6 0h+mk xxist between your feet and the floor if you are not to slide?   

  What is the maximum accele5o0:nlf3jw i vration a car can undergo if the coefficient of static friction belf woj5:3i0vn tween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normquc9ub **tb6pw:haz:a /ii ec0.w4nkr t/;yv al street pavement is about 0.8. On how steep a b:ipctubzak;hu0v q:re6/nyi wcw4 *a9* /t.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 -4.80-vv:ct*goex lvhb k e((4)ro/ $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 3 n1e -;hr9iebc0$^{\circ}$ 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 coefyi.x;q vxf7qzdn 1r(x 89j+;pc b/ocwficient of static.pdb x;i( q79 vwzr8c/nf x1cj;qo+ yx 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 kibcfxw:p .p0z. iso-6c 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 ijwrr;o7k 2+s a mass would box A have to have to prevent any motion fro+o7i krj2r;ws m occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will i6bitj ry2irk , xlg(k4ef*/icx(f 5e) t go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initialeyf*(fi lg(j r4t ,)cx2 rie6ixk/b5k speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizontawe 7,/hbqdhd)fy h c(om9yv57zxma(5l surface (Fig. 4-54). A 629h(b5w v/5o)m az7yfmy x,e 7q hhdc(d0$-\mathrm{N}$ 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 rq0k5kpm7y ,jriect a1 ..ohi.jk-;s crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab okh7pek15.rji k ct-sj0 .,ri q a.yo;mf the truck?   

On an icy day, you worry about parking your ;ces:.t1ya,)3icu2m fzn ndicar in your driveway, which has an incline of 3 cz12t,ue:csmfindin.y;a) 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 t:xc) o2;xdapz1d+ezt* opb / 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 9u1dgd8x2gvmfm,.p 2w.hx fvlies 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 anfc lmc3prx..e45hnd ysafp3v7 1do - : initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed,nmc4lbbeue ar)gvd0 87(ud g;f .;sr 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 againswj,orwr.mt c (w3op16t a rough wall by someone pushing on it with a force door tjc(m.6wwpw, 3 1rirected 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 +gxd g 2frsxu3 v/*uyr 1((unzroofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof wzxu2n*y(+x/3srg 1 (gdf rvuuith 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 disnv /tzr m07 3qkm5ydh6tance for an automobile traveling at speed v isd5mv/0 t hm76zynqk3r equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when tpepfq*n,amub ag8v qd -wjs, 8ea +517he driver decelerates from 4 efga - aq ,7mp+u*apvq8sdnb518 we,j5 $\mathrm{~km} / \mathrm{h}$ 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 infuia5o8c1af 53ki wcn6qxc /* itial 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 la- n i4jvq0i:where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero sp04vi:ja ni-q leed. 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 coefficie n d.s*.tw,rwnnt of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass ;un,jtfke r 0 v3v(3sk65 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 mammalian heart, at each pulset1msd6lh10j n-b r ag8 t7lz8e approximately 81sjht7l6ant-rl08bzm1d e g20 g of 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 the decn0y68l5ef(vauwq v )g 6gqepeoa** lj)* v5vyeleration is no morv(e)e qwqa6ujyogn lg0 vp**laf5y v*5e 8)6v e than 30 " 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 accelerati3vv yxsvqo6 ho6; btv 9bpf;i*u x9.v:on produced by an earthquake 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 *vy 9iv3o.; 6bhfx;:sbv tq9 ov vu6xp $\mu_{\mathrm{s}}=a / g$ . (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 accided .rx+ gc )exrno)3d;tnt involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber ax)dg ;. 3noct+ edrrx)nd the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down ky 1+0s nmz /o/mcougsf.e/t-a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevatm/ /zf/1t cs.-n ke+ysoog0muion change is 1 m). How fast 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 ofqo yhd bzf050* the Leaning Tower of Pisa and falls 55 m before reaching tf hq*0y5z 0dobhe ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mu;d -ezt:dyxp0 ddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without0tdy ;-zdx e:p 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 oijh74cgxz 7y. f a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills wit.i gx74hyjc 7zhout 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 exper7ii rqw+eh 98 +y/xturiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Shet9 yrruiei8x+7 q +wh/ 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 supex9 y g4c(emx:vrmarket, there are to be several ramps connecting different parts of the store(mec: v49xxyg.
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 nejbihd1 w* 6h ,)h9hulueded to lift the piano (mass M ) using the pulley apparatus s9,i6h wh*)uh dlbu j1hhown 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 accea f auoc0qc- p))vi8)mlerating 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 processbaalv 01pz 0;5z6: xn0ililqy for a child-restraint chair, an engineer considers the following set x 5lynip1z6l l00vb;z a a:q0iof 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 6c7fun31r si67q;yke7cf suc.zst5 + l 60 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. Karen's r w--toydzlu 2.1v vld5ope 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 aty1.d-l2o vvd l z5uw-bout 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 q;pic.s:x +hvblgxjo2yd s*u59ba: xmj ((b; using 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 i 0ib8bz kmzp;1h3i-r fl-d4vfs 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 rop0n7 3 dhbr: l.oy0kinmed together are ascending an ice field inclinem7.n3:0hi bo 0dyrln kd 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.