Why does a child in a wagon seem to fall backwb7r qxz,)cwaenf(+- o7m i /rjard when you give the wagon a sharp p o+ z)jnab(qx7iwfr ,-c7erm/ull forward?

A box rests on the (442g hbpfwzy50bo ihm3 t ltq4v7 ya-5frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the iw-y5 vh 34b 52f70l4m4yaqzthtbo gp 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 ;p94wvx0 fkk ap*,u9rvoo yw: an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. r marjt/j4neur.5) .r;yto5b Can the object have zero acceleration? Can it hm)j/o5 ; abr..n r45j errtyutave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a 91cx) : 7 l*c af y(gueczh*kgl)ce)tnforce needed to make it bounce back up? (bxfu)llnz7kcg yc9*: ecg*1)e ( aht)c) If so, what exerts the force?

If you walk along a log floating on a lagooj7bkc 95s*ke, why does the log move in the opposite di c*k5ojobs9g7 rection?

Why might your foot hurt if you kick a heavy desk or x5fye4ka 7ey)a wall?

  When you are running and want xcgjrj dc-9(d 8 ,d9ugto stop 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 of a person runnig(xr9 d98gc,-djjc d ung at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sa )x.v,hgk/ v8yrnjf6s me thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow asfxj6nh r8ygv)v k/., nd steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock:dz5dx1* u kbquo7y 4j. Why then doesn’t the heavier rock fadxu1yo5d4ujk :*7q bzll faster?

Would a spring scale carried bys qrwu4)i3 ko)g5fn t*-er8to the Moon give accurate results if the scale had been calibratu8onrw fqb3)e)5 yr-*s4itg ked (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frioun +qrf4w/. 3 n4cfbwi4ut.hctionless 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) increasnw uqcbir/ wt 4f4fuh4+. .3one, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is dyy8d1vy/mu nd6);m a a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and oppv 6d)uya8yy d /mdm;n1osite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you areh+xbi cnej4wnv; 6 ;z) on the Moon with the force nez;ci;wn) en v4hj 6x+beded 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 7 bjh*rviqy 0r 3a gib.*:+mgna tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whichb b+*myh vr3a.g7qgnj r:i i0* team will win?

A person exerts an upward force of 40 N to hold a bag o;nuoj7 / 8macyf groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it isn;/um o8a 7yjc exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a fohq e8thc0r +:xrce does the ground exert on you? Why doesn’8 xcht +:h0qert this force make you rise up into the air?

Whiplash sometimes results from an automobile accident wp b4fl(v54o3 y:ib glehen the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backwarl(pbl4i:4feyv3 gbo 5d in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, ibuqv5m )3w9xthe crate remains where it is on the truck, so it, too, accelerates. What force causes ) q59buvmi3xw the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blou.amv6rqn)8 a jkii35ck reaches its highest point, it slides back down but the magnitude of its acceleratiok)nvaujqim . 6i85 3ran is less on the descent than on the ascent. Why?

What would your bathroom scale ree -6a6*zqsvu tad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angae*t s v-q6zu6le.

  What force is needed to accelerate a child on a slesci/lq- 62+ylbf.+fi8cj zpu d at 1.25m/s$^2$?   

  A net force of 265 N accelerai(tj)j sakappx :r(3 1,iwc7wtes a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wit0p (m1/an/glqo8e bithstand 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 / ixdpcsi4. l -9psd)p $76-\mathrm{kg}$ 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 reyudi4kfm. s:/,f jr-vd bjp+ +quired to stop an 1100-kg car in 8.0 s if the car is traveling at p./vjdfj4: f+- m+ krsu ,yidb95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet frompb -ed.:skl qz( c9j)s rest to 125m/s over a dib( ).ql:jpkz e-c9dss stance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerataz7 3(t+,d6wzckeic *so k-u qion of 2.suw6okk73(,ic-a dcze*z q+t5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 renxi u7x7d-sf 83yh8kxw l,w 1gnn34cover a quarter-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 maximug2r9bnmand7 , m acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert9mnr ,bg 2dan7 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 motionlzz b nx4*h,)aless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s *zhaxz,n) l4bregular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength lu0p5f, a8nur*qeh y( of 21,750 N. What maximum upward acc,fnp r(quyehu58a l 0*eleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of t *-yb2flq,lf bwo falling sky divers (mass 132 kg including parachute) when the upward force2 f*bflb,-lyq of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the grouv*/-ikppa) k4rim,qq nd below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso 4pv k rp*m/ikq )-iq,a(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 tvh+ws8/uw pv+-i cw:uzvw9 v;he box runs vertically upwv/ih w wcsu u8 w+v+wpv;:-vz9ard 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 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 basketballr30-+l8yynt/jydq qh 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) at the moment it is hit9f**n*znn7c er nfgt 7 by the bat, and again (b) after it has left the bat and is flying toward tn 7n*cfg9nf**7en zrthe outfield.

A 650-N force acts in a northwesterly directfbu /g, b;8i (g5d6:5ia;vi9sytfwqi 1uz bqjion. A second 650-N force must be exerted in what direction so tha8f19u6;,gjwa/;bsi d qb5( q5ufi g iitv bzy:t the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally tizt*2;*kiz zbetween two buildings 10.0 m apart. The sag iiz*tkt;2zzi * n 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 hand l-+ m0oynfo*ihjk0. a*6onrging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.v9.juze)n k p40$-\mathrm{kg}$ 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 tor5ejh4x u(5o i a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of t(ixer o45 uhj5he 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 pullx+9rh hp 94*w: clgepning two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomoti rlwgexnh+pp94:h c *9ve 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 herself upward using the bucket-pulley az-(-( 1ssxnqvh )hh sipparatus shown in Fig. 4-48. (a) How hard must she (s-1ixh v)(znss qhh-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, jj,3 .rl.hvqz6/fuo od 9uv3t 3vrslh/e :zc6a 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 bszi;*:/um,l6bcj c bblock (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 co;zumrxuu1 :.ontact with each other, as shown1r:m;ou z ux.u 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 xwb98rqjq do 951d(ebu5qsb*initially 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: 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. Assumwbo 5rd q8*dbs199 qxuq( eb5je it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are con.eb,npsh uzdq 30: 5uenected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the bs , e3dn uuq5:.pze0hfree-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+:a c3lktd.7/vc mzo l 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 bnw tmu1kx7 6cc,/o3v9hq2fito 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 minimum chueq5 a87m4 w* 3cw3k ,yxtuonoefficient of static friction must exist between your feet and the floo3u mnaoy,3hxwt wq4e 75u*8c kr if you are not to slide?   

  What is the maximum accelerationm e-vlx(sn my7 vr*6* 88tjtui a car can undergo if the coefficient of static friction between mju*6lriv(mnt-8 ty8x*v s7e the tires and the ground is 0.80?   

  The coefficient of static frictitfc: o +,87+gvsn cxdxon between hard rubber and normal street pavement is about 0.8. On how st+ nd+vtxo,fc 8c:7gs xeep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80 balq9t54),/u ov tl/l5a cdry $\mathrm{~m} / \mathrm{s}^{2}$ 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 ro 6 hil+ov2j)wcugh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffwrtl-6:ylqm l b;g/vp-m0 7 onicient orm7lwvtpng-/6: o y-m;b qll0f static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction 6syrh*(* ;dzre onix -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 (t 5j)9 g5 govc hxj/6m+jjii:gExample 4-20) how large a mass would box A have to have to prevent anygx v+:5iijh6/cm )jog9j tj 5g motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wilg6+ik y,b0 +gdham +xikqt7hlg ;ht 09l it go, given that theh ,gqg9ik hkmhta+b 6;i tyx0+l+7dg0 coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and a,h ) u)oz4n7 bp:k;8xeen npnit rest on a horizontal surface (F z8nnpx) nk b7eh, inp4u;:oe)ig. 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 heavl2wtk*4(e)-a zij n3d rydoi4y crate. The coefficient of static friction betweed -*e44 nkd(3oi wty rz2ijl)an 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 of the truck?   

On an icy day, you worry about parking your car in your drivewayxq ax/aud lw3d1 738bg, which has an in3ug 3dd7xlb1aaw8 q /xcline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a c/j sis/h. )ge-8mnx s28$^{\circ}$ 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 zcao mt7*2w4ua 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 o ::ncft(* cir 4tssq.nf 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 react -m s4-2hj;ub hk8t8wf+gd mhhes the top 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 agains z 6epcca-uv8e:by0e:6/pfvit a rough wall by someone pushing on it with a force directed upward at cy6vp/ veeuicp z8 -a:b:fe6 028$^{\circ}$ 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 cank uq.wij:/+8skdn ; fv become dangerous projectiles as they melt. Cons8nk w/j:d kisq.;v fu+ider 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 distance for an automobile trave*my xl(+bod2fling at speed v f(ld2xbo m*y+ is 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 pb )q73g xp0bz rqb7re b.3jgz5,qfu7 when the driver 7 xfgquqr)bbr33b e gp7pqz,.bzj750decelerates 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 dww1h(3 vfx5k is given 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 co( 8)oj5f3 +yzr ejfwcynveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the fina+z) 3yy5ffw(j ro8jec l 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 frictionydb(yk rtnw,mtbb e eo9rb78w h7+3/,7:ibx d 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 n.+wj.x5x:wcx kph;pkx8p3e0k t j -b (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 eacle iwv1hpgpzx h6**7 1p preuh/fn,7 2h pulse approximately 20 g of blood is accelerated from 0.61egi7l 2p/v hp7,u1phwp hre*zn xf* 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 tht*0uy0au.gv6l9k5 jutw-oq r0u uwd8 e deceleration is no more than 30 " g 's." Calculate the force on a 705 60ko djga.*u-tq ww 0ulu9v0tu8ru y$-\mathrm{kg}$ 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 producel fi:;nms7v.pw6 uqj 0d by an earthquake is a , and if an object is going to "honf ;i0m wq67vjul ps:.ld 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 involvingq;h4jpa )tq1i6fnzp m ed) t*, 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 rubbertp1if6jn dt qp)meh4;,z )* qa 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 hilt(c*7h9 csj r nx92vjd)l w8rql (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55wr9xs ljdvc*qr(n 2j h7t)c89 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 Leanv-hpx3 *kff (wing Tower of Pisa and falls 55 m wfh pfv3(- xk*before reaching the 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 mud9veka+h k4(rdyr*r 3hdy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon em4dyrv(k3 e9hrk +* raherging?   

  A city planner is working on the redesign of ekym 4qb-7x0tg q3( oia hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level roadty ei3-4m07kbog q(xq 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 8fm3;m-dmhqpfrom a thin piece of string while the jetliner she is in takes off fpf -38mdmq; hmrom JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connnlw+z16 zmqtu 3 /f2gnecting different parts o +t/lnnwmz236z q guf1f the store.
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 lift the pial2 dm 8g9x 4nkldkx.3ld+g bx-no (mass M ) using the pulley apparatus sdlxl8xdggk4 l+b3- nk92. xd mhown 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 acceleratin2 (eg:qhpvh: vg 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, anl8nn3lb0zqr v/ ,yv +e engineer considers the following set v,q+lrv0 8ebn/l3ny zof conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metr 1ld)n :ipgf7yx +m*seic 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,q uhwl m0aks3m upd/ s4o+9hue 7r1q3)to//dq 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 pulm1)3po mdq/d eqr 9uquuo43/lka7/0thh s s+w l on him? Which climber is more likely to be hurt?

A fisherman in a boat is usin 73dt bxe*fw9xjm2l4 dg a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum irx)x;a:b 0gxo-vp .vspeed 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 asce(sbfd th0y,,hb dteyuo 6, r(6nding an ice field inclineodt 0,ebf h(y(,trds6yu6, bhd 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.